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List of most small twins of form k*2^n+/-1
1 Attachment(s)
To whom may be interested,
I went through an excercise to find an easy way to get most of the primes of the form k * 2 ^ n +/- 1 with small values of k. What I did was I extracted all of the k's and n's from the RPS site, the Primesearch site, and the Proth search site into Excel spreadsheets. I then used Excel formulas to match up primes for the -1 sites (RPS and Primesearch) to the +1 site (Proth). The largest value of k that I could use was 599 because that is the highest that the Proth search site goes to. Attached is a Notepad file that shows what I came up with. The first part is sorted by n. The second part by k. Although the largest twins that I found don't come close to the top 10 or 20 twins, I think it's good to have comprehensive lists like this as 'building blocks' for future searches. The largest twins that I found from the effort are: 1. 459 * 2 ^ 8529 +/- 1 2. 291 * 2 ^ 1553 +/- 1 3. 177 * 2 ^ 1032 +/- 1 Not too bad considering I could only match up to k=599. Obviously this list is constrainted by the lower limits of how far each k has been searched for BOTH Riesel primes and Proth primes. If anyone knows of a more comprehensive list of Proth primes (i.e. of the form k * 2^n + 1) where k > 600 like we have at RPS for Rielsel primes, I'll extend this effort to include more k's. Gary |
Here are twins from k=1 to 10145 (used this limit as LLR is faster for these k's) and corresponding twin n's upto n=250. Would like to extend these further, anyone want to help. I think k=1-300 have been searched enough.
[code] 3 1 3 2 3 6 3 18 9 1 9 3 9 7 9 43 9 63 9 211 15 1 15 2 15 4 15 10 21 1 21 7 27 2 27 4 33 6 33 22 39 3 45 2 45 9 45 14 45 29 45 189 51 1 51 9 57 2 57 8 57 10 63 14 69 1 69 19 75 1 75 3 75 6 75 43 81 5 81 21 81 27 87 2 87 8 93 4 93 10 99 1 99 5 99 11 99 65 105 2 105 5 105 8 105 155 117 4 117 6 117 16 129 3 129 5 129 59 135 1 135 10 135 238 141 1 141 7 141 61 147 44 147 60 165 2 165 3 165 5 165 12 165 39 165 84 177 12 177 48 195 4 195 8 195 14 201 3 201 9 207 2 213 36 213 80 231 1 231 7 243 12 243 18 243 24 255 2 255 41 261 1 261 3 261 9 267 4 267 34 267 40 273 2 273 10 285 1 297 14 309 1 309 143 315 22 315 72 321 1 321 5 327 4 333 54 339 3 339 11 345 4 345 15 345 30 345 40 345 150 357 2 357 10 357 14 363 2 369 13 375 3 375 14 375 26 375 33 381 17 381 21 387 28 387 88 399 11 405 1 405 2 405 46 405 80 411 1 411 19 417 2 417 8 417 62 423 8 429 1 429 9 429 37 435 4 441 1 441 3 441 13 441 181 447 2 447 20 453 48 459 3 459 9 465 6 465 9 471 3 483 2 483 18 483 22 489 5 495 16 495 33 507 2 507 26 513 6 513 12 519 11 519 55 525 1 525 6 525 8 525 26 525 190 531 1 537 6 537 102 549 11 555 9 555 27 561 7 567 2 585 2 585 32 585 57 591 5 597 70 603 10 603 76 609 19 615 1 615 14 621 3 627 6 633 32 639 1 639 13 645 1 645 5 645 7 651 1 657 58 663 24 669 11 675 5 675 9 675 15 675 26 681 31 687 34 699 5 699 125 705 3 705 6 711 17 717 12 723 6 723 16 735 3 735 20 735 21 741 1 741 7 741 11 741 35 747 6 759 17 765 4 765 10 765 12 765 18 765 22 765 25 765 168 777 10 795 3 813 2 813 4 813 58 819 3 819 63 825 2 831 9 843 2 843 20 849 1 849 3 849 45 849 91 855 4 855 10 855 11 861 1 861 25 867 2 867 8 879 17 885 2 885 14 885 17 891 3 897 28 903 4 903 6 915 22 915 25 915 55 915 70 921 15 927 50 933 40 939 1 945 3 945 8 945 12 951 13 957 22 963 2 975 1 975 24 975 37 981 5 993 4 993 8 993 14 999 1 999 13 1005 2 1011 3 1017 12 1023 2 1023 242 1029 3 1029 7 1035 8 1035 14 1041 1 1053 14 1065 1 1065 2 1065 28 1065 56 1071 1 1071 7 1071 25 1089 5 1089 15 1089 131 1095 9 1095 42 1101 37 1107 50 1119 1 1119 13 1125 3 1125 51 1125 58 1125 63 1125 123 1131 15 1137 2 1143 4 1155 1 1155 3 1155 18 1155 31 1179 3 1179 11 1179 23 1179 51 1179 141 1185 25 1191 1 1191 61 1197 2 1197 10 1197 16 1197 52 1197 70 1197 206 1203 104 1209 9 1215 3 1221 3 1233 2 1233 16 1245 5 1251 3 1257 6 1263 6 1269 37 1275 1 1275 2 1275 31 1281 17 1281 23 1287 8 1299 11 1305 5 1305 32 1323 106 1329 1 1329 65 1335 15 1347 12 1353 4 1365 1 1365 4 1365 12 1365 39 1383 176 1389 21 1395 1 1395 3 1395 7 1395 21 1395 43 1401 1 1401 17 1401 37 1407 12 1413 2 1419 3 1419 15 1419 147 1431 23 1437 6 1443 8 1455 16 1455 85 1455 133 1467 2 1467 6 1467 14 1467 92 1479 3 1479 19 1485 1 1485 17 1485 58 1491 5 1491 17 1491 29 1491 47 1497 122 1509 3 1509 21 1509 125 1515 5 1515 105 1527 16 1527 20 1533 2 1539 7 1545 10 1545 34 1545 82 1551 9 1551 33 1575 2 1575 6 1575 13 1575 16 1575 20 1581 5 1587 76 1593 26 1599 9 1605 12 1611 19 1617 10 1617 20 1623 22 1623 52 1623 64 1629 1 1629 7 1629 13 1629 87 1635 11 1641 11 1659 5 1665 1 1665 2 1665 5 1665 25 1677 14 1695 1 1695 2 1695 46 1707 2 1713 4 1719 33 1725 23 1725 26 1731 1 1731 39 1737 2 1737 4 1743 14 1743 28 1755 204 1761 17 1767 50 1779 1 1785 30 1791 1 1791 7 1797 4 1803 2 1809 15 1815 16 1827 2 1827 6 1833 2 1833 16 1863 20 1863 32 1869 7 1869 17 1869 23 1869 47 1875 17 1881 15 1881 169 1887 2 1887 12 1887 62 1893 8 1899 19 1911 1 1911 3 1911 5 1911 41 1923 22 1935 8 1935 12 1935 188 1941 49 1941 175 1947 4 1953 4 1959 1 1959 7 1959 49 1965 1 1965 10 1983 4 1983 124 1989 5 1995 5 1995 6 1995 14 1995 16 1995 21 1995 26 1995 39 2001 1 2001 19 2001 29 2001 53 2013 6 2025 1 2037 6 2055 2 2055 20 2061 9 2061 35 2067 4 2067 12 2067 22 2073 2 2079 1 2079 3 2079 31 2079 81 2079 103 2091 7 2097 2 2097 14 2097 36 2103 6 2109 1 2115 1 2115 14 2115 173 2121 1 2121 163 2127 4 2127 22 2127 50 2133 4 2133 58 2139 5 2151 3 2151 15 2157 2 2157 4 2157 124 2163 16 2163 20 2163 60 2169 1 2175 6 2175 43 2175 111 2181 29 2181 33 2181 131 2187 6 2187 30 2187 36 2205 2 2205 4 2205 7 2205 19 2205 40 2205 110 2211 1 2211 7 2211 19 2211 49 2217 12 2229 5 2241 1 2241 5 2241 13 2253 2 2253 20 2259 1 2265 3 2265 81 2271 5 2271 9 2271 45 2277 10 2277 178 2283 4 2289 3 2289 9 2289 11 2295 14 2295 47 2313 14 2319 1 2319 7 2319 61 2325 1 2325 4 2331 21 2343 30 2349 5 2355 2 2355 12 2355 32 2361 1 2361 25 2373 36 2385 3 2385 6 2385 22 2397 6 2403 4 2403 52 2409 11 2415 9 2415 10 2415 54 2433 32 2445 15 2457 46 2457 74 2463 16 2469 3 2469 7 2469 67 2487 6 2487 12 2487 18 2493 184 2499 3 2499 17 2499 21 2505 1 2511 1 2517 2 2517 62 2523 2 2523 20 2529 3 2535 2 2535 53 2547 10 2547 14 2553 4 2565 126 2571 21 2571 231 2577 4 2577 76 2583 2 2583 6 2595 4 2595 7 2595 46 2601 3 2601 5 2607 2 2607 6 2607 20 2613 24 2625 2 2625 21 2625 31 2631 7 2649 3 2655 7 2655 49 2661 19 2673 8 2673 116 2679 49 2685 9 2685 54 2691 5 2691 9 2697 10 2697 12 2697 28 2697 78 2703 14 2703 16 2709 1 2709 19 2715 2 2715 13 2721 1 2721 105 2733 48 2739 1 2739 9 2739 13 2745 7 2751 1 2757 40 2769 5 2769 33 2775 5 2781 7 2787 14 2793 2 2805 15 2805 27 2811 15 2817 6 2829 1 2829 5 2835 63 2847 172 2859 17 2865 30 2871 1 2889 7 2895 5 2895 8 2895 11 2895 51 2913 26 2919 35 2925 1 2925 2 2925 13 2925 37 2925 67 2937 44 2943 20 2955 5 2955 7 2961 3 2961 7 2961 17 2967 10 2967 16 2979 3 2985 2 2985 14 2985 66 2997 10 2997 50 3003 6 3015 16 3027 2 3027 18 3039 11 3045 1 3045 22 3057 18 3057 52 3063 2 3063 44 3069 11 3075 4 3081 7 3081 73 3087 4 3087 6 3087 112 3093 10 3093 38 3099 1 3105 8 3105 134 3111 27 3111 41 3117 6 3117 132 3123 34 3129 3 3129 15 3135 1 3135 2 3135 44 3135 74 3153 2 3153 14 3153 30 3165 5 3165 10 3165 20 3183 12 3189 9 3195 17 3213 16 3213 56 3219 7 3219 29 3225 1 3225 3 3225 13 3231 3 3231 5 3231 15 3243 12 3243 16 3249 5 3249 29 3249 41 3255 11 3255 32 3273 24 3273 60 3285 1 3285 7 3285 57 3303 118 3315 21 3315 27 3321 89 3327 4 3339 3 3339 13 3339 37 3339 93 3345 1 3351 1 3351 9 3363 8 3369 3 3369 9 3369 15 3375 10 3375 26 3381 1 3381 5 3399 11 3399 15 3399 23 3399 33 3399 57 3405 3 3405 5 3405 8 3405 27 3405 227 3417 16 3423 2 3429 61 3435 1 3435 3 3435 33 3441 3 3441 15 3447 20 3453 42 3465 4 3465 5 3465 10 3465 14 3465 24 3465 35 3465 80 3471 7 3477 4 3477 12 3477 24 3477 52 3483 2 3489 35 3495 6 3495 28 3507 10 3507 46 3513 4 3513 70 3519 13 3525 9 3525 44 3537 10 3549 19 3555 5 3555 16 3555 137 3579 15 3591 7 3591 63 3591 77 3597 2 3603 34 3615 212 3627 14 3633 14 3633 54 3639 41 3651 3 3651 111 3657 2 3663 22 3663 78 3669 25 3675 1 3675 3 3675 12 3675 29 3675 36 3681 79 3693 20 3699 23 3705 15 3717 2 3717 4 3717 16 3717 164 3729 1 3735 3 3741 153 3747 94 3765 8 3765 10 3765 35 3771 7 3777 20 3783 36 3789 9 3795 1 3795 5 3795 52 3801 5 3813 30 3819 5 3825 5 3825 11 3837 8 3849 7 3855 3 3855 33 3861 5 3867 38 3879 1 3879 11 3879 29 3879 35 3885 3 3885 6 3885 7 3885 8 3885 20 3909 9 3915 3 3915 123 3915 147 3927 10 3933 2 3933 4 3933 10 3933 14 3939 1 3939 3 3957 4 3957 120 3963 10 3963 38 3969 11 3975 1 3975 4 3981 3 3981 13 3981 61 3993 2 3993 12 4005 1 4005 8 4011 11 4011 27 4011 51 4017 2 4017 16 4029 23 4029 29 4035 2 4035 5 4035 8 4035 23 4035 60 4035 62 4047 2 4059 7 4059 25 4059 31 4059 241 4065 12 4077 12 4089 35 4089 83 4095 4 4095 18 4095 125 4107 100 4113 2 4119 9 4125 27 4125 87 4131 49 4137 82 4143 140 4155 56 4155 174 4161 3 4161 75 4167 6 4173 2 4173 10 4173 32 4185 14 4191 7 4209 9 4215 1 4215 106 4221 3 4221 11 4221 35 4239 5 4245 2 4245 198 4257 2 4257 4 4263 4 4269 1 4275 10 4275 39 4281 5 4287 180 4299 1 4299 125 4305 4 4305 16 4311 11 4311 77 4323 2 4323 6 4323 8 4323 12 4323 36 4329 15 4347 2 4347 6 4347 8 4353 10 4359 81 4365 51 4383 14 4389 17 4395 2 4407 20 4419 1 4431 1 4431 3 4437 2 4449 3 4449 29 4449 39 4449 53 4455 6 4461 13 4467 4 4467 124 4467 128 4473 26 4473 76 4473 92 4485 1 4485 28 4497 2 4497 68 4497 152 4509 7 4515 2 4515 5 4515 19 4521 1 4521 7 4521 29 4527 24 4527 58 4533 2 4533 8 4545 13 4557 6 4563 2 4569 27 4575 8 4575 9 4575 104 4599 3 4599 19 4605 4 4605 10 4611 15 4623 6 4635 2 4635 4 4641 1 4647 8 4671 1 4677 10 4695 7 4695 10 4713 132 4719 1 4719 5 4725 35 4731 1 4731 83 4743 6 4749 3 4749 5 4749 11 4749 35 4749 41 4755 4 4761 11 4761 17 4767 42 4773 4 4773 64 4785 2 4785 47 4791 3 4791 15 4803 2 4803 10 4803 32 4809 5 4815 1 4815 5 4821 3 4821 13 4821 49 4827 6 4833 6 4839 1 4839 3 4845 2 4845 7 4851 9 4857 2 4857 4 4857 8 4857 22 4857 32 4857 58 4863 22 4869 141 4887 4 4893 6 4899 7 4905 3 4905 19 4929 1 4929 79 4935 7 4935 12 4935 14 4935 16 4935 17 4947 4 4947 28 4953 14 4965 1 4965 37 4977 4 4977 8 4995 6 5001 5 5001 11 5013 4 5013 10 5019 1 5019 3 5019 19 5019 45 5025 20 5025 125 5031 19 5037 2 5043 8 5043 14 5049 7 5055 10 5055 40 5055 68 5061 23 5073 12 5079 5 5091 7 5097 4 5103 4 5115 9 5115 30 5115 58 5127 2 5127 6 5127 12 5133 6 5139 5 5139 17 5145 39 5145 48 5151 1 5151 41 5163 6 5163 116 5187 2 5187 20 5193 2 5193 44 5205 47 5229 1 5229 77 5241 15 5247 6 5253 2 5259 3 5259 69 5259 153 5265 1 5265 2 5271 41 5277 10 5283 168 5295 14 5295 50 5301 3 5325 4 5331 11 5343 6 5343 28 5343 36 5349 5 5355 1 5355 3 5373 2 5379 9 5385 9 5385 39 5385 40 5385 57 5397 2 5397 4 5397 14 5403 2 5403 16 5415 3 5415 6 5433 4 5433 14 5439 5 5445 1 5445 4 5445 8 5451 3 5451 7 5451 27 5451 33 5469 1 5469 13 5475 13 5475 25 5475 103 5481 5 5481 11 5481 185 5493 34 5499 11 5505 5 5505 57 5505 80 5511 3 5511 21 5523 2 5523 6 5523 32 5529 1 5529 205 5535 1 5535 3 5535 7 5535 48 5535 78 5541 9 5547 6 5553 16 5559 1 5559 5 5559 11 5565 7 5565 13 5565 14 5565 119 5571 29 5577 6 5583 8 5589 99 5595 4 5595 30 5607 14 5607 24 5625 5 5625 69 5643 2 5643 38 5649 9 5649 23 5655 2 5655 19 5655 44 5661 51 5679 9 5679 13 5685 2 5685 8 5697 4 5697 76 5709 15 5715 2 5715 14 5715 149 5727 14 5727 26 5733 16 5745 1 5745 10 5757 2 5757 12 5769 5 5775 1 5775 4 5775 7 5775 19 5781 7 5787 12 5787 48 5793 84 5799 5 5805 3 5805 18 5805 84 5823 2 5835 3 5835 9 5835 27 5835 45 5835 129 5847 22 5859 1 5859 27 5859 31 5859 81 5859 215 5865 7 5865 26 5865 50 5871 25 5889 1 5901 5 5907 2 5919 3 5925 15 5925 35 5943 4 5943 10 5949 5 5949 11 5955 7 5955 16 5961 117 5967 8 5985 1 6015 3 6015 13 6015 36 6021 1 6021 25 6027 2 6027 12 6027 42 6033 20 6033 32 6033 38 6039 3 6039 39 6045 2 6045 8 6051 3 6057 22 6063 20 6063 40 6063 130 6069 9 6081 1 6081 3 6087 6 6093 2 6093 12 6099 19 6105 2 6105 10 6105 16 6105 17 6105 46 6105 80 6117 56 6123 24 6129 3 6129 135 6147 50 6159 7 6165 4 6165 34 6171 3 6177 20 6183 4 6183 82 6189 1 6195 20 6195 26 6195 57 6195 92 6201 19 6207 54 6225 7 6231 7 6231 79 6237 46 6249 3 6249 13 6249 37 6249 63 6273 8 6273 10 6273 16 6279 5 6279 33 6285 5 6285 56 6297 14 6321 41 6327 2 6327 80 6333 24 6333 54 6345 20 6351 99 6369 5 6375 4 6375 13 6375 18 6381 9 6393 18 6405 3 6411 1 6417 34 6435 3 6435 36 6441 17 6459 1 6465 3 6465 14 6471 3 6477 22 6483 2 6489 9 6501 1 6501 45 6501 175 6531 5 6531 13 6549 5 6549 9 6549 15 6549 59 6555 11 6555 21 6555 162 6555 221 6561 33 6561 43 6567 116 6573 12 6573 22 6579 7 6585 4 6585 52 6591 5 6609 1 6615 217 6627 4 6627 12 6627 18 6639 95 6645 4 6645 6 6645 9 6645 37 6669 1 6669 21 6675 2 6675 15 6675 51 6687 6 6693 80 6699 1 6699 3 6705 5 6705 7 6705 10 6705 25 6711 19 6717 6 6717 12 6723 2 6729 61 6735 34 6765 2 6765 6 6765 30 6771 19 6777 2 6783 6 6783 12 6783 60 6795 19 6795 45 6807 6 6807 8 6825 4 6825 30 6825 42 6825 60 6831 23 6831 29 6837 10 6843 44 6855 1 6861 1 6879 1 6885 2 6891 5 6897 10 6897 108 6903 142 6915 1 6915 31 6915 37 6927 14 6927 56 6939 1 6945 4 6945 7 6951 1 6951 9 6957 20 6963 6 6963 12 6963 16 6969 5 6975 6 6975 11 6975 12 6975 59 6975 74 6981 27 6981 205 6987 28 6999 1 6999 41 7005 1 7005 3 7023 24 7023 64 7029 23 7029 35 7029 71 7035 8 7035 48 7035 122 7041 1 7041 7 7059 9 7059 11 7059 23 7065 4 7065 6 7065 39 7065 66 7071 25 7077 2 7083 4 7083 28 7089 3 7089 7 7095 17 7095 30 7101 3 7101 5 7107 6 7119 7 7125 1 7125 8 7125 20 7137 2 7137 6 7143 2 7143 6 7143 24 7143 30 7149 3 7155 2 7155 5 7155 8 7155 13 7161 1 7161 15 7161 57 7167 8 7179 9 7179 11 7179 15 7179 39 7179 45 7185 8 7191 3 7191 9 7197 4 7203 10 7203 28 7203 32 7215 34 7221 185 7245 5 7245 12 7245 14 7245 17 7245 69 7245 102 7245 107 7257 10 7257 88 7263 8 7269 3 7275 1 7281 1 7281 17 7281 19 7293 4 7299 3 7305 3 7305 119 7305 128 7311 11 7317 12 7329 5 7329 61 7335 7 7335 11 7335 35 7341 15 7341 135 7347 2 7347 6 7347 8 7347 108 7353 8 7359 9 7365 4 7377 94 7383 10 7383 172 7389 11 7395 20 7401 3 7401 25 7419 7 7425 4 7443 4 7449 17 7455 60 7455 74 7473 6 7479 29 7485 12 7485 40 7485 57 7491 5 7503 2 7503 4 7515 17 7515 33 7521 3 7533 8 7533 52 7539 35 7539 75 7545 19 7545 31 7545 103 7551 37 7569 1 7569 159 7575 11 7575 25 7581 3 7593 16 7611 3 7617 2 7623 2 7623 30 7635 1 7635 6 7647 6 7653 6 7665 1 7665 10 7665 40 7671 5 7671 7 7671 35 7677 6 7695 3 7695 9 7695 93 7713 2 7719 33 7725 111 7731 5 7737 96 7737 166 7749 7 7749 9 7755 10 7755 17 7755 47 7767 26 7791 1 7797 10 7809 21 7809 29 7809 47 7821 1 7821 7 7845 6 7845 30 7851 5 7851 99 7857 8 7863 6 7863 22 7863 60 7869 1 7875 11 7881 103 7887 114 7917 6 7923 14 7929 61 7935 32 7947 222 7953 4 7977 12 7989 21 7995 5 7995 8 7995 47 8001 5 8001 15 8007 2 8007 4 8013 10 8019 3 8025 5 8031 1 8037 16 8037 76 8055 43 8061 77 8067 14 8067 26 8079 53 8085 44 8085 61 8091 25 8097 6 8097 46 8097 52 8103 2 8103 12 8109 11 8109 21 8115 1 8115 3 8115 10 8115 189 8121 53 8121 139 8127 18 8127 26 8133 2 8133 14 8133 34 8145 45 8157 24 8163 74 8175 8 8175 13 8181 1 8181 3 8193 6 8199 7 8205 7 8205 16 8205 26 8211 7 8211 35 8223 18 8223 28 8235 2 8235 5 8235 12 8235 27 8241 3 8241 21 8241 31 8253 4 8265 97 8265 199 8283 4 8289 5 8289 7 8289 13 8289 55 8295 2 8295 3 8319 21 8325 1 8325 10 8325 12 8325 70 8337 2 8337 192 8355 30 8367 6 8373 8 8373 10 8385 28 8397 2 8397 14 8409 3 8415 1 8415 11 8415 13 8415 23 8415 29 8415 38 8421 13 8421 15 8421 107 8427 52 8433 6 8445 5 8445 23 8451 1 8457 2 8457 56 8469 17 8475 4 8493 6 8499 5 8499 11 8499 25 8505 7 8505 51 8511 5 8511 49 8511 185 8517 6 8523 12 8535 3 8535 6 8535 39 8541 5 8541 47 8547 4 8547 8 8553 2 8559 43 8565 2 8565 15 8565 135 8571 45 8583 34 8589 3 8589 7 8595 1 8613 6 8619 37 8625 2 8625 44 8631 7 8631 9 8631 19 8649 3 8649 21 8655 6 8673 14 8673 18 8673 62 8679 83 8685 22 8691 11 8691 27 8697 6 8709 1 8709 5 8715 5 8715 6 8715 30 8721 127 8727 12 8727 60 8739 125 8745 1 8745 9 8745 12 8757 74 8763 2 8775 3 8775 51 8781 11 8787 16 8793 32 8799 1 8805 23 8811 3 8823 26 8829 1 8835 10 8841 1 8841 5 8841 9 8841 19 8841 29 8841 99 8847 14 8853 16 8859 5 8859 69 8865 3 8865 8 8877 2 8877 116 8883 2 8883 68 8895 1 8901 5 8907 6 8913 4 8919 1 8919 7 8919 31 8925 6 8949 5 8955 1 8955 21 8955 24 8961 1 8961 5 8973 4 8973 10 8979 1 8985 3 9003 2 9009 17 9021 1 9021 3 9021 9 9021 37 9027 2 9033 20 9033 50 9039 199 9051 13 9051 217 9057 20 9063 4 9063 6 9063 166 9069 23 9081 3 9087 16 9087 22 9087 34 9087 62 9093 16 9099 5 9105 4 9105 6 9105 13 9105 19 9105 60 9117 2 9117 8 9117 20 9123 4 9135 18 9135 24 9135 30 9141 25 9141 67 9159 15 9159 21 9165 13 9165 16 9189 51 9195 2 9195 12 9201 3 9207 82 9219 13 9225 2 9225 5 9225 11 9225 17 9225 101 9225 214 9231 3 9231 43 9237 24 9243 8 9249 15 9249 51 9255 2 9255 56 9261 1 9273 96 9279 9 9285 9 9285 77 9285 78 9291 15 9297 10 9297 20 9303 24 9327 2 9327 6 9345 3 9345 4 9345 55 9345 93 9357 4 9375 16 9381 5 9387 2 9387 20 9393 2 9405 27 9405 95 9411 17 9417 6 9423 2 9423 4 9435 4 9435 10 9435 76 9441 15 9453 2 9459 1 9459 37 9465 8 9465 35 9483 12 9483 34 9483 36 9489 5 9489 39 9495 78 9519 65 9525 6 9549 17 9555 5 9555 30 9555 91 9567 4 9585 6 9585 21 9591 1 9591 23 9591 47 9603 8 9609 3 9609 13 9615 2 9615 14 9615 17 9621 5 9621 17 9645 5 9651 67 9663 2 9681 11 9687 2 9687 10 9693 28 9693 42 9699 15 9699 99 9705 36 9711 1 9711 3 9717 10 9717 16 9723 22 9735 1 9741 5 9741 29 9747 48 9753 36 9753 196 9759 23 9765 21 9771 1 9789 9 9801 7 9801 35 9807 2 9807 24 9825 5 9825 6 9837 6 9843 2 9843 20 9849 1 9849 11 9849 121 9861 3 9861 33 9867 108 9873 32 9885 7 9885 32 9897 14 9903 6 9909 5 9909 65 9915 11 9915 245 9921 1 9945 1 9945 3 9945 16 9951 75 9957 2 9975 8 9975 11 9975 17 9975 61 9981 1 9987 4 9987 6 9987 18 9999 81 10005 4 10011 1 10011 61 10017 40 10017 112 10017 184 10023 32 10029 3 10035 9 10041 5 10047 4 10047 40 10059 3 10059 7 10059 9 10059 39 10065 199 10083 24 10083 104 10101 15 10107 2 10107 38 10125 92 10131 3 10131 13 10131 39 10137 70 10143 4 [/code] |
Thanks, Citrix, for adding to my list. I think it's great to have a comprehensive list of all primes and twin primes of certain forms up to certain limits of k and n before going after the really big primes.
For my list, I unofficially tested k=1 to 600 (i.e. ran no programs) up to the lower limit of where primes were tested to on the Riesel and Proth search sites by matching up the k's and n's. This has usually been up to at least n=200K because both Riesel and Proth primes have been mostly tested at least that high for all k's < 600. So I think doing any further twin testing for k < 600 would not be worthwile because even trying to find one twin above n=200K would take months and possibly years without a large coordinated effort. I have 3 decent-speed machines working on other prime efforts right now that I want to continue on for several weeks yet and a very slow older machine that I use for sieving while the others are prime testing. I think I'll do 3 things here to continue this process: 1. Specify exactly how far each of the k's on my list have been tested. Yours are specifically tested to n=250, but I can't say for sure how high of an n each k is tested on mine without looking more closely at the various sites. 2. Add your primes to my list. 3. Once my slow-speed machine (333 mhz) is done with it's current sieve in about 2 days, I'll use it to test your k's to higher n's for twins. As slow as it is, I'll either limit the n's to 1000 or limit the k's to 2000 and allow the n's to go up to 10000 or so. Obviously these are very rough estimates only. Also to be determined for my list...what gaps exist in the primes for the k's listed on the RPS, i.e. 15k, site, the Primesearch site, and the Proth search site. It's not immediately obvious where gaps exists. One gap that I know of for sure on Riesel primes is for k=289 from n=300K to n=501991. I checked around on another area in this forum and no one could say for sure that the range had been tested so I reserved it. I currently have my highest-speed dual-core machine working on the entire range. Any other Riesel prime that I find in that range will also be tested for a twin or checked for the same n on the Proth search site. Gary |
Combined list with testing limit included
1 Attachment(s)
Citrix,
Actually, k=1 to 600 have been searched enough since that's how far the Proth search site goes up to and so is how far up I matched the site with ours. I wasn't able to do any more testing yet but I combined your list with mine and added the value of n that each k has been tested through. Of course all of yours are 250. I also added odd k's divisbile by 3 (i.e. k=3 mod 6) up to k < 1000 where no twins were found and showed (none) by them. People might like to test those with a little more vigor in the future. I suspect there will be plenty of k's that have no twin primes found. It will be interesting to see if the lowest value of k=3 mod 6 where there are no twins really turns out to be k=111 like it is now. It has technically been tested to n=350K. I should be able to extend the search for k > 600 a little on Tuesday sometime. Thanks for your help so far. This might turn out to be an interesting effort and could give us a good base to work from if we wish to find somewhat large triplets, quadruplets, 5-tuples, etc. in the future. My changes are attached. Gary |
Twins upto n=500. These twins are really rare..
165 264 165 282 555 282 573 344 615 391 669 333 969 269 1023 380 1215 255 1701 387 1743 418 1899 291 1995 492 2085 455 2373 294 2475 260 2565 468 2667 288 2805 259 3321 371 3381 281 3921 443 4101 443 4323 458 5049 361 5139 251 5253 338 5415 435 5547 470 6405 299 7173 294 7503 488 7605 314 7785 355 7791 331 8613 458 8787 472 9063 456 9129 359 9345 445 9369 365 9543 310 9609 297 9789 263 9951 257 9993 308 10071 327 |
Complete twin list k=1-100K and n=1-5K
1 Attachment(s)
Attached is a complete list of all twin primes for k = 1 to 100K and n = 1 to 5K for the form k * 2^n +/- 1. It also includes the twin 459 * 2 ^ 8529 +/- 1 from my earlier effort to match up all known Riesel and Proth primes. There are a total of 17717 twins in the list.
I hope someone finds this useful in searches for more 'exotic' primes such as triplets, quads, 5-tuples, etc. Eventually I want to expand the list for all k < 1M and all n < 100K. If anyone wants to contribute to the effort, let me know. I'll be sieving to n=10K later this week, which won't take long. n's > 66K make the current top-20 twin prime list. Gary |
How sieving multiple k's and n's on twins ?
[quote=Citrix;109183]Twins upto n=500. These twins are really rare..
[/quote] Sorry we duplicated efforts there Citrix. Yes, twins are rare, which makes them special. :smile: Imagine triplets or quads! I checked my new extended list and all of yours are on there. I'm curious...how are you sieving multiple k's and n's on twins? Here's what I'm doing but I'm thinking there must be a better way: 1. Use NewPGen and have it increment the n by 1 each time after it searches the range of k (in my case was 1 to 100000) that I want. For n < 2500, I just let it do each n almost instantly by sieving to only 1M since LLR is finding them rapidly. For n > 2500, I sieved to 100M. But these were just guesses because of the problem in #2. 2. #1 has the annoying problem of creating 1 file for each n, which I can't seem to get around. So I'm forced to then copy all of the files into one big file. I've been doing them 500 n's at a time. 3. Fortunately LLR, being the great program that it is, is able to accept one big file with many lines of XXXX:T:0:2:3 throughout the middle of it so it's able to handle many k's and n's in the same file. I found the above to still be far faster than attempting to use the very slow Proth program and letting it both sieve and find primes. Do you know of a faster (or at least cleaner) way to sieve multiple k's and n's into one file? If there's some other software out there that would be better, could you provide a link to it? I get all of these various sites confused at times. It doesn't take too long to copy 500 files into 1 file and then delete the 500 files. But the main problem with it only sieving 1 n at a time is that I can't get an accurate estimate of how many primes are being removed per second. I mean for 1 n, it might be removing only 1 per second but if it were sieving all 500 n at once, it might be removing 500 per second. But I don't know yet because in only sieving to 100M, it finishes fast enough that it doesn't show the rate. I finally resorted to just writing down the starting and ending time on my watch to determine how much total sieving and LLR time it was taking for each range of 500 n to get an idea of when to increase my sieve limit. Thanks, Gary |
What is the goal of all this? Is it supposed to help the TPS project some way? I don't quite get what you guys are doing.
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It's in the process
[quote=Joshua2;109252]What is the goal of all this? Is it supposed to help the TPS project some way? I don't quite get what you guys are doing.[/quote]
What is our goal? We're finding twin primes! I believe the goal of these forums is to find all of the primes of certain forms; not just the large ones. Our goal here is to find all of the TWIN primes of a certain form. Some people prefer to find very few large primes. We here prefer to find all of the small primes and gradually build our way up to the large primes. Since very few people are interested in this sort of 'dirty work', that is our task here. This is no different than our < 300 site. It doesn't show just large primes, it shows them all. The great 19th-century mathematician Carl Friedrich Gauss didn't start trying to manually calculate prime numbers beginning at 1 billion or higher just to make a big splash or set some sort of calculation record. He painstakingly started where others had left off and manually calculated ALL primes up to 3 million in order to construct some of the greatest mathematical proofs and theories of all time. It is only in the painstaking process of starting with the elementary building blocks of a process that one can glean the information needed in order to gain a deeper understanding of the process as a whole. :smile: Gary |
List of twins completed to n=10K
1 Attachment(s)
I've completed searching for twins up to n=10K for k=1 to 100K. The list is attached. There are only 23 twins between n=5K and 10K. I can see that I'm going to need to expand the list up to k=1M or 10M to get any significant # of twins for n>10K. (no surprise there!)
I also checked the list for triplets and quadruplets. The largest of all 3 kinds that I've found so far are: Twins: 33891*2^9869-1,+1 Triplets: 32811*2^2707-1,+1,+5 Quads: 3741*2^153-1,+1,+5,+7 I also checked triplets and quads for the form of k*2^n-7,-5,-1,+1 and k*2^n-5,-1,+1 but there were none as large. -7, -5, +5, and +7 primes were checked at [URL]http://www.alpertron.com.ar/ECM.HTM[/URL]. The largest ones were also checked with Primo software. Although the list looks small now, it only takes an exponent of 10475 to make the top-10 triplets list and an exponent of 3489 to make the top-10 quads list. Largest k-tuplets are shown at [URL="http://www.ltkz.demon.co.uk/ktuplets.htm"]www.ltkz.demon.co.uk/ktuplets.htm[/URL]. Gary |
TPS extended to n=15K up to k < 1M.
1 Attachment(s)
I have now extended the Riesel-Proth twin prime search up to n=15K for all k < 1M.
I am attaching two lists: 1. The original list for k < 100K extended to n=15K sorted by k. 8 additional twins were found at this low level of k. To find them easily, you'll probably need to look at the list in #2. 2. A new list for k < 1M for 10K < n <= 15K sorted by n. There were a total of 85 twins in this range. Note that it includes the 8 twins from #1. The most interesting find was 915 * 2 ^ 11455 +/- 1. It is the only twin that I've seen where k is < 1K and n is > 10K. In doing a search of the top-5000 site archives for twins, I see that it has already been found but there are none greater for k < 1K. A further analysis of the top-5000 archives shows that 80 of these 85 twins were never stored there so there is plenty of new information here. I did tests for both +5 and -5 triplets on all 85 new twins. None were found. Eventually it would be interesting to extend the k to 1M for n < 10K and see if some higher triplets or quads can be found then what was posted last time but NOT to list more small twins. The chances are slim that a triplet or quad will be found for k < 1M for n > 15K. I am now sieving for twins in the range of 15K < n <= 20K and k < 1M. Gary |
[QUOTE=gd_barnes;112763]I am now sieving for twins in the range of 15K < n <= 20K and k < 1M.
Gary[/QUOTE] Just out of curiosity, what software are you using to sieve that range? |
Sieving software used for all TPS
[quote=MooooMoo;112801]Just out of curiosity, what software are you using to sieve that range?[/quote]
I'm using NewPGen with the increment counter turned on but it is anything but ideal. Unfortunately there is no real good software that I am aware of to sieve for twins across both multiple k's and n's. Proth works well at low n but is much too slow at the level of n that I'm now at. NewPGen overcomes some of the issue because it is very fast on a fixed n search but still not nearly as efficient as being able to sieve the entire range of k's and n's at once. What I do is sieve each n to P=5G, which takes just over a minute on a high-speed machine, and then it automatically goes on to the next n. Unfortunately it creates one file per n so every 1000 n, I copy all 1000 files into one big sieve file and feed it to LLR. Fortunately LLR doesn't care if the T:0:2:3 line is embedded multiple times in the sieve. Thus the copy doesn't require any extra editing by me and the big file is only around 11-12 MB for 1000 n. At P=5G for a range of k=1 to 1M for each n, it's removing candidates at about 0.8-0.9 sec. each. LLR at n=15K is taking about 0.4 secs. for each candidate so that's a little high to sieve but it will probably be pretty close as n approaches 20K. I also prefer to sieve a little too far instead of not far enough. Since it's not sieving the entire range at once like you're able to do for a fixed n search on the n=333333 TPS project, this is certainly not a particularly efficient approach but is the best that I could come up with for the time being. I thought of sieving for Riesel's, using the output to sieve for Proth's, and then LLR what is left but the files got very big real quick for such a large range of k, causing extra effort to have to split them up. What I really need is a combination of Srsieve for a multi-k search and NewPGen's TPS algorithm. If anyone can improve on my method here, I'm all ears! :smile: Gary |
TPS extended to n=17K to k < 1M
1 Attachment(s)
I had a request to post my latest on this effort. Attached is the Riesel-Proth twin prime search up to n=17K for all k < 1M. There were 16 twins for 15K < n <= 17K for k < 1M. Two of them were k < 100K.
With this effort, I also tested all Riesel primes for k < 1M shown on the RPS site, i.e. [URL="http://www.15k.org"]www.15k.org[/URL], for Proth primes. The continuous tested ranges of k shown on one of the listings take this into account. No additional twins were found above what I've already found. I now have 2 high-speed cores LLRing up to n=20K. They should be done within a week and I'll post an updated list at that time. I tested all 16 new twins for -5 and +5 triplets. None were found. Gary |
That reminded me...
[url]http://tech.groups.yahoo.com/group/primenumbers/message/9836[/url] |
[quote=XYYXF;115328]That reminded me...
[URL]http://tech.groups.yahoo.com/group/primenumbers/message/9836[/URL][/quote] A very interesting list indeed. I spot-checked about 40-50 of this list where k < 100K vs. my own and found no problems. If you know someone in the forum there, perhaps you could ask them to expand the list to include the first prime odd-k for each n up to n=10K. That would be interesting to see. My LLR is up to n=20K for k < 1M now. See next post... Thanks for sharing! Gary |
Riesel-Proth TPS up to n=20K for k < 1M
1 Attachment(s)
Attached are Riesel-Proth twin prime search lists up to n=20K for all k < 1M. There were 40 twins for 15K<n<=20K. A surprising 9 of them were for k < 100K.
I have also started a web page to list all of these twins. It's in its initial stages of creation. Right now, it only includes k's < 1M that have twins for 10K<=n<=20K and ALL twins for k<100K that has a twin for n>=10K. Eventually I will have all twins currently in the attachments here on the page. Here it is... [URL="http://gbarnes017.googlepages.com/twinsk1-1Mn10K-20K.htm"]gbarnes017.googlepages.com/twinsk1-1Mn10K-20K.htm[/URL]. Sieving is now complete up to n=25K and LLR has just begun. I'll continue posting in n=5K pieces until n=30K and then drop back to n=10K pieces after that. Gary |
New web pages for twins
The web page in the above message is no longer valid. I have now created two web pages that have all twins previously listed in the attachments in this thread. They are here:
[URL]http://www.noprimeleftbehind.net/gary/twins100K.htm[/URL] [URL]http://www.noprimeleftbehind.net/gary/twins1M.htm[/URL] A special thanks to Karsten Bonath (kar_bon) for helping out by writing a script to format the twins on the k<100K page. Gary |
[QUOTE=gd_barnes;115888]A very interesting list indeed. I spot-checked about 40-50 of this list where k < 100K vs. my own and found no problems.
If you know someone in the forum there, perhaps you could ask them to expand the list to include the first prime odd-k for each n up to n=10K. That would be interesting to see.[/QUOTE]It was me who posted this list on that forum. :wink: I'll try to find the data I used to generate it... |
[QUOTE=gd_barnes;115888]If you know someone in the forum there, perhaps you could ask them to expand the list to include the first prime odd-k for each n up to n=10K. That would be interesting to see.
Gary[/QUOTE] [very masculine voice] THIS SOUNDS LIKE A JOB FOR...PFGW!!! [/very masculine voice] Now, if I could just find my PFGW suit. It's got 'PFGW Man' written on the front, and it shows off my anatomy so well that I've been banned from wearing it in a few places. |
[quote=jasong;116365][very masculine voice]
THIS SOUNDS LIKE A JOB FOR...PFGW!!! [/very masculine voice] Now, if I could just find my PFGW suit. It's got 'PFGW Man' written on the front, and it shows off my anatomy so well that I've been banned from wearing it in a few places.[/quote] :lol::missingteeth::lol: Good one, Jasong! Had me rolling on the floor! I agree, PFGW would be excellent for creating such a list. Gary |
[quote=XYYXF;116326]It was me who posted this list on that forum. :wink: I'll try to find the data I used to generate it...[/quote]
Excellent! My goal with all of this is to have the most complete and accurate list of Riesel-Proth twin primes anywhere on the web. The more information, the merrier! :grin: Gary |
[QUOTE=gd_barnes;116368]Excellent! My goal with all of this is to have the most complete and accurate list of Riesel-Proth twin primes anywhere on the web. The more information, the merrier! :grin:
Gary[/QUOTE] Did u think to find twin primes as big as we want by finding a general formula ???? I wish all the best for u and all mathematicians . Sghodeif , :question: |
No general formula that I am aware of for primes of any kind. That's what prime-searchers everywhere are hoping to find! :smile:
G |
My Riesel/Proth twin search for k<1M is now up to n=23.5K. See the aforemention web pages for all of the twins found. I'll most likely put a 2nd core on this in the near future. It's getting quite a bit slower past n=20K.
Gary |
Gosh this is a major piece of work. GL in your search!!!!
|
Tks & another side effort
[quote=robert44444uk;118692]Gosh this is a major piece of work. GL in your search!!!![/quote]
Thanks, Robert. I'll be hitting n=25K here on core 1 in the next couple of days. Sieving is now up to n=35K and LLRing is speeding up with the addition of a 2nd core to the effort. (Core 2 has tested n=25K-25.6K so far.) We're only averaging about 3 twins for each n=1K range now for k < 1M and the last twin for k < 100K was at n=22312. I expect plenty more but they're thinning out rapidly. I now update the web page about twice for every n=1K range that I test. You might be interested in another 'side effort' that I have going on. I have a web page now for all known primes of the form k*10^n-1 where k < 10M at [URL="http://gbarnes017.googlepages.com/primes-kx10n-1.htm"]gbarnes017.googlepages.com/primes-kx10n-1.htm[/URL]. The page is intended for k's of all sizes and I do have several extremely high-weight k's > 10M listed but there are still many primes > 10M from the top-5000 site that aren't on there yet. I thought you might be interested in the page because Jens Andersen and Axn1 have been battling it out for the k with the most primes and we've got some very large highly prolific k's now! I know how you like super-large super-high-weight k's. The testing is being coordinated in the Riesel Prime Search project here at this thread: [URL="http://mersenneforum.org/showthread.php?t=9578"]mersenneforum.org/showthread.php?t=9578[/URL]. Come over and try to beat our top record of 56 primes on a 20-digit k! :smile: Gary |
The "all-twin" search for k < 1M is now up to n=25.6K. See the web pages in this thread.
Gary |
The "all-twin" search for k < 1M is now complete to n=30K. They are all shown at:
[URL]http://gbarnes017.googlepages.com/twins100K.htm[/URL] [URL]http://gbarnes017.googlepages.com/twins1M.htm[/URL] Here are some statistics for n=20K-30K: 1 twin for k < 10K: 7485*2^20023+/-1 2 twins for 10K < k < 100K: 70497*2^27652+/-1 31257*2^22312+/-1 39 twins for 100K < k < 1M: (highest 10 listed; see 'twins1M' web page for rest) 815751*2^29705+/-1 953337*2^28520+/-1 771843*2^28494+/-1 445569*2^28353+/-1 198417*2^27858+/-1 293445*2^27643+/-1 939015*2^27542+/-1 228015*2^27509+/-1 294723*2^27504+/-1 766293*2^27110+/-1 (etc.) All checked for triplets...no luck. Testing is currently at n=30.4K and sieving at n=40K. The search on 2 cores continues to n=100K. A 3rd core will be added at n=40K. Gary |
The "all-twin" search for k < 1M is now up to n=36.1K. See the web pages in this thread.
There were 11 twins from n=30K-36.1K. Also found was the [B]largest known Riesel/Proth twin for k<100K[/B]. Here is the complete list for the range: k<100K: 51315*2^32430+/-1 100K<k<1M: 892881*2^36075+/-1 338205*2^35351+/-1 959715*2^34895+/-1 143835*2^33826+/-1 649545*2^33398+/-1 440685*2^31989+/-1 249435*2^30977+/-1 282891*2^30309+/-1 383775*2^30279+/-1 523851*2^30197+/-1 Current known Riesel/Proth twin prime records: k<1M 134583*2^80828+/-1 (from top-5K site) k<100K 51315*2^32430+/-1 (from this effort) k<10K 7485*2^20023+/-1 (from top-5K site) k<1K 915*2^11455+/-1 (from top-5K site) Gary |
I posted 2 days too early. In just another 100n up to n=36.2K, I found 2 more twins, one for k<100K!:
47553*2^36172+/-1 296139*2^36125+/-1 The first one is the new standard to beat for k<100K. Gary |
[QUOTE=gd_barnes;115888]
If you know someone in the forum there, perhaps you could ask them to expand the list to include the first prime odd-k for each n up to n=10K. That would be interesting to see. Gary[/QUOTE] [QUOTE=jasong;116365][very masculine voice] THIS SOUNDS LIKE A JOB FOR...PFGW!!! [/very masculine voice] Now, if I could just find my PFGW suit. It's got 'PFGW Man' written on the front, and it shows off my anatomy so well that I've been banned from wearing it in a few places.[/QUOTE] It appears that Jasong couldn't find his PFGW suit, perhaps it was in a closet marked "unwanted Xmas gifts" Anyway, analysing Gary's <100K site produces the following table: I will try to fill up to n=500 Regards Robert [code] n 1st k 1 3 2 1 3 9 4 15 5 81 6 3 7 9 8 57 9 45 10 15 11 99 12 165 13 369 14 45 15 345 16 117 17 381 18 3 19 69 20 447 21 81 22 33 23 1179 24 243 25 765 26 375 27 81 28 387 29 45 30 345 31 681 32 585 33 375 34 267 35 741 36 213 37 429 38 3093 39 165 40 267 41 255 42 1095 43 9 44 147 45 849 46 405 47 1491 48 177 49 1941 50 927 51 1125 52 1197 53 2001 54 333 55 519 56 1065 57 585 58 657 59 129 60 147 61 141 62 417 63 9 64 1623 65 99 66 2985 67 2469 68 4497 69 5259 70 597 71 7029 72 315 73 3081 74 2457 75 4161 76 603 77 3591 78 2697 79 3681 80 213 81 2079 82 1545 83 4089 84 165 85 1455 86 10287 87 1629 88 387 89 3321 90 14487 91 849 92 1467 93 3339 94 3747 95 6639 96 7737 97 8265 98 15735 99 5589 100 4107 101 9225 102 537 103 2079 104 1203 105 1515 106 1323 107 7245 108 6897 109 20631 110 2205 111 2175 112 3087 113 11145 114 7887 115 14841 116 2673 117 5961 118 3303 119 5565 120 3957 121 9849 122 1497 123 1125 124 1983 125 699 126 2565 127 8721 128 4467 129 5835 130 6063 131 1089 132 3117 133 1455 134 3105 135 6129 136 22365 137 3555 138 24453 139 8121 140 4143 141 1179 142 6903 143 309 144 11505 145 14121 146 17037 147 1419 148 17157 149 5715 150 345 151 13179 152 4497 153 3741 154 10803 155 105 156 30657 157 14439 158 14445 159 7569 160 17295 161 25425 162 6555 163 2121 164 3717 165 13731 166 7737 167 18711 168 765 169 1881 170 19335 171 32361 172 2847 173 2115 174 4155 175 1941 176 1383 177 24771 178 2277 179 10479 180 4287 181 441 182 19617 183 27261 184 2493 185 5481 186 28227 187 20175 188 1935 189 45 190 525 191 13719 192 8337 193 12495 194 18087 195 27099 196 9753 197 56745 198 4245 199 8265 200 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10125 817 64401 821 49041 824 66975 827 12285 828 78375 829 1365 831 24609 833 49539 837 62361 841 86679 844 87303 846 61785 847 5265 852 53763 853 18885 856 87495 857 88095 858 63135 861 37359 863 93765 865 31575 867 60681 873 55209 874 75783 875 50565 877 31005 880 4107 882 17145 884 25833 886 87465 888 45675 889 59421 896 11925 898 59925 899 68901 903 23901 906 24747 908 88407 914 5673 921 94629 922 10533 925 50595 927 80139 928 79623 929 83271 933 94335 934 41727 936 52953 940 5955 945 60729 947 27825 948 61425 949 23805 950 13503 953 21741 954 45243 957 77805 958 66417 961 98061 965 7995 966 82995 969 77565 973 16011 976 68313 983 10485 988 97323 992 56685 994 24963 1007 37275 1008 48225 1013 74091 1014 35523 1018 19887 1028 98493 1032 177 1034 16233 1037 71421 1045 94065 1048 3885 1052 85845 1055 91755 1056 88515 1057 33405 1059 60099 1066 90165 1067 85911 1070 70623 1075 13131 1076 50025 1084 15315 1084 16665 1086 69417 1098 58287 1102 27435 1104 4275 1107 48681 1110 11007 1122 60513 1134 83205 1142 11007 1156 1035 1167 54339 1168 62823 1173 52461 1175 46791 1188 65613 1193 84435 1197 45201 1217 14199 1221 88329 1228 79203 1229 42399 1237 74109 1241 13629 1244 64233 1245 88575 1251 75705 1256 53865 1261 32265 1267 95229 1270 71805 1272 50655 1274 95847 1282 99105 1286 9183 1295 49119 1299 3339 1312 15657 1314 46965 1321 1065 1325 62265 1327 2625 1338 92115 1354 38565 1355 62289 1367 7755 1383 67821 1389 97899 1390 14877 1391 76479 1394 88155 1402 80103 1406 18003 1408 98475 1425 86205 1431 75519 1440 10083 1441 74031 1446 93837 1447 51651 1462 15927 1466 74505 1468 85077 1471 81489 1475 66381 1483 57891 1500 32547 1509 86361 1532 83973 1533 36045 1553 291 1556 81255 1566 42507 1599 15375 1603 89895 1616 78327 1623 33549 1625 65835 1640 34215 1652 33957 1660 20733 1672 56685 1676 96897 1677 24969 1678 34725 1689 27765 1718 51747 1721 45951 1757 41229 1763 29481 1767 84159 1786 42825 1793 95151 1794 98583 1820 79335 1823 57495 1849 87585 1858 29835 1860 13317 1869 82275 1880 22035 1900 4425 1933 39171 1954 8007 1966 63237 1971 3885 1985 31545 2024 10095 2083 84609 2112 59553 2129 11655 2138 40215 2162 33117 2182 53955 2185 66729 2191 4359 2196 24405 2213 6201 2253 75219 2255 7419 2278 43947 2280 25293 2333 43089 2470 60957 2473 52935 2498 56727 2501 86085 2518 94815 2529 33939 2569 79029 2637 89115 2679 61269 2685 93429 2695 59415 2707 32811 2743 52011 2748 84255 2821 6075 2827 20805 2834 61947 2844 58053 2846 10725 2867 36159 2887 88629 2899 69735 2945 12195 3004 57267 3017 5559 3074 90705 3104 58143 3179 41205 3215 43095 3229 49449 3283 1149 3426 34365 3460 2403 3503 83331 3551 36159 3553 4845 3587 51591 3601 88311 3641 69069 3646 40713 3722 5373 3826 4935 3830 21417 3846 24015 3867 31539 3873 88071 3891 80661 3942 34407 3989 49455 4335 32721 4619 66969 4787 74565 4884 22767 4901 2565 4997 31569 5147 58311 5154 88335 5316 43923 5396 85107 5459 82005 5738 58983 5907 5775 6177 79515 6593 45639 6634 4737 6885 33801 7170 77367 7618 74313 7631 54729 7727 74229 7768 33957 8060 69927 8160 31335 8335 3975 8529 459 8825 53985 9154 61593 9869 33891 10601 10941 10929 34911 11455 915 11493 57201 11710 78045 12178 73005 13153 3981 13466 44943 15263 88665 15770 74193 17372 77517 17527 14439 17705 96321 17987 88269 18989 56361 19742 98067 19817 53889 20023 7485 22312 31257 27652 70497 32430 51315 36172 47553 [/code] |
low k for each n to 1000
Here is a table of lowest k for each twin to n=1000
Does anyone want to take further? * denotes jumping champion [code] 1 3* 2 1 3 9* 4 15* 5 81* 6 3 7 9 8 57 9 45 10 15 11 99* 12 165* 13 369* 14 45 15 345 16 117 17 381* 18 3 19 69 20 447* 21 81 22 33 23 1179* 24 243 25 765 26 375 27 81 28 387 29 45 30 345 31 681 32 585 33 375 34 267 35 741 36 213 37 429 38 3093* 39 165 40 267 41 255 42 1095 43 9 44 147 45 849 46 405 47 1491 48 177 49 1941 50 927 51 1125 52 1197 53 2001 54 333 55 519 56 1065 57 585 58 657 59 129 60 147 61 141 62 417 63 9 64 1623 65 99 66 2985 67 2469 68 4497* 69 5259* 70 597 71 7029* 72 315 73 3081 74 2457 75 4161 76 603 77 3591 78 2697 79 3681 80 213 81 2079 82 1545 83 4089 84 165 85 1455 86 10287* 87 1629 88 387 89 3321 90 14487* 91 849 92 1467 93 3339 94 3747 95 6639 96 7737 97 8265 98 15735* 99 5589 100 4107 101 9225 102 537 103 2079 104 1203 105 1515 106 1323 107 7245 108 6897 109 20631* 110 2205 111 2175 112 3087 113 11145 114 7887 115 14841 116 2673 117 5961 118 3303 119 5565 120 3957 121 9849 122 1497 123 1125 124 1983 125 699 126 2565 127 8721 128 4467 129 5835 130 6063 131 1089 132 3117 133 1455 134 3105 135 6129 136 22365* 137 3555 138 24453* 139 8121 140 4143 141 1179 142 6903 143 309 144 11505 145 14121 146 17037 147 1419 148 17157 149 5715 150 345 151 13179 152 4497 153 3741 154 10803 155 105 156 30657* 157 14439 158 14445 159 7569 160 17295 161 25425 162 6555 163 2121 164 3717 165 13731 166 7737 167 18711 168 765 169 1881 170 19335 171 32361* 172 2847 173 2115 174 4155 175 1941 176 1383 177 24771 178 2277 179 10479 180 4287 181 441 182 19617 183 27261 184 2493 185 5481 186 28227 187 20175 188 1935 189 45 190 525 191 13719 192 8337 193 12495 194 18087 195 27099 196 9753 197 56745* 198 4245 199 8265 200 63855* 201 27261 202 69855* 203 14199 204 1755 205 5529 206 1197 207 54639 208 69753 209 10461 210 10575 211 9 212 3615 213 26145 214 9225 215 5859 216 12255 217 6615 218 16653 219 18531 220 24087 221 6555 222 7947 223 12909 224 49203 225 49341 226 10857 227 3405 228 25665 229 19041 230 21255 231 2571 232 30015 233 47079 234 24915 235 77751* 236 33333 237 16641 238 135 239 17289 240 10197 241 4059 242 1023 243 50319 244 22113 245 9915 246 17535 247 19041 248 15795 249 168831* 250 23007 251 5139 252 17787 253 15519 254 12957 255 1215 256 64647 257 9951 258 74253 259 2805 260 2475 261 15711 262 25767 263 9789 264 165 265 13209 266 19593 267 33105 268 45213 269 969 270 98907 271 19335 272 22317 273 10635 274 13713 275 34245 276 41085 277 24129 278 26025 279 24579 280 128505 281 3381 282 165 283 20175 284 23853 285 25881 286 61647 287 39315 288 2667 289 67695 290 34647 291 1899 292 33735 293 48861 294 2373 295 58179 296 66507 297 9609 298 20085 299 6405 300 230085* 301 44529 302 16575 303 22815 304 99297 305 21015 306 21075 307 91455 308 9993 309 15069 310 9543 311 79719 312 36195 313 14649 314 7605 315 67461 316 16035 317 12951 318 20295 319 41349 320 82473 321 20781 322 19293 323 88791 324 55605 325 23295 326 25473 327 10071 328 28653 329 48489 330 12477 331 7791 332 345675* 333 669 334 16437 335 42699 336 93765 337 12909 338 5253 339 23415 340 128625 341 21585 342 76995 343 153645 344 573 345 31719 346 15717 347 43011 348 33765 349 28149 350 71253 351 127305 352 14727 353 85431 354 10545 355 7785 356 38853 357 70851 358 65385 359 9129 360 162243 361 5049 362 49815 363 26871 364 210447 365 9369 366 74763 367 18669 368 16905 369 49299 370 12543 371 3321 372 138765 373 151839 374 40257 375 26679 376 14223 377 23709 378 22713 379 66039 380 1023 381 67749 382 34683 383 114951 384 126747 385 72609 386 114687 387 1701 388 56817 389 10791 390 39345 391 615 392 108195 393 95151 394 67023 395 21315 396 28065 397 24039 398 19065 399 102795 400 48207 401 28941 402 83337 403 101535 404 22887 405 74085 406 35253 407 79215 408 31635 409 36825 410 50835 411 273429 412 58065 413 86061 414 39513 415 17061 416 32025 417 30705 418 1743 419 71919 420 224415 421 66075 422 84057 423 81651 424 65337 425 237765 426 251475 427 83139 428 36903 429 39039 430 110157 431 66219 432 69477 433 50181 434 54033 435 5415 436 30987 437 102309 438 24693 439 56259 440 25077 441 15255 442 18795 443 3921 444 35793 445 9345 446 18663 447 30849 448 57717 449 69285 450 155463 451 26355 452 258345 453 17631 454 65193 455 2085 456 9063 457 15561 458 4323 459 104661 460 34725 461 92235 462 229227 463 53991 464 63903 465 24351 466 12147 467 33351 468 2565 469 108795 470 5547 471 139935 472 8787 473 184281 474 49053 475 13935 476 33375 477 33315 478 141315 479 53019 480 162897 481 233115 482 143163 483 150939 484 50295 485 27975 486 101055 487 156051 488 7503 489 73671 490 37095 491 37719 492 1995 493 97449 494 39207 495 27261 496 208845 497 99015 498 37755 499 131439 500 52305 501 207945 502 35397 503 66735 504 35877 505 74985 506 103107 507 5565 508 216243 509 107631 510 262035 511 43485 512 51765 513 134115 514 53355 515 87951 516 12045 517 66375 518 366555* 519 83211 520 4257 521 17709 522 80175 523 76089 524 47403 525 5775 526 62337 527 43371 528 43137 529 10365 530 74367 531 104409 532 347457 533 396441* 534 84627 535 278535 536 49893 537 23541 538 2007 539 12711 540 174297 541 8031 542 121065 543 40119 544 330015 545 18801 546 297 547 5979 548 97293 549 157209 550 26853 551 4035 552 29187 553 190485 554 70923 555 67329 556 130227 557 105381 558 80385 559 300561 560 39243 561 112581 562 176205 563 199989 564 117243 565 120069 566 75225 567 28131 568 239247 569 60411 570 25485 571 27909 572 20037 573 14259 574 70107 575 38835 576 247035 577 126615 578 136413 579 404871* 580 88257 581 76569 582 22587 583 28005 584 15177 585 210051 586 83175 587 173355 588 50235 589 133911 590 42777 591 389799 592 86385 593 45315 594 179163 595 257529 596 41625 597 268461 598 147135 599 74229 600 82023 601 135585 602 190695 603 33885 604 113475 605 264849 606 129705 607 368775 608 217143 609 228651 610 86973 611 8781 612 47313 613 94005 614 261075 615 34059 616 79353 617 29919 618 54015 619 18429 620 55203 621 46035 622 87795 623 12285 624 143265 625 104091 626 16323 627 140739 628 137907 629 223569 630 643737* 631 229749 632 506475 633 123891 634 242523 635 52419 636 78033 637 137835 638 227283 639 198459 640 558087 641 664941* 642 394203 643 91629 644 84045 645 274395 646 250923 647 24249 648 78453 649 109809 650 3723 651 205251 652 375843 653 624165 654 61353 655 38835 656 256605 657 21999 658 75447 659 101661 660 50943 661 77505 662 32067 663 374901 664 567573 665 258651 666 249345 667 127041 668 144717 669 58725 670 392013 671 130689 672 15993 673 178689 674 252693 675 376929 676 257613 677 3405 678 169893 679 469755 680 7605 681 217221 682 386127 683 151845 684 24537 685 243879 686 141705 687 246405 688 224625 689 13689 690 46545 691 38229 692 47937 693 152421 694 13197 695 2985 696 96813 697 102789 698 157587 699 436095 700 179865 701 317481 702 169827 703 5355 704 253995 705 330171 706 312387 707 37149 708 270177 709 158115 710 60693 711 25029 712 700005* 713 92529 714 35817 715 629211 716 118413 717 78561 718 86193 719 101361 720 89577 721 119721 722 150567 723 715449* 724 102213 725 20115 726 213 727 35589 728 30933 729 343359 730 308853 731 111285 732 142047 733 597339 734 50025 735 123585 736 5013 737 11175 738 95937 739 140481 740 51975 741 170625 742 58683 743 48075 744 9753 745 9165 746 131937 747 113271 748 42777 749 227871 750 22407 751 1025925 752 140967 753 110775 754 797433* 755 490281 756 490107 757 125169 758 84057 759 133521 760 404775 761 913671* 762 48615 763 242445 764 141243 765 73059 766 988437* 767 315 768 65475 769 484455 770 354417 771 56199 772 743433 773 62391 774 173667 775 125385 776 26775 777 188979 778 410187 779 239271 780 51777 781 88299 782 406707 783 108351 784 364203 785 193515 786 58257 787 17481 788 20997 789 19485 790 116103 791 217809 792 488805 793 98649 794 18495 795 119259 796 212157 797 526701 798 679623 799 95565 800 207663 801 291951 802 353127 803 267795 804 442227 805 72861 806 613383 807 136119 808 142785 809 47055 810 539157 811 70539 812 191085 813 10125 814 105537 815 234315 816 385887 817 64401 818 789453 819 377451 820 125385 821 49041 822 640677 823 268101 824 66975 825 134481 826 515955 827 12285 828 78375 829 1365 830 554925 831 24609 832 524217 833 49539 834 130323 835 155085 836 1175493* 837 62361 838 127905 839 238395 840 916815 841 86679 842 129237 843 122685 844 87303 845 451209 846 61785 847 5265 848 255693 849 163965 850 278427 851 382875 852 53763 853 18885 854 169407 855 157251 856 87495 857 88095 858 63135 859 555039 860 629997 861 37359 862 798315 863 93765 864 722967 865 31575 866 1744257* 867 60681 868 483735 869 399591 870 167967 871 1767711* 872 111027 873 55209 874 75783 875 50565 876 272085 877 31005 878 296043 879 622671 880 4107 881 134511 882 17145 883 430389 884 25833 885 1097925 886 87465 887 895101 888 45675 889 59421 890 910923 891 149091 892 115845 893 248349 894 173283 895 133875 896 11925 897 498981 898 59925 899 68901 900 105177 901 109305 902 1039227 903 23901 904 141615 905 344949 906 24747 907 248781 908 88407 909 179091 910 107457 911 551979 912 313485 913 127689 914 5673 915 136881 916 106413 917 233349 918 163377 919 280929 920 367023 921 94629 922 10533 923 382035 924 773367 925 50595 926 143403 927 80139 928 79623 929 83271 930 424167 931 2035431* 932 116385 933 94335 934 41727 935 390099 936 52953 937 164829 938 165537 939 369381 940 5955 941 202335 942 112053 943 317955 944 164787 945 60729 946 170085 947 27825 948 61425 949 23805 950 13503 951 385695 952 178173 953 21741 954 45243 955 351765 956 232947 957 77805 958 66417 959 399105 960 770193 961 98061 962 312297 963 1170699 964 177255 965 7995 966 82995 967 703701 968 514437 969 77565 970 113745 971 1390269 972 493173 973 16011 974 192255 975 947859 976 68313 977 230439 978 582717 979 262575 980 441357 981 402141 982 626943 983 10485 984 163497 985 411081 986 706773 987 1305255 988 97323 989 349521 990 417375 991 234291 992 56685 993 179445 994 24963 995 219069 996 237675 997 400941 998 330075 999 586899 1000 467343 [/code] |
[QUOTE=robert44444uk;126329]Here is a table of lowest k for each twin to n=1000
Does anyone want to take further? * denotes jumping champion [/QUOTE] hi robert, i hope you spent not much time in that! please have a look here: [url]http://www.rieselprime.org/FirstKTwin.htm[/url]. i made this page 4 months ago after i found a link on this first twin for a k (see page). all n upto 1130 are filled in there and with gaps upto 1400. i want to expand this page but found no time yet! karsten |
[QUOTE=kar_bon;126450]hi robert,
i hope you spent not much time in that! please have a look here: [url]http://www.rieselprime.org/FirstKTwin.htm[/url]. i made this page 4 months ago after i found a link on this first twin for a k (see page). all n upto 1130 are filled in there and with gaps upto 1400. i want to expand this page but found no time yet! karsten[/QUOTE] No only spent about an hour or so fiddling about. I think it is an interesting exercise because of the statistics of series like this. If you plot all the values then it increases gently and there is a nice curve bounding 95% of values, but the outer envelope of the rogue 5% seem to be increasing on a much steeper curve. I have a hunch that you could look at really rather a large set of consecutive n's then you would be certain to find a twin prime over a relatively small k range, and that would be more efficient that the current k*2^333333+/-1 twin search, as 333333 might be just such a rogue!! Statisticians could I think define such a range of manageable k and n to produce 99% probability of getting a twin. Whereas n=333333 - who knows! |
[quote=robert44444uk;126813]No only spent about an hour or so fiddling about.
I think it is an interesting exercise because of the statistics of series like this. If you plot all the values then it increases gently and there is a nice curve bounding 95% of values, but the outer envelope of the rogue 5% seem to be increasing on a much steeper curve. I have a hunch that you could look at really rather a large set of consecutive n's then you would be certain to find a twin prime over a relatively small k range, and that would be more efficient that the current k*2^333333+/-1 twin search, as 333333 might be just such a rogue!! Statisticians could I think define such a range of manageable k and n to produce 99% probability of getting a twin. Whereas n=333333 - who knows![/quote] I agree completely Robert. I suggested this to MooMoo, the TPS project leader, in an Email several weeks ago. I didn't hear anything back. I think they've already decided that they'll do a fixed-n search on n=500K after they find a twin for n=333333. IMHO, searching a moderate-sized range of consecutive n over a much smaller range of k-values is more effecient in the long run due to the LLRing efficiency gained from the smaller k-values. In theory, the chances are the same either way of accidently searching a bad range. The TPS way, it's a 'rogue' n-value. Using the way I did it, you'd have the same number of candidates with more n-values but less k-values but still the same chance of catching a rogue k/n range. But the reason why I think it is more efficient is because smaller k's LLR so much faster. Even though you lose sieving depth and efficiency, LLRing is a large percentage of any prime search so more effort should be given towards minimizing LLR time instead of sieve time. To get to where I've searched so far on my effort, it's only taken a few months of 2 pretty slow older 2.66 Ghz P4's. If I put 10-12 faster CPU's on it, I could most likely search n=36K-100K faster than I did just getting to n=36K. Gary |
A simple exercise to prove the above.
Take the first instance k for the first 1,000 n, shown in the table posted above on 21 February. Take all combinations of 15 consecutive n, and calulate the average of the k values chosen (=A), and the minimum k in the range. Multiply the minimum by 15 (=B), and compare to the average. A is smaller than B in 197 cases, but B is smaller than A in 788 cases. The broader the range so the number of cases that B<A increases: range of n A/B B<A as % of total cases 10 371/619 62.5% 15 197/788 80.0% 20 109/871 88.9% 25 74/901 92.4% 30 54/916 94.4% So I really do not understand the 333333 search!!!! |
[quote=robert44444uk;126329]Here is a table of lowest k for each twin to n=1000
Does anyone want to take further? * denotes jumping champion [code] 1 3* 2 1 3 9* 4 15* 5 81* 6 3 7 9 8 57 9 45 10 15 11 99* 12 165* 13 369* 14 45 15 345 16 117 17 381* 18 3 19 69 20 447* 21 81 22 33 23 1179* 24 243 25 765 26 375 27 81 28 387 29 45 30 345 31 681 32 585 33 375 34 267 35 741 36 213 37 429 38 3093* 39 165 40 267 41 255 42 1095 43 9 44 147 45 849 46 405 47 1491 48 177 49 1941 50 927 51 1125 52 1197 53 2001 54 333 55 519 56 1065 57 585 58 657 59 129 60 147 61 141 62 417 63 9 64 1623 65 99 66 2985 67 2469 68 4497* 69 5259* 70 597 71 7029* 72 315 73 3081 74 2457 75 4161 76 603 77 3591 78 2697 79 3681 80 213 81 2079 82 1545 83 4089 84 165 85 1455 86 10287* 87 1629 88 387 89 3321 90 14487* 91 849 92 1467 93 3339 94 3747 95 6639 96 7737 97 8265 98 15735* 99 5589 100 4107 101 9225 102 537 103 2079 104 1203 105 1515 106 1323 107 7245 108 6897 109 20631* 110 2205 111 2175 112 3087 113 11145 114 7887 115 14841 116 2673 117 5961 118 3303 119 5565 120 3957 121 9849 122 1497 123 1125 124 1983 125 699 126 2565 127 8721 128 4467 129 5835 130 6063 131 1089 132 3117 133 1455 134 3105 135 6129 136 22365* 137 3555 138 24453* 139 8121 140 4143 141 1179 142 6903 143 309 144 11505 145 14121 146 17037 147 1419 148 17157 149 5715 150 345 151 13179 152 4497 153 3741 154 10803 155 105 156 30657* 157 14439 158 14445 159 7569 160 17295 161 25425 162 6555 163 2121 164 3717 165 13731 166 7737 167 18711 168 765 169 1881 170 19335 171 32361* 172 2847 173 2115 174 4155 175 1941 176 1383 177 24771 178 2277 179 10479 180 4287 181 441 182 19617 183 27261 184 2493 185 5481 186 28227 187 20175 188 1935 189 45 190 525 191 13719 192 8337 193 12495 194 18087 195 27099 196 9753 197 56745* 198 4245 199 8265 200 63855* 201 27261 202 69855* 203 14199 204 1755 205 5529 206 1197 207 54639 208 69753 209 10461 210 10575 211 9 212 3615 213 26145 214 9225 215 5859 216 12255 217 6615 218 16653 219 18531 220 24087 221 6555 222 7947 223 12909 224 49203 225 49341 226 10857 227 3405 228 25665 229 19041 230 21255 231 2571 232 30015 233 47079 234 24915 235 77751* 236 33333 237 16641 238 135 239 17289 240 10197 241 4059 242 1023 243 50319 244 22113 245 9915 246 17535 247 19041 248 15795 249 168831* 250 23007 251 5139 252 17787 253 15519 254 12957 255 1215 256 64647 257 9951 258 74253 259 2805 260 2475 261 15711 262 25767 263 9789 264 165 265 13209 266 19593 267 33105 268 45213 269 969 270 98907 271 19335 272 22317 273 10635 274 13713 275 34245 276 41085 277 24129 278 26025 279 24579 280 128505 281 3381 282 165 283 20175 284 23853 285 25881 286 61647 287 39315 288 2667 289 67695 290 34647 291 1899 292 33735 293 48861 294 2373 295 58179 296 66507 297 9609 298 20085 299 6405 300 230085* 301 44529 302 16575 303 22815 304 99297 305 21015 306 21075 307 91455 308 9993 309 15069 310 9543 311 79719 312 36195 313 14649 314 7605 315 67461 316 16035 317 12951 318 20295 319 41349 320 82473 321 20781 322 19293 323 88791 324 55605 325 23295 326 25473 327 10071 328 28653 329 48489 330 12477 331 7791 332 345675* 333 669 334 16437 335 42699 336 93765 337 12909 338 5253 339 23415 340 128625 341 21585 342 76995 343 153645 344 573 345 31719 346 15717 347 43011 348 33765 349 28149 350 71253 351 127305 352 14727 353 85431 354 10545 355 7785 356 38853 357 70851 358 65385 359 9129 360 162243 361 5049 362 49815 363 26871 364 210447 365 9369 366 74763 367 18669 368 16905 369 49299 370 12543 371 3321 372 138765 373 151839 374 40257 375 26679 376 14223 377 23709 378 22713 379 66039 380 1023 381 67749 382 34683 383 114951 384 126747 385 72609 386 114687 387 1701 388 56817 389 10791 390 39345 391 615 392 108195 393 95151 394 67023 395 21315 396 28065 397 24039 398 19065 399 102795 400 48207 401 28941 402 83337 403 101535 404 22887 405 74085 406 35253 407 79215 408 31635 409 36825 410 50835 411 273429 412 58065 413 86061 414 39513 415 17061 416 32025 417 30705 418 1743 419 71919 420 224415 421 66075 422 84057 423 81651 424 65337 425 237765 426 251475 427 83139 428 36903 429 39039 430 110157 431 66219 432 69477 433 50181 434 54033 435 5415 436 30987 437 102309 438 24693 439 56259 440 25077 441 15255 442 18795 443 3921 444 35793 445 9345 446 18663 447 30849 448 57717 449 69285 450 155463 451 26355 452 258345 453 17631 454 65193 455 2085 456 9063 457 15561 458 4323 459 104661 460 34725 461 92235 462 229227 463 53991 464 63903 465 24351 466 12147 467 33351 468 2565 469 108795 470 5547 471 139935 472 8787 473 184281 474 49053 475 13935 476 33375 477 33315 478 141315 479 53019 480 162897 481 233115 482 143163 483 150939 484 50295 485 27975 486 101055 487 156051 488 7503 489 73671 490 37095 491 37719 492 1995 493 97449 494 39207 495 27261 496 208845 497 99015 498 37755 499 131439 500 52305 501 207945 502 35397 503 66735 504 35877 505 74985 506 103107 507 5565 508 216243 509 107631 510 262035 511 43485 512 51765 513 134115 514 53355 515 87951 516 12045 517 66375 518 366555* 519 83211 520 4257 521 17709 522 80175 523 76089 524 47403 525 5775 526 62337 527 43371 528 43137 529 10365 530 74367 531 104409 532 347457 533 396441* 534 84627 535 278535 536 49893 537 23541 538 2007 539 12711 540 174297 541 8031 542 121065 543 40119 544 330015 545 18801 546 297 547 5979 548 97293 549 157209 550 26853 551 4035 552 29187 553 190485 554 70923 555 67329 556 130227 557 105381 558 80385 559 300561 560 39243 561 112581 562 176205 563 199989 564 117243 565 120069 566 75225 567 28131 568 239247 569 60411 570 25485 571 27909 572 20037 573 14259 574 70107 575 38835 576 247035 577 126615 578 136413 579 404871* 580 88257 581 76569 582 22587 583 28005 584 15177 585 210051 586 83175 587 173355 588 50235 589 133911 590 42777 591 389799 592 86385 593 45315 594 179163 595 257529 596 41625 597 268461 598 147135 599 74229 600 82023 601 135585 602 190695 603 33885 604 113475 605 264849 606 129705 607 368775 608 217143 609 228651 610 86973 611 8781 612 47313 613 94005 614 261075 615 34059 616 79353 617 29919 618 54015 619 18429 620 55203 621 46035 622 87795 623 12285 624 143265 625 104091 626 16323 627 140739 628 137907 629 223569 630 643737* 631 229749 632 506475 633 123891 634 242523 635 52419 636 78033 637 137835 638 227283 639 198459 640 558087 641 664941* 642 394203 643 91629 644 84045 645 274395 646 250923 647 24249 648 78453 649 109809 650 3723 651 205251 652 375843 653 624165 654 61353 655 38835 656 256605 657 21999 658 75447 659 101661 660 50943 661 77505 662 32067 663 374901 664 567573 665 258651 666 249345 667 127041 668 144717 669 58725 670 392013 671 130689 672 15993 673 178689 674 252693 675 376929 676 257613 677 3405 678 169893 679 469755 680 7605 681 217221 682 386127 683 151845 684 24537 685 243879 686 141705 687 246405 688 224625 689 13689 690 46545 691 38229 692 47937 693 152421 694 13197 695 2985 696 96813 697 102789 698 157587 699 436095 700 179865 701 317481 702 169827 703 5355 704 253995 705 330171 706 312387 707 37149 708 270177 709 158115 710 60693 711 25029 712 700005* 713 92529 714 35817 715 629211 716 118413 717 78561 718 86193 719 101361 720 89577 721 119721 722 150567 723 715449* 724 102213 725 20115 726 213 727 35589 728 30933 729 343359 730 308853 731 111285 732 142047 733 597339 734 50025 735 123585 736 5013 737 11175 738 95937 739 140481 740 51975 741 170625 742 58683 743 48075 744 9753 745 9165 746 131937 747 113271 748 42777 749 227871 750 22407 751 1025925 752 140967 753 110775 754 797433* 755 490281 756 490107 757 125169 758 84057 759 133521 760 404775 761 913671* 762 48615 763 242445 764 141243 765 73059 766 988437* 767 315 768 65475 769 484455 770 354417 771 56199 772 743433 773 62391 774 173667 775 125385 776 26775 777 188979 778 410187 779 239271 780 51777 781 88299 782 406707 783 108351 784 364203 785 193515 786 58257 787 17481 788 20997 789 19485 790 116103 791 217809 792 488805 793 98649 794 18495 795 119259 796 212157 797 526701 798 679623 799 95565 800 207663 801 291951 802 353127 803 267795 804 442227 805 72861 806 613383 807 136119 808 142785 809 47055 810 539157 811 70539 812 191085 813 10125 814 105537 815 234315 816 385887 817 64401 818 789453 819 377451 820 125385 821 49041 822 640677 823 268101 824 66975 825 134481 826 515955 827 12285 828 78375 829 1365 830 554925 831 24609 832 524217 833 49539 834 130323 835 155085 836 1175493* 837 62361 838 127905 839 238395 840 916815 841 86679 842 129237 843 122685 844 87303 845 451209 846 61785 847 5265 848 255693 849 163965 850 278427 851 382875 852 53763 853 18885 854 169407 855 157251 856 87495 857 88095 858 63135 859 555039 860 629997 861 37359 862 798315 863 93765 864 722967 865 31575 866 1744257* 867 60681 868 483735 869 399591 870 167967 871 1767711* 872 111027 873 55209 874 75783 875 50565 876 272085 877 31005 878 296043 879 622671 880 4107 881 134511 882 17145 883 430389 884 25833 885 1097925 886 87465 887 895101 888 45675 889 59421 890 910923 891 149091 892 115845 893 248349 894 173283 895 133875 896 11925 897 498981 898 59925 899 68901 900 105177 901 109305 902 1039227 903 23901 904 141615 905 344949 906 24747 907 248781 908 88407 909 179091 910 107457 911 551979 912 313485 913 127689 914 5673 915 136881 916 106413 917 233349 918 163377 919 280929 920 367023 921 94629 922 10533 923 382035 924 773367 925 50595 926 143403 927 80139 928 79623 929 83271 930 424167 931 2035431* 932 116385 933 94335 934 41727 935 390099 936 52953 937 164829 938 165537 939 369381 940 5955 941 202335 942 112053 943 317955 944 164787 945 60729 946 170085 947 27825 948 61425 949 23805 950 13503 951 385695 952 178173 953 21741 954 45243 955 351765 956 232947 957 77805 958 66417 959 399105 960 770193 961 98061 962 312297 963 1170699 964 177255 965 7995 966 82995 967 703701 968 514437 969 77565 970 113745 971 1390269 972 493173 973 16011 974 192255 975 947859 976 68313 977 230439 978 582717 979 262575 980 441357 981 402141 982 626943 983 10485 984 163497 985 411081 986 706773 987 1305255 988 97323 989 349521 990 417375 991 234291 992 56685 993 179445 994 24963 995 219069 996 237675 997 400941 998 330075 999 586899 1000 467343 [/code][/quote] The value of n=1 should be k=2 instead of k=3, i.e.: 2*2^1-1=3 and 2*2^1+1=5. Trivial result...the only twin prime for an even k, as shown on my web page. Gary |
Gary/ Karsten
Decided to take a break from Very Prime Series and give a hand here. I have two machines (albeit with no CPU power) working on first instance (k) primes up to n=3000. Results of first instance primes to 1400 show a rather nice curve when plotting ln(k/n) against n. Best fit looks to be logarithmic as well. Would be interested to know if this might be a good way to target large twins. For example, [U]if[/U] the extrapolation of the best fit to n=333333, gave A= ln(k/n)= 9, then the first twin would be, on average, at k=2.70103*10^9 then the test might look at n from 333333 to n 333433, say at A=8.999 to 9.001 or k=2.69833*10^9 to 2.70373*10^9. A 50 million k range, sieved to 1T would provide about 4,000 candidates for prime checking or 400,000 overall for a 100 k range. Mind you I am not sure A= 9 is right for n=333333. But maybe someone could extrapolate and work out the odds of finding a twin in the suggested k/n matrix. Also the plot of ln(ln(k/n)) looks as if it heading to a value of 2 with over 87% of values between 1.5 and 2 for n from 1 to 1383, and 92% from n=1 to 1383. |
Oooer,
Think I am a long way out on my forecast for n=333333, but maybe mathematicians can come to the rescue!! |
Here are the results for 1000 to 2000, with asterisked jumping champions:
[CODE] 1001 282285 1002 1028307 1003 140691 1004 519915 1005 370605 1006 176877 1007 37275 1008 48225 1009 551679 1010 258483 1011 895221 1012 334137 1013 74091 1014 35523 1015 424125 1016 314217 1017 320931 1018 19887 1019 122595 1020 313023 1021 341871 1022 292215 1023 622485 1024 254697 1025 258621 1026 155925 1027 711885 1028 98493 1029 938931 1030 416883 1031 461889 1032 177 1033 364365 1034 16233 1035 130869 1036 328497 1037 71421 1038 145035 1039 249429 1040 356433 1041 200655 1042 255807 1043 373965 1044 1391775 1045 94065 1046 124743 1047 109809 1048 3885 1049 217365 1050 312147 1051 437955 1052 85845 1053 212265 1054 461175 1055 91755 1056 88515 1057 33405 1058 620595 1059 60099 1060 265593 1061 1063875 1062 126963 1063 122325 1064 243183 1065 290955 1066 90165 1067 85911 1068 193443 1069 132525 1070 70623 1071 2092731* 1072 142443 1073 291231 1074 371997 1075 13131 1076 50025 1077 181521 1078 419145 1079 143781 1080 193347 1081 427611 1082 533187 1083 818961 1084 15315 1085 156615 1086 69417 1087 161289 1088 117225 1089 121719 1090 393687 1091 773475 1092 147417 1093 651939 1094 188793 1095 803589 1096 701433 1097 116805 1098 58287 1099 342189 1100 355065 1101 384981 1102 27435 1103 170115 1104 4275 1105 738375 1106 300135 1107 48681 1108 413103 1109 3525165* 1110 11007 1111 2439999 1112 111765 1113 196455 1114 843003 1115 1041429 1116 175803 1117 819225 1118 528783 1119 155445 1120 121365 1121 465891 1122 60513 1123 831105 1124 1504797 1125 148935 1126 1098363 1127 152835 1128 224973 1129 508131 1130 580923 1131 518091 1132 850785 1133 142125 1134 83205 1135 618735 1136 317793 1137 221979 1138 798135 1139 168195 1140 282873 1141 269745 1142 11007 1143 1057989 1144 162177 1145 1037355 1146 184923 1147 251175 1148 1398117 1149 487785 1150 232755 1151 1617651 1152 336315 1153 827451 1154 729543 1155 256491 1156 1035 1157 312651 1158 1120767 1159 1108365 1160 167013 1161 723411 1162 341427 1163 811269 1164 228093 1165 798891 1166 258117 1167 54339 1168 62823 1169 353679 1170 1053327 1171 300585 1172 1524225 1173 52461 1174 1078677 1175 46791 1176 147063 1177 964179 1178 337287 1179 613029 1180 830835 1181 261855 1182 656877 1183 924855 1184 396843 1185 1647891 1186 320223 1187 1173099 1188 65613 1189 955089 1190 154605 1191 1066371 1192 625365 1193 84435 1194 176085 1195 175785 1196 324915 1197 45201 1198 185157 1199 268191 1200 724545 1201 544929 1202 1055583 1203 2016501 1204 121275 1205 356415 1206 273957 1207 869541 1208 990165 1209 537369 1210 463983 1211 994269 1212 666495 1213 1280439 1214 2475495 1215 364455 1216 130803 1217 14199 1218 1267887 1219 188589 1220 825105 1221 88329 1222 1023483 1223 542151 1224 775365 1225 652335 1226 1653435 1227 662799 1228 79203 1229 42399 1230 3452103 1231 753849 1232 988593 1233 389895 1234 513813 1235 1115085 1236 1392603 1237 74109 1238 252753 1239 3267021 1240 334293 1241 13629 1242 298797 1243 529719 1244 64233 1245 88575 1246 621147 1247 3058299 1248 129315 1249 243819 1250 597465 1251 75705 1252 206655 1253 515679 1254 2396175 1255 763701 1256 53865 1257 187521 1258 635025 1259 484341 1260 147387 1261 32265 1262 2045985 1263 979605 1264 467595 1265 533805 1266 774807 1267 95229 1268 817797 1269 802431 1270 71805 1271 682881 1272 50655 1273 235845 1274 95847 1275 456549 1276 475515 1277 613971 1278 388005 1279 152091 1280 1318815 1281 2160741 1282 99105 1283 3124995 1284 426657 1285 322041 1286 9183 1287 5629461* 1288 1793223 1289 808101 1290 230085 1291 114105 1292 1462605 1293 186921 1294 341367 1295 49119 1296 1186755 1297 764001 1298 248163 1299 3339 1300 264915 1301 275619 1302 734325 1303 633381 1304 205503 1305 190881 1306 499917 1307 163731 1308 1501665 1309 270075 1310 384993 1311 1033569 1312 15657 1313 571581 1314 46965 1315 471795 1316 580623 1317 1627791 1318 438075 1319 304065 1320 1733043 1321 1065 1322 230223 1323 1033569 1324 969387 1325 62265 1326 996987 1327 2625 1328 1553745 1329 1281075 1330 754215 1331 3307209 1332 209853 1333 132225 1334 1143255 1335 480165 1336 1199463 1337 560391 1338 92115 1339 142185 1340 1857213 1341 422385 1342 1224117 1343 117975 1344 1280295 1345 351015 1346 853875 1347 582729 1348 1252053 1349 919881 1350 245325 1351 878415 1352 1236897 1353 263571 1354 38565 1355 62289 1356 998823 1357 158355 1358 1416285 1359 313551 1360 456645 1361 268485 1362 158043 1363 998205 1364 471537 1365 365691 1366 769293 1367 7755 1368 682743 1369 249285 1370 290133 1371 518529 1372 395787 1373 188475 1374 1108203 1375 125601 1376 147777 1377 1157415 1378 2088045 1379 570699 1380 1462017 1381 856821 1382 941577 1383 67821 1384 751497 1385 106449 1386 708885 1387 175905 1388 107205 1389 97899 1390 14877 1391 76479 1392 1984383 1393 370749 1394 88155 1395 870741 1396 1342773 1397 542805 1398 658935 1399 1186401 1400 797373 1401 878385 1402 80103 1403 1414851 1404 761427 1405 891891 1406 18003 1407 2122659 1408 98475 1409 174009 1410 939915 1411 173229 1412 2561475 1413 1041609 1414 893937 1415 207519 1416 726975 1417 2445081 1418 285153 1419 689589 1420 1655163 1421 203949 1422 797955 1423 1522551 1424 136065 1425 86205 1426 232365 1427 1946031 1428 2266035 1429 170379 1430 438645 1431 75519 1432 379317 1433 297591 1434 1132857 1435 2376429 1436 961797 1437 1592955 1438 686343 1439 1993755 1440 10083 1441 74031 1442 702927 1443 613095 1444 316275 1445 1140285 1446 93837 1447 51651 1448 518787 1449 575949 1450 650757 1451 769209 1452 1122567 1453 632541 1454 442635 1455 849261 1456 3351873 1457 515535 1458 611433 1459 113931 1460 1605915 1461 141099 1462 15927 1463 1233519 1464 455445 1465 114681 1466 74505 1467 1252569 1468 85077 1469 571071 1470 273765 1471 81489 1472 131025 1473 330201 1474 1524045 1475 66381 1476 751005 1477 129645 1478 1114995 1479 385971 1480 677613 1481 3420999 1482 1436103 1483 57891 1484 167745 1485 377349 1486 704373 1487 1912131 1488 524727 1489 1231161 1490 3160707 1491 338649 1492 1267167 1493 1246179 1494 471945 1495 187509 1496 521073 1497 1408449 1498 2480883 1499 306939 1500 32547 1501 1778709 1502 652323 1503 2676891 1504 1424085 1505 1327329 1506 910305 1507 323895 1508 132093 1509 86361 1510 2608005 1511 1934409 1512 858315 1513 577179 1514 1200675 1515 3154659 1516 303345 1517 2700279 1518 1270677 1519 937071 1520 3027615 1521 381699 1522 5690025* 1523 133725 1524 187155 1525 1759851 1526 302415 1527 362619 1528 465015 1529 1916355 1530 137427 1531 519765 1532 83973 1533 36045 1534 2798223 1535 263505 1536 1682853 1537 587505 1538 1581567 1539 568809 1540 369837 1541 1562889 1542 318075 1543 442191 1544 606537 1545 135831 1546 657417 1547 286581 1548 583275 1549 3521211 1550 427143 1551 447711 1552 297627 1553 291 1554 1979757 1555 1585425 1556 81255 1557 349395 1558 924657 1559 2046261 1560 108885 1561 1726149 1562 201645 1563 2062539 1564 1439853 1565 882459 1566 42507 1567 601515 1568 1326975 1569 1108371 1570 935943 1571 822555 1572 715995 1573 324129 1574 424617 1575 620055 1576 246045 1577 586755 1578 118893 1579 238509 1580 4894863 1581 763935 1582 285423 1583 682179 1584 849357 1585 339621 1586 566475 1587 1013535 1588 142197 1589 1483749 1590 118773 1591 1408785 1592 1439703 1593 239745 1594 360513 1595 303939 1596 1277775 1597 1704015 1598 937233 1599 15375 1600 2037615 1601 128619 1602 2329245 1603 89895 1604 4199007 1605 1274121 1606 923853 1607 3542361 1608 992037 1609 390621 1610 222783 1611 2597511 1612 3516297 1613 417711 1614 219693 1615 876975 1616 78327 1617 799335 1618 605283 1619 133155 1620 2564265 1621 942615 1622 1283757 1623 33549 1624 832413 1625 65835 1626 501447 1627 1149735 1628 1153323 1629 2937105 1630 166173 1631 2852121 1632 1530903 1633 202551 1634 216573 1635 1623171 1636 264327 1637 4553769 1638 213897 1639 517215 1640 34215 1641 164271 1642 620433 1643 3030975 1644 1387347 1645 2923179 1646 1206135 1647 183855 1648 160587 1649 269541 1650 1873503 1651 884751 1652 33957 1653 323031 1654 682113 1655 876849 1656 1595433 1657 566445 1658 3824937 1659 1813611 1660 20733 1661 589281 1662 260757 1663 1216815 1664 1183377 1665 885909 1666 3120063 1667 2131941 1668 1262193 1669 1022901 1670 960075 1671 552771 1672 56685 1673 1112175 1674 1859853 1675 917541 1676 96897 1677 24969 1678 34725 1679 520719 1680 832947 1681 602331 1682 292407 1683 1367541 1684 3336843 1685 239715 1686 2610675 1687 228111 1688 153513 1689 27765 1690 674133 1691 598875 1692 1520523 1693 747711 1694 401055 1695 570831 1696 592563 1697 1189089 1698 1627455 1699 285861 1700 241455 1701 2189229 1702 5434023 1703 1377975 1704 151827 1705 312405 1706 1362567 1707 1403001 1708 270633 1709 497991 1710 3470667 1711 1458675 1712 635163 1713 213201 1714 1036635 1715 4239039 1716 5862777* 1717 1717869 1718 51747 1719 386061 1720 3976863 1721 45951 1722 1887375 1723 650859 1724 379323 1725 787395 1726 435345 1727 1444089 1728 1652577 1729 174915 1730 3604917 1731 970335 1732 1796067 1733 840315 1734 2362815 1735 1639251 1736 679977 1737 620571 1738 2231685 1739 595581 1740 377787 1741 872055 1742 1824297 1743 967425 1744 1424145 1745 260289 1746 2503953 1747 2776215 1748 645327 1749 2970279 1750 274323 1751 373185 1752 1260717 1753 3720729 1754 1073577 1755 2880981 1756 2120643 1757 41229 1758 1585017 1759 300351 1760 3314793 1761 289095 1762 402687 1763 29481 1764 984987 1765 426105 1766 447465 1767 84159 1768 1820583 1769 285009 1770 1596045 1771 691419 1772 333663 1773 2318871 1774 3654177 1775 1090125 1776 595053 1777 358875 1778 602337 1779 842529 1780 2161035 1781 2065071 1782 219495 1783 851709 1784 2669145 1785 243399 1786 42825 1787 1118181 1788 2421057 1789 428631 1790 383313 1791 113025 1792 1904805 1793 95151 1794 98583 1795 453741 1796 2079255 1797 2800941 1798 1172337 1799 2568609 1800 732567 1801 4073949 1802 3368655 1803 2079045 1804 1003533 1805 674505 1806 1206513 1807 474249 1808 211527 1809 2702121 1810 381687 1811 1009869 1812 994107 1813 948789 1814 153537 1815 2490609 1816 119217 1817 1262079 1818 2999217 1819 5680095 1820 79335 1821 208101 1822 2517873 1823 57495 1824 1047153 1825 2028459 1826 943863 1827 943941 1828 5392107 1829 3421551 1830 2098275 1831 1688079 1832 1186437 1833 4735311 1834 529983 1835 535395 1836 1230183 1837 1388661 1838 434085 1839 584829 1840 2480025 1841 525759 1842 560313 1843 734361 1844 2615235 1845 4198689 1846 1177785 1847 1019379 1848 674847 1849 87585 1850 4155033 1851 317649 1852 626703 1853 4020069 1854 699963 1855 203211 1856 2185443 1857 3799731 1858 29835 1859 1685445 1860 13317 1861 331731 1862 843273 1863 4007301 1864 166353 1865 508911 1866 2739747 1867 475719 1868 1142103 1869 82275 1870 311067 1871 1838235 1872 845973 1873 569451 1874 226293 1875 1002141 1876 3964035 1877 2332491 1878 1327095 1879 1345965 1880 22035 1881 354189 1882 1104123 1883 919335 1884 563217 1885 191505 1886 531717 1887 2096265 1888 800457 1889 3173061 1890 3049323 1891 922749 1892 2294307 1893 849849 1894 249417 1895 417045 1896 4020993 1897 413271 1898 675255 1899 1567515 1900 4425 1901 441531 1902 1436775 1903 435609 1904 3037815 1905 520215 1906 328557 1907 589455 1908 1018797 1909 459291 1910 1456293 1911 4789059 1912 4947147 1913 426615 1914 2018727 1915 2202885 1916 558183 1917 1542735 1918 1434207 1919 164835 1920 588453 1921 1274835 1922 362613 1923 228525 1924 935265 1925 1019949 1926 891273 1927 826575 1928 1216137 1929 1132989 1930 426165 1931 1126005 1932 298965 1933 39171 1934 605973 1935 2497911 1936 101505 1937 485181 1938 2986623 1939 245481 1940 1342107 1941 2349669 1942 2730237 1943 819189 1944 335097 1945 704409 1946 4290147 1947 5837991 1948 1731387 1949 1217601 1950 1105407 1951 928965 1952 491337 1953 197139 1954 8007 1955 396669 1956 616893 1957 700569 1958 1550433 1959 1748631 1960 1373625 1961 2612919 1962 303147 1963 822435 1964 1738983 1965 3094341 1966 63237 1967 1843419 1968 1330095 1969 637341 1970 570597 1971 3885 1972 295503 1973 2244459 1974 3217737 1975 1017381 1976 2980953 1977 4103841 1978 1088085 1979 3564789 1980 3550827 1981 800109 1982 2046087 1983 182319 1984 429777 1985 31545 1986 880317 1987 3175779 1988 207213 1989 103239 1990 2965107 1991 2852079 1992 1963113 1993 1301685 1994 1780785 1995 1314885 1996 284655 1997 2378895 1998 377085 1999 3400089 2000 4605615 [/CODE] |
hey, great work robert!
i will include them here [url]www.rieselprime.org/FirstKTwin.htm[/url] when i got time! thanks! |
Here are first instance twins from n=2000 to n=3000. Now a good way towards n=4000
[code] n first k 2001 133641 2002 649683 2003 2930049 2004 1427463 2005 411801 2006 595665 2007 1154619 2008 1100385 2009 934875 2010 667275 2011 954759 2012 606633 2013 2595345 2014 166845 2015 1190745 2016 1527327 2017 4675869 2018 720387 2019 2345859 2020 3118845 2021 2558685 2022 622365 2023 1517451 2024 10095 2025 3632955 2026 773193 2027 2129109 2028 2235525 2029 1885245 2030 111483 2031 1974135 2032 5717397 2033 1332465 2034 852807 2035 1580595 2036 1151973 2037 451959 2038 1018803 2039 181635 2040 615927 2041 3436125 2042 390345 2043 1551489 2044 395835 2045 2897031 2046 689187 2047 3666651 2048 442533 2049 2094795 2050 2451435 2051 243309 2052 260715 2053 1735629 2054 3096345 2055 1001985 2056 1874007 2057 784581 2058 4510305 2059 2444265 2060 329613 2061 357159 2062 7147317* 2063 1119579 2064 2763243 2065 825315 2066 4315755 2067 1284945 2068 1066533 2069 2132229 2070 1902303 2071 176829 2072 2144103 2073 606879 2074 687363 2075 1871289 2076 457005 2077 2539431 2078 1590315 2079 1473615 2080 1370817 2081 2558949 2082 2970705 2083 84609 2084 1662657 2085 2956539 2086 542673 2087 2364531 2088 2206503 2089 1019235 2090 3338835 2091 3359289 2092 1375155 2093 281415 2094 3084393 2095 2336349 2096 189837 2097 123165 2098 1733655 2099 3562065 2100 191823 2101 161511 2102 757173 2103 2760621 2104 1676493 2105 1231005 2106 423327 2107 1070481 2108 8173875* 2109 981171 2110 251235 2111 3498669 2112 59553 2113 661341 2114 3489753 2115 1983459 2116 269877 2117 1766541 2118 374757 2119 2165961 2120 969993 2121 368379 2122 966537 2123 3632469 2124 2199687 2125 927249 2126 1339323 2127 1189311 2128 373077 2129 11655 2130 1796025 2131 1320969 2132 387015 2133 3241005 2134 4231827 2135 403971 2136 794463 2137 358101 2138 40215 2139 808635 2140 1206507 2141 3789009 2142 2047887 2143 723555 2144 215307 2145 557925 2146 2486253 2147 623661 2148 647787 2149 878571 2150 959757 2151 4665759 2152 250977 2153 2285889 2154 4471203 2155 401025 2156 769737 2157 380499 2158 4913103 2159 477075 2160 5649675 2161 1045821 2162 33117 2163 2489541 2164 1547013 2165 1314579 2166 1123593 2167 6311811 2168 2865393 2169 408471 2170 1281513 2171 2061111 2172 467577 2173 2655471 2174 1231593 2175 3716169 2176 1172205 2177 3578565 2178 287103 2179 8715615* 2180 480777 2181 706431 2182 53955 2183 7423941 2184 1803315 2185 66729 2186 810897 2187 1295271 2188 2439885 2189 602595 2190 4485507 2191 4359 2192 1844283 2193 425031 2194 4654305 2195 179745 2196 24405 2197 4499175 2198 895257 2199 6930819 2200 4012377 2201 2984799 2202 903375 2203 1317555 2204 640707 2205 806271 2206 2327703 2207 603495 2208 2644593 2209 1214331 2210 1505997 2211 436515 2212 1612533 2213 6201 2214 1405647 2215 3203205 2216 3028725 2217 879501 2218 863343 2219 416721 2220 13939725* 2221 1566255 2222 3628233 2223 1892385 2224 3047007 2225 976011 2226 923205 2227 6554205 2228 2935587 2229 2972529 2230 2126025 2231 5493585 2232 3593625 2233 2826081 2234 509823 2235 3665961 2236 113685 2237 644385 2238 143427 2239 1264095 2240 2389677 2241 1436769 2242 2657433 2243 823179 2244 3927957 2245 963429 2246 141165 2247 908919 2248 1814997 2249 1636011 2250 1208235 2251 1513965 2252 3355227 2253 75219 2254 7286685 2255 7419 2256 488733 2257 109599 2258 402567 2259 2707365 2260 5754897 2261 538905 2262 2540235 2263 1268265 2264 334863 2265 1755045 2266 619695 2267 812025 2268 1441893 2269 4040391 2270 684123 2271 719925 2272 1486575 2273 378291 2274 1294263 2275 211365 2276 5279163 2277 255999 2278 43947 2279 2458665 2280 25293 2281 3015531 2282 1120767 2283 1025139 2284 11455353 2285 3492885 2286 3932037 2287 3226839 2288 3184605 2289 928329 2290 3743943 2291 1571535 2292 6518367 2293 117705 2294 4774575 2295 2711271 2296 2494323 2297 1601151 2298 965373 2299 1155231 2300 4387947 2301 261609 2302 3444303 2303 545955 2304 3792927 2305 533079 2306 4193055 2307 1764471 2308 848127 2309 2331879 2310 1491345 2311 257319 2312 723477 2313 5870889 2314 470625 2315 2635581 2316 1501227 2317 298599 2318 149955 2319 1017279 2320 1449825 2321 625821 2322 3600657 2323 2401035 2324 825027 2325 2895951 2326 1821477 2327 1671075 2328 143925 2329 1786041 2330 900645 2331 3034155 2332 3049125 2333 43089 2334 2249907 2335 554811 2336 7262457 2337 2613825 2338 1122063 2339 1208025 2340 131373 2341 3225699 2342 1730217 2343 4251891 2344 1293297 2345 4404261 2346 2074233 2347 3894099 2348 1607295 2349 256359 2350 4011873 2351 3974571 2352 2129943 2353 756471 2354 1179975 2355 5739951 2356 3090843 2357 3325329 2358 660993 2359 2272311 2360 2209227 2361 140319 2362 808935 2363 900021 2364 486087 2365 606621 2366 3500433 2367 988899 2368 1419837 2369 410799 2370 231915 2371 1438809 2372 2782503 2373 2746149 2374 420267 2375 403521 2376 194367 2377 2408769 2378 5432883 2379 317145 2380 459807 2381 1413381 2382 1804275 2383 1068699 2384 1526997 2385 2721639 2386 1397865 2387 604989 2388 2572503 2389 699531 2390 1073703 2391 820761 2392 936465 2393 5188569 2394 554055 2395 6620265 2396 1045113 2397 451845 2398 540057 2399 3925809 2400 12123027 2401 753489 2402 2858337 2403 9618801 2404 2873163 2405 687099 2406 6860187 2407 859329 2408 162183 2409 942441 2410 913425 2411 2101551 2412 2205837 2413 591579 2414 684813 2415 650709 2416 708897 2417 4326885 2418 2249355 2419 6996435 2420 399027 2421 1501815 2422 5330073 2423 617295 2424 351237 2425 2331489 2426 1700745 2427 2249355 2428 1426815 2429 379401 2430 3521445 2431 2713935 2432 10912485 2433 3965685 2434 11808915 2435 740181 2436 4112013 2437 1503909 2438 11136945 2439 1511241 2440 1282917 2441 379005 2442 3267045 2443 1231011 2444 1565493 2445 2883729 2446 6014253 2447 1715181 2448 5903835 2449 6606249 2450 1273023 2451 10357665 2452 175245 2453 6871845 2454 3140505 2455 11621685 2456 484047 2457 708795 2458 778317 2459 1261359 2460 331545 2461 2476005 2462 2178705 2463 1972995 2464 4438875 2465 2459565 2466 7927227 2467 1052541 2468 2009427 2469 605901 2470 60957 2471 1469061 2472 1557105 2473 52935 2474 271947 2475 3044661 2476 572223 2477 4678059 2478 2677083 2479 845949 2480 2485287 2481 639159 2482 1859067 2483 4125519 2484 1958313 2485 775749 2486 568767 2487 150111 2488 1874823 2489 804801 2490 4571175 2491 1925415 2492 1934517 2493 1275999 2494 1869555 2495 398385 2496 7484367 2497 766611 2498 56727 2499 1694595 2500 575745 2501 86085 2502 416007 2503 3248349 2504 1706667 2505 562809 2506 244407 2507 1906821 2508 2473527 2509 3935829 2510 1539285 2511 2696031 2512 705795 2513 1694475 2514 3419607 2515 812355 2516 343395 2517 6644109 2518 94815 2519 1857729 2520 4990947 2521 1296699 2522 245895 2523 878481 2524 4332453 2525 2165169 2526 1427127 2527 3986631 2528 6039603 2529 33939 2530 1311975 2531 9119961 2532 2946213 2533 1834041 2534 1990185 2535 207939 2536 2664915 2537 3206295 2538 731673 2539 2443209 2540 2645943 2541 454989 2542 1231077 2543 3092235 2544 5280615 2545 1466271 2546 3537933 2547 4499871 2548 258417 2549 1182471 2550 4024653 2551 1694625 2552 4992807 2553 1204719 2554 106455 2555 4458441 2556 2796033 2557 1669449 2558 2196375 2559 4229589 2560 100995 2561 2443431 2562 260295 2563 903861 2564 3509157 2565 621045 2566 1949103 2567 114201 2568 1097505 2569 79029 2570 780807 2571 886329 2572 712215 2573 4769349 2574 475863 2575 704649 2576 416937 2577 2264481 2578 1247493 2579 1081539 2580 590517 2581 2458455 2582 181287 2583 5741505 2584 3556737 2585 2617089 2586 348873 2587 4053015 2588 1299693 2589 8371671 2590 1045233 2591 372849 2592 2753643 2593 1696365 2594 1162773 2595 671781 2596 6094713 2597 183039 2598 3030753 2599 236049 2600 5675475 2601 2153811 2602 190815 2603 3151935 2604 1817643 2605 1666821 2606 12924117 2607 4004469 2608 2879193 2609 139989 2610 426045 2611 662241 2612 934683 2613 1333929 2614 5152947 2615 2439525 2616 4649697 2617 3453555 2618 5695893 2619 2897379 2620 193845 2621 4290441 2622 1154877 2623 5846175 2624 2032425 2625 1030431 2626 736773 2627 377685 2628 577365 2629 1129701 2630 1323357 2631 3091221 2632 589335 2633 410001 2634 166605 2635 1122171 2636 595365 2637 89115 2638 5478003 2639 3811335 2640 985215 2641 2310279 2642 2835045 2643 4563471 2644 573627 2645 4521171 2646 1888575 2647 1511181 2648 2547693 2649 4619499 2650 3437817 2651 1015815 2652 1216857 2653 1221885 2654 7059063 2655 2516745 2656 2727627 2657 5563359 2658 3372297 2659 1835409 2660 240495 2661 3673761 2662 1500213 2663 1548429 2664 3605595 2665 1573299 2666 968583 2667 7326225 2668 1080345 2669 1259829 2670 2277663 2671 2420439 2672 3083613 2673 11958531 2674 4792023 2675 1161735 2676 4933443 2677 643641 2678 10203777 2679 61269 2680 1436325 2681 2024211 2682 8889465 2683 4113411 2684 4908435 2685 93429 2686 3934047 2687 3287829 2688 7006263 2689 1060011 2690 1041795 2691 398589 2692 7944825 2693 964149 2694 1350795 2695 59415 2696 902343 2697 1074075 2698 6025185 2699 1113525 2700 1925445 2701 1549605 2702 6286287 2703 5440785 2704 2354745 2705 1053399 2706 977427 2707 32811 2708 5547693 2709 5487639 2710 481605 2711 437835 2712 1341195 2713 1060089 2714 1808097 2715 1783239 2716 1843857 2717 16812351* 2718 5734713 2719 2510079 2720 482103 2721 6000501 2722 1479627 2723 2945835 2724 2860125 2725 1531395 2726 792537 2727 3262599 2728 3397107 2729 3935889 2730 2321433 2731 7364859 2732 14301783 2733 3360051 2734 1315497 2735 2263065 2736 14572653 2737 6372735 2738 481545 2739 6473169 2740 340065 2741 2700729 2742 421845 2743 52011 2744 1766127 2745 1049505 2746 1573557 2747 1362159 2748 84255 2749 9000045 2750 2069775 2751 3219225 2752 2133207 2753 2330175 2754 1615203 2755 213255 2756 2106765 2757 11027769 2758 2996775 2759 238881 2760 1667967 2761 5267661 2762 3044367 2763 5110275 2764 7759845 2765 2507301 2766 1068525 2767 292209 2768 11093037 2769 566409 2770 661635 2771 3098649 2772 640455 2773 5088489 2774 2575803 2775 467661 2776 617433 2777 4566309 2778 2330307 2779 556779 2780 14337705 2781 3220305 2782 689613 2783 2996889 2784 5921757 2785 5956461 2786 9335997 2787 4640235 2788 3797235 2789 1327221 2790 4215237 2791 4254195 2792 2704953 2793 630081 2794 1293315 2795 17255511* 2796 727563 2797 139755 2798 5603163 2799 5940429 2800 1967433 2801 2207439 2802 458055 2803 1702281 2804 2313933 2805 288015 2806 3456585 2807 16158471 2808 466455 2809 2227269 2810 1106493 2811 5634765 2812 1217523 2813 3071601 2814 5801007 2815 2203269 2816 2200113 2817 3194055 2818 204357 2819 1695369 2820 2646273 2821 6075 2822 287217 2823 288615 2824 4327503 2825 923289 2826 2103813 2827 20805 2828 909843 2829 1550049 2830 2468193 2831 2106699 2832 1014393 2833 1653951 2834 61947 2835 2778309 2836 6207087 2837 3304581 2838 10169775 2839 884205 2840 1612197 2841 4633191 2842 3495975 2843 4715439 2844 58053 2845 627381 2846 10725 2847 511065 2848 1123515 2849 935529 2850 1309137 2851 323601 2852 815517 2853 3369525 2854 2537325 2855 4427595 2856 4030533 2857 1534119 2858 3585705 2859 1536981 2860 4051923 2861 368595 2862 614187 2863 1922361 2864 3812463 2865 3370299 2866 2223795 2867 36159 2868 705933 2869 1398321 2870 1571097 2871 6877731 2872 512253 2873 6672081 2874 3596667 2875 539421 2876 800757 2877 8503521 2878 1886403 2879 13157931 2880 7072905 2881 3142449 2882 684015 2883 627735 2884 1975953 2885 5101209 2886 2311773 2887 88629 2888 275325 2889 2333019 2890 6826905 2891 3037191 2892 6122265 2893 4464465 2894 980265 2895 2823849 2896 1508925 2897 4519521 2898 1095363 2899 69735 2900 1371135 2901 5099181 2902 157893 2903 696405 2904 9783483 2905 328545 2906 11411613 2907 1678275 2908 2838123 2909 1841685 2910 4322745 2911 3445101 2912 791253 2913 2804205 2914 14275353 2915 6891045 2916 1539597 2917 11005071 2918 12413187 2919 6586779 2920 1629573 2921 1202271 2922 4129863 2923 5256165 2924 1206873 2925 836325 2926 2107245 2927 1020141 2928 1763907 2929 6573231 2930 4244325 2931 757491 2932 2291283 2933 7475019 2934 3297507 2935 8714775 2936 3430953 2937 2713569 2938 1426413 2939 6322515 2940 1538163 2941 2765475 2942 6645657 2943 7253025 2944 2681937 2945 12195 2946 1294725 2947 809979 2948 3103845 2949 4511325 2950 7214457 2951 4022535 2952 5410377 2953 1721469 2954 3229527 2955 3246201 2956 265977 2957 3353631 2958 2484813 2959 4155909 2960 7358085 2961 1303029 2962 4964043 2963 1839639 2964 3869667 2965 1957191 2966 429717 2967 3586251 2968 1604385 2969 3225009 2970 1524735 2971 8492799 2972 1057923 2973 482991 2974 6391455 2975 584529 2976 2337513 2977 1918329 2978 385815 2979 1990299 2980 2580915 2981 561669 2982 149013 2983 1473291 2984 547623 2985 962211 2986 5351445 2987 4388559 2988 4109163 2989 2880939 2990 6570627 2991 4028841 2992 4792815 2993 224025 2994 5546193 2995 1838061 2996 3545457 2997 1325205 2998 4013547 2999 2016735 3000 1298973 [/CODE] |
all data are now available here: [url]www.rieselprime.org/FirstKTwin.htm[/url].
|
Hi, I think I'll pitch in a bit here as well.
Reserving n=8825 to n=10000, don't know how long it will take though... Is there any more efficient method than just using NewPGen for sieving with the auto-increase n and pfgw for testing? roger |
Hi Roger, happy for you to work at the far end of the first 10000 spectrum. I am doing this rather manually, I write a .bat file for cnewpgen that contains a 100 lines like:
cnewpgen -wp=02.txt -v -t=2 -base=2 -n=3108 -kmin=2 -kmax=5000000 -own -osp=5000000000 for a range of 100n This is newpgen for command line, and would create a file called 02.txt with k checked from 2 to 5 million, stopping at p=5 million for n=3108 and finish the .bat file with copy *.txt merged.log del *.txt //(you should be doing this in a subdirectory with no .txt files!!!) Then I run the .bat file through the DOS window and then run merged.log through LLR version 3.7 I extract the first twin found and then create another .bat file for those with no twins and check the next 5 million k cnewpgen -wp=02.txt -v -t=2 -base=2 -n=3108 -kmin=5000000 -kmax=10000000 -own -osp=5000000000 It would be nice to have a programme that linked the two activities cnewpgen and LLR, and for LLR to stop when it finds a twin. That would allow much larger cnewpgen files to be created and the whole thing to run uninterrupted |
[QUOTE=robert44444uk;129274]Hi Roger, happy for you to work at the far end of the first 10000 spectrum. I am doing this rather manually, I write a .bat file for cnewpgen that contains a 100 lines like:
cnewpgen -wp=02.txt -v -t=2 -base=2 -n=3108 -kmin=2 -kmax=5000000 -own -osp=5000000000 for a range of 100n This is newpgen for command line, and would create a file called 02.txt with k checked from 2 to 5 million, stopping at p=5 million for n=3108 and finish the .bat file with copy *.txt merged.log del *.txt //(you should be doing this in a subdirectory with no .txt files!!!) Then I run the .bat file through the DOS window and then run merged.log through LLR version 3.7 I extract the first twin found and then create another .bat file for those with no twins and check the next 5 million k cnewpgen -wp=02.txt -v -t=2 -base=2 -n=3108 -kmin=5000000 -kmax=10000000 -own -osp=5000000000 It would be nice to have a programme that linked the two activities cnewpgen and LLR, and for LLR to stop when it finds a twin. That would allow much larger cnewpgen files to be created and the whole thing to run uninterrupted[/QUOTE] Hi, LLR (or cllr) has an option to stop on success : add the line: StopOnSuccess=1 in the .ini file, or use cllr -oStopOnSuccess=1 Newpgen, or cnewpgen has an option to call PFGW when the stop condition is reached ; I could add the option to call another program, such as cllr, as soon as possible... Regards, Jean |
efficient method
i made two WIN-batches to do a range of k's with first twins:
this first batch (named 'do_range.bat') takes a range of k to determine and calls the second batch with parameter k (here the range from k=100 to k=120 will be done): [code] FOR /L %%k IN (100,1,120) DO call do_one.bat %%k [/code] the second (named 'do_one.bat') batch takes one k (parameter %1) and determine the first twin, makes a file with all results in '<k>_lresults.txt' and the twin in '<k>.res' and lists the twin found in 'all_twins.txt': [code] cnewpgen -wp=%1.npg -v -t=2 -base=2 -n=%1 -kmin=2 -kmax=5000000 -own -osp=5000000000 cllr -oStopOnSuccess=1 %1.npg ren lresults.txt %1_lresults.txt FOR /F "skip=1 tokens=1,2" %%i in (%1.res) DO @echo %%j %%i >>all_twins.txt [/code] modifications: - call the second batch with parameter for kmax and/or pmax other values like 'call do_one.bat %%k 20000000 3000000000' and edit the second batch first line in '(...) -kmin=2 -kmax=%2 -own -osp=%3' - all found twins will be stored in 'all_twins.txt' so the other files are not needed anymore. append a delete in the second batch: [code] del %1.npg %1.res %1_lresults.txt [/code] next step is to check if a twin was found. if not do another n-range for this k. hope this helps! happy hunting :grin: karsten |
Sorry, I am incredibly thick, but where do you get cllr from, it is not on Jean's LLR download page
|
[quote=robert44444uk;129322]Sorry, I am incredibly thick, but where do you get cllr from, it is not on Jean's LLR download page[/quote]
It's listed as "LLR 3.7.1c, Windows command line version". :smile: It's essentially Linux LLR, but compiled for Windows (so it has all the command-line functions instead of the GUI, and thus is more suitable for being driven by a script.) |
Brilliant, thanks, was looking on the wrong page on Jean's site
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And here is the list from 3000 to 4000
I am well on the way from 4000 to 6000 with the automated code provided by Karsten, thank you for that, works like a dream. At some stage I need to recheck 1000 to 4000 which did not use the automated code. [CODE] 3001 11327799 3002 1778253 3003 1228629 3004 57267 3005 4266951 3006 5456133 3007 2224539 3008 4473543 3009 4801101 3010 877683 3011 4739259 3012 7339713 3013 1022649 3014 713397 3015 1964121 3016 4105647 3017 5559 3018 2289465 3019 8539635 3020 683067 3021 5840355 3022 1794267 3023 940701 3024 18221067* 3025 1645569 3026 5786403 3027 352725 3028 5748195 3029 752385 3030 4376367 3031 856821 3032 1102707 3033 9239505 3034 762747 3035 5483421 3036 10970487 3037 3655371 3038 1088283 3039 962241 3040 1107615 3041 480039 3042 1994403 3043 6655221 3044 906315 3045 491775 3046 3854685 3047 477081 3048 1778775 3049 206379 3050 539007 3051 2204871 3052 8402763 3053 6772875 3054 513807 3055 1130211 3056 1183083 3057 798849 3058 1094667 3059 2196411 3060 3037767 3061 1944705 3062 4358805 3063 13991565 3064 5439987 3065 1183281 3066 1015245 3067 11058201 3068 441927 3069 773481 3070 2701977 3071 454065 3072 2380107 3073 5862771 3074 90705 3075 1149405 3076 5134215 3077 2384571 3078 496377 3079 2197749 3080 2605137 3081 19703565* 3082 497457 3083 1676619 3084 1740963 3085 653721 3086 1652493 3087 4630311 3088 1145373 3089 3498249 3090 1789533 3091 1590171 3092 7180893 3093 5691159 3094 1868853 3095 9388239 3096 1828047 3097 2913681 3098 1129173 3099 1856661 3100 1103985 3101 1631535 3102 765063 3103 3953985 3104 58143 3105 1948095 3106 1795197 3107 309561 3108 5026887 3109 5350731 3110 6887175 3111 1590039 3112 450735 3113 2419425 3114 1938765 3115 4567785 3116 5099007 3117 496479 3118 3543135 3119 13625325 3120 2047533 3121 6107235 3122 809367 3123 8354685 3124 7728117 3125 241455 3126 2477823 3127 2886675 3128 1651593 3129 2370669 3130 2248785 3131 8646975 3132 383505 3133 4011981 3134 464205 3135 7882395 3136 984717 3137 1379685 3138 3811017 3139 2726079 3140 15630843 3141 3922149 3142 1658103 3143 954759 3144 549057 3145 1406259 3146 2326785 3147 505995 3148 9680385 3149 2541885 3150 5548827 3151 779781 3152 446583 3153 5462559 3154 4618833 3155 2680005 3156 3039447 3157 846531 3158 11184363 3159 4404729 3160 3632445 3161 5644779 3162 1747365 3163 2523519 3164 5062557 3165 2799249 3166 1497537 3167 2585829 3168 5876553 3169 4788369 3170 935955 3171 3218091 3172 3946545 3173 883935 3174 2259183 3175 1039635 3176 3854235 3177 8884479 3178 10648245 3179 41205 3180 1322913 3181 2193381 3182 2402883 3183 6439521 3184 4259613 3185 619011 3186 5678823 3187 1537821 3188 3136983 3189 6050265 3190 386727 3191 1740705 3192 1504617 3193 1254615 3194 4940457 3195 2211135 3196 2722173 3197 11827029 3198 7151895 3199 4207401 3200 7398465 3201 4461975 3202 10062717 3203 3171771 3204 1524645 3205 2049525 3206 5548497 3207 739581 3208 3511683 3209 260019 3210 6222993 3211 298965 3212 4527783 3213 1831191 3214 1210623 3215 43095 3216 778845 3217 2851371 3218 1339197 3219 1755141 3220 1828227 3221 3487221 3222 440937 3223 2243331 3224 5077743 3225 530649 3226 4166037 3227 803919 3228 1568847 3229 49449 3230 1827027 3231 5412141 3232 7204995 3233 4335201 3234 1335987 3235 401625 3236 17617383 3237 3673605 3238 2342415 3239 6042315 3240 171195 3241 17263281 3242 896697 3243 2027349 3244 2780367 3245 6265311 3246 1646235 3247 1524819 3248 4659897 3249 1811199 3250 2445885 3251 1378101 3252 2788275 3253 4794165 3254 3638265 3255 4167849 3256 1868277 3257 688761 3258 1274457 3259 646245 3260 2544633 3261 9907545 3262 6993903 3263 11213535 3264 4938003 3265 859479 3266 10618413 3267 2066649 3268 6828453 3269 4123479 3270 2393823 3271 1322985 3272 1603773 3273 4133805 3274 1165143 3275 4763205 3276 1414233 3277 540645 3278 2790477 3279 5075961 3280 9053913 3281 1038855 3282 2311563 3283 1149 3284 5411685 3285 10112589 3286 6481113 3287 189675 3288 6339525 3289 4826541 3290 2308215 3291 11034189 3292 311823 3293 1014675 3294 4391343 3295 2058225 3296 4023837 3297 6713031 3298 1230063 3299 11068569 3300 7820355 3301 220341 3302 4873485 3303 1563705 3304 5631213 3305 750879 3306 793707 3307 15529215 3308 3006795 3309 10797021 3310 2324205 3311 10376619 3312 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3854 16622085 3855 345975 3856 12845043 3857 313425 3858 6067215 3859 10665879 3860 3436173 3861 15938241 3862 4307835 3863 11008731 3864 3198135 3865 11608029 3866 6879243 3867 31539 3868 2401203 3869 727485 3870 4268667 3871 6845475 3872 3763395 3873 88071 3874 3109155 3875 6900405 3876 3830265 3877 4271889 3878 804993 3879 851319 3880 2025897 3881 6122841 3882 7790097 3883 3274959 3884 2825067 3885 583215 3886 1371495 3887 704739 3888 1150803 3889 4750881 3890 163713 3891 80661 3892 4168257 3893 13037079 3894 7722837 3895 2644749 3896 6221445 3897 1991259 3898 2168025 3899 2822931 3900 2592915 3901 956271 3902 10436037 3903 16066479 3904 868533 3905 10067649 3906 19038357 3907 5179959 3908 6706725 3909 558999 3910 5138097 3911 5984979 3912 183447 3913 2684409 3914 2158167 3915 458631 3916 387603 3917 168675 3918 897867 3919 3219945 3920 1848927 3921 668061 3922 21628257 3923 653559 3924 5505147 3925 5991099 3926 6394893 3927 488721 3928 695703 3929 1724961 3930 3839253 3931 10069089 3932 1756443 3933 1135071 3934 1346967 3935 7439481 3936 884775 3937 4559961 3938 986205 3939 833271 3940 437487 3941 760449 3942 34407 3943 4179405 3944 778305 3945 1185681 3946 4312245 3947 2862591 3948 2280063 3949 3054765 3950 1696317 3951 2821191 3952 7339773 3953 3097815 3954 7194483 3955 6812415 3956 6337785 3957 3683241 3958 3434685 3959 4097649 3960 1203207 3961 10633029 3962 1316613 3963 1068609 3964 1243293 3965 1080099 3966 653685 3967 4908591 3968 6922125 3969 13950291 3970 4853193 3971 5027079 3972 13371057 3973 1099329 3974 10041783 3975 11829141 3976 7373997 3977 1169811 3978 6481113 3979 2615559 3980 3727485 3981 2637075 3982 7703085 3983 20695455 3984 24731145 3985 11197851 3986 13448553 3987 1152459 3988 541437 3989 49455 3990 2894133 3991 8764455 3992 1254585 3993 1886619 3994 6410487 3995 1657929 3996 2346255 3997 8545521 3998 2564187 3999 9635589 4000 2515263 [/CODE] |
[QUOTE=robert44444uk;128009]Gary/ Karsten
Results of first instance primes to 1400 show a rather nice curve when plotting ln(k/n) against n. Best fit looks to be logarithmic as well. Would be interested to know if this might be a good way to target large twins. For example, [U]if[/U] the extrapolation of the best fit to n=333333, gave A= ln(k/n)= 9, then the first twin would be, on average, at k=2.70103*10^9 then the test might look at n from 333333 to n 333433, say at A=8.999 to 9.001 or k=2.69833*10^9 to 2.70373*10^9. A 50 million k range, sieved to 1T would provide about 4,000 candidates for prime checking or 400,000 overall for a 100 k range. [/QUOTE] Values within x% either side of the of the forecasted first value for each of the first 4000n: 1% 20 2% 56 3% 84 4% 109 5% 145 6% 168 7% 192 8% 215 9% 238 10% 261 No apparent abnormal density factors at play here |
Where can I get this automated code Karsten did?
Unfortunately, my range is going slowly, as I have only found 55 (5%), and sieved for 390 (33%). It should improve as my search continues, when it is more organized :redface: roger |
data for n upto 4000 are online!
to roger: to get the scripts look some posts above! |
It is important to pick quite a large range of k to sieve, and sieve to a suitable depth, I suggest k=0.5*2^n. The automated script will stop on success. LLRing takes the most time
|
Are the scripts referred to cLLR? Or cNewPGen? I don't see an attached file, but are the codes kar_bon posted what I'm looking for?
Thanks! BTW: at the moment, I'm using NewPGen to sieve for 0<k<20M as 10M just doesn't seem to be enough. And yes, the LLRing is taking a lot longer than the sieving. |
cllr (LLR console application) can be found here: [url]http://jpenne.free.fr/llr3/cllr371c.zip[/url]
cnewpgen (NewPGen console version) can be found here: [url]http://jpenne.free.fr/NewPGen/[/url] the scripts are all you need: two WIN-batch files. that's all. copy the 2 code-sections in the named files, put these with cllr and cnewpgen i the same folder and start the first with your range (and 2nd with some other parameters for nmax and pmax). [b]these few[/b] lines of code is all you need!!! simple! and much time!!!!! |
Got a bit of a chat going with Bob Silverman and others about the mathematics, found here:
[url]http://www.mersenneforum.org/showthread.php?p=129815#post129815[/url] |
[quote=robert44444uk;129823]Got a bit of a chat going with Bob Silverman and others about the mathematics, found here:
[URL]http://www.mersenneforum.org/showthread.php?p=129815#post129815[/URL][/quote] BRILLIANT ANALYSIS on the reason to search less k over a range of n instead of a fixed-n for a twin prime search! Before getting to that post where you used the median first k for your analysis, I was about to post in there that I thought the median would be a much better measure than the mean. When I saw that you concluded it and then did the statistical analysis to MATHEMATICALLY PROVE that it makes more sense to search a much smaller range of k over a range of n instead of doing a fixed-n search, I felt vindicated because I had originally stated it in this thread (weeks after suggesting it to the leader of TPS) and it seemed clear to me in my 'ALL twin prime search' that it is a much more effective way to search for large twins. Of course my reason was different: The time saved in LLRing lower k's well more than makes up for the sieving time saved on a twin prime search on a fixed-n. So now we have TWO reasons! On a related side note; I haven't see this mentioned in any thread about twin prime searching: It is NOT proven that there is NOT a highest twin prime. Of course it seems almost certain that there is not a highest twin, but we can't say for sure. There is a possibility, however infinitesimal it may be, that TPS is searching above the highest possible twin. It's funny to even think that might be a possibility. BTW, I got word that PrimeGrid is going to attempt a Twin and Sophie Germain prime search for a fixed n=666666. Sounds crazy to me. What do you think of that? Now we'll get a bunch of n=666666 primes on top-5000. (yuck!) But this confused me. I thought TPS was going to do a fixed-n twin search on n=500K. Have you heard about either of these efforts? Gary |
What are the changes in searching for these twins then?
Are we doing a range of some millions around where the twin is expected to be found, then search below if one is found to be sure? Are we still searching by the n-value, like in NewPGen? roger |
I think it is true to say that it is not mathematically proven, despite Gary's kind works, but I have extended comparison at 0.24*n^2 and it still holds.
I have also shown that searching around the expected value does not provide any greater chance of finding a prime, see post #53, by searching around the level of this median value. What the median formula provides, however are some reasoned bounds around testing levels to arrive at close to 100% chance of finding a twin, this calculation provides a significant reduction over the 100G searched in the TPS 333333 search down to about 43G, using the first tenth of a percentile over a range of 1,000 n. TPS was lucky with the 190000 search level, finding the twin in the 2G range, whereas 0.24*n^2=8.6G. It might me worth experimenting a bit with this, but at a lower n, to make sure we are happy with the approach, after all we have all of the tools we need right now, except a distributed approach. We could test this at say n=30000, according to the approach, we could check n from 29975 to 30025, which is 50 n, and check therefore up to the second percentile of 0.24*30000^2 -> k=4320000, we should obtain one twin. At the same time check all of the first instance k for this range to see its median is close to the forecast of 216M. If we look at variance in a graph of median versus the formula, then the median was >200% for the formula only in four instances (3925,3939,3940,3941), and was never <50%. I think that an interesting observation is that there has not been any really rogue n value, whereby you might find no twins, the asterisked champions are at relatively low values. |
Ugh, my last post was horribly written, it was posted between power cuts (which are very frequent here) and it was too late to edit after the power came back. Apologies for that.
Checking this particular k=29975-30025 range is interesting as we already know from Gary's work that there is no twin up to k=1M in the range. The range of k to be sieved is 800% of median, as we are also looking to actually find the first k for each n in the range. i.e from k=1M to k=1.6G. As far as checking for twin+SG, I think 666666 is not very logical at all. To begin with checking takes time, by checking SG & twin you are eliminating some k which are either SG or twin, i.e. those which are twin but for which SG partner has no small factors and vice versa. Much more sensible is to check not too far above the current record of n=195000, say n=200000 using the approach we are discussing. We would find a record much faster than TPS or PrimeGrid, all they will do is find top 5000 primes, which is not so exciting after the first few. No one talks about Mr X and his 25674165667*2^333333-1 find, ranked 4345th biggest prime ever (made that up), but a new twin record and you are in the books for ever. Will probably post 4000-5000 today |
to Robert:
do you use the scripts i gave? how they work? any problems? what are the current parameters (nmax and pmax for cnewpgen) you use? how long do the scripts run? timings? i'll try to firgure out how i can enhance them for a k when no twin is found. and to continue a work when canceled. karsten |
Karsten, script works fine, I just have no computing power. I tend to vary the scripts based on where I am , but I am setting the upper k limit for cnewpgen at 10*0.24^n^2 or thereabouts. Checking lots of k adds no time, and therefore I don't have to worry about stoponsuccess not kicking in, it always does. pmax tends to be not too high..5G at n=5000.
The only problem is that I am using del commands on each n, and sometimes the del kicks in before the write to alltwins.log. But that happens only one time in a couple of hundred, so I need a small delay command, but I can't remember what that is. Long time since I used dos. |
Karsten:
I've got the scripts working now (they work great so far!), and haven't had any problems. The parameters I'm using right now are: kmax=20,000,000; pmax=25,000,000,000 which leaves around 15,000 candidates. The sieving takes around 4.1 minutes per n-value. Each k takes between 150 and 350 ms (depending on the k-value). The stop on success option will help lower the time it will take, as well as running two instances, but it will still take a while... EDIT: Robert, do you mean kmax=10*0.24 * n^2? |
also, I deleted the line that erases the lresults.txt, for archive purposes and to doublecheck that a twin/no twins have been found, and the range.
|
to Robert:
to wait a time try this: [code] CHOICE /C:YN /T:Y,5 >nul [/code] this command waits 5 seconds before continuing the batch. the 'choice' command was standard in old DOS-versions. if it's not in your distribution (like mine for XP) you can download it here: [url]ftp://ftp.microsoft.com/Services/TechNet/Windows/msdos/RESKIT/SUPPDISK/[/url] hope it helps. |
[QUOTE=roger;130230]Karsten:
I've got the scripts working now (they work great so far!), and haven't had any problems. The parameters I'm using right now are: kmax=20,000,000; pmax=25,000,000,000 which leaves around 15,000 candidates. The sieving takes around 4.1 minutes per n-value. Each k takes between 150 and 350 ms (depending on the k-value). The stop on success option will help lower the time it will take, as well as running two instances, but it will still take a while... EDIT: Robert, do you mean kmax=10*0.24 * n^2?[/QUOTE] I think you should greatly expand the k you are testing - at the n=8500, suggestion is k up to 173 million using my kmax formula. 20 million and you are only above the median by a bit, and you will have to do the whole exercise all over outside of automated programme. As you will not be actually using most of these k (9/10ths will be above the median), then there is no reason to sieve very deeply, and your sieve computation should assume therefore that the you will LLR only to the median. In that case, the time of the sieve should be such that sieve time+LLR time is minimised. You will have to test about 13000 candidates to get to the median, and this will take approx 43 minutes at 5 per second. So in principle, you could sieve a little higher, as long as the candidates are being eliminated at 10* the time taken to run an LLR test. But to me p=50 billion is probably not horribly off mark. I always hope that I will find the twin really quickly and I hate it when the LLR runs close to kmax, only then do I rue not sieving higher. |
We find for n=9999 : k=594501 found in 5 minutes
I have also a suggestion for kmax: upperlimit for k-candidates is: number of candidates=(( n * ln(2) ) / ln(pmax^2) *1.1 )^2 You get for n<10000 about a k range from 0 to 35000000 and a good chance to find a twin with a special n. regards |
I'll change my kmax to 50M, and see what happens. It takes a long time to test so many k's: for kmax=50M, with ~0.075% (37500) candidates remaining, that's 2.6 hours per n :shock: though with the stoponsuccess option, it will be considerably less time.
|
For n=10000: is 10642317 * 2^10000+/-1 the smallest twin.
BTW, k=44.1 G is the upper limit for the 333333 project. My hint : 425******** x 2^333333 +/- 1 is twin :-) |
Hi Cybertronic, welcome to the debate.
At 44.1G you are into the median expected values. But the density of twins is no better here than anywhere else, but I will bet that if there is no twin found <44.1G, then there will be one before 350G !!! But that is a lot still to check, I think. But GL in finding your 333333 twin. Hope you turn out to be right in your forecast. |
Thanks for n=9999 Cybertronic, but I already have n=10000. If you want to reserve a range, by all means, do so.
It looks like the reserved/completed ranges are: 0->5000, 8825->10000. |
which ranges are free ?
|
perhaps also from interest
I have checked all n up to 4000
1 candidate is also quadruplet :n=153 42 candidates are triplets. 1179 *2^ 23 +5 429 *2^ 37 +5 429 *2^ 37 -5 519 *2^ 55 -5 657 *2^ 58 +5 147 *2^ 60 -5 1623 *2^ 64 +5 2469 *2^ 67 -5 4497 *2^ 68 +5 7029 *2^ 71 +5 14487 *2^ 90 -5 4107 *2^ 100 -5 1203 *2^ 104 -5 1983 *2^ 124 -5 3741 *2^ 153 +5 13719 *2^ 191 -5 24087 *2^ 220 +5 77751 *2^ 235 -5 99297 *2^ 304 -5 14649 *2^ 313 +5 88791 *2^ 323 +5 18669 *2^ 367 +5 83211 *2^ 519 -5 47403 *2^ 524 -5 228651 *2^ 609 +5 526701 *2^ 797 -5 163497 *2^ 984 +5 193443 *2^ 1068 +5 818961 *2^ 1083 -5 42399 *2^ 1229 -5 856821 *2^ 1381 -5 849261 *2^ 1455 +5 884751 *2^ 1651 -5 96897 *2^ 1676 +5 3934047 *2^ 2686 +5 32811 *2^ 2707 +5 3353631 *2^ 2957 -5 877683 *2^ 3010 -5 549057 *2^ 3144 +5 440937 *2^ 3222 +5 1868277 *2^ 3256 -5 5991099 *2^ 3925 +5 |
It looks like the free ranges are n=5000->8824, and anything above n=10000. Use the batch files kar_bon posted above along with cLLR and cNewPGen (links posted above).
|
Whoa
Hold up here. I have already gone a fair way through 5000-6500. So please lets get co-ordinated! Thank you for checking 1-4000, I hope there were no errors, and below is 4000-5000. Only 3 new jumping champions. [CODE] 4001 4147569 4002 5197923 4003 9237201 4004 1752213 4005 7392921 4006 1173417 4007 20778009 4008 1767783 4009 1929279 4010 9192093 4011 2000241 4012 1056495 4013 5072781 4014 21829155 4015 3025125 4016 2271237 4017 3079239 4018 7446675 4019 1325265 4020 10499793 4021 15669051 4022 700473 4023 512601 4024 4710525 4025 12373245 4026 25752855 4027 9886899 4028 3744483 4029 17085729 4030 559995 4031 3738909 4032 7092237 4033 11309235 4034 555723 4035 1711971 4036 4689015 4037 2634645 4038 1412535 4039 4782045 4040 3622107 4041 1741005 4042 263433 4043 567405 4044 1929993 4045 1462035 4046 13007817 4047 1762521 4048 4768785 4049 11351295 4050 4382823 4051 8548335 4052 9731337 4053 14791299 4054 5432307 4055 863199 4056 4503723 4057 2052315 4058 3951753 4059 4845939 4060 2304645 4061 2198175 4062 3257805 4063 6871479 4064 1771017 4065 7095429 4066 339087 4067 3011271 4068 9340845 4069 2449719 4070 2476533 4071 654579 4072 4517913 4073 1471365 4074 713685 4075 3316269 4076 718665 4077 12635481 4078 19312347 4079 4869411 4080 2631717 4081 174879 4082 4784613 4083 10594581 4084 14811573 4085 9038949 4086 16140675 4087 2990205 4088 243795 4089 352389 4090 6723393 4091 2609769 4092 6747153 4093 907725 4094 2719305 4095 982335 4096 2130693 4097 4399545 4098 8337483 4099 9711471 4100 12136155 4101 8713581 4102 4163985 4103 717525 4104 4354287 4105 2898471 4106 1813155 4107 4587585 4108 1742307 4109 836751 4110 6181347 4111 4095729 4112 1859865 4113 2534661 4114 116313 4115 4173981 4116 1082037 4117 3767961 4118 928683 4119 16632609 4120 42572193* 4121 1443771 4122 17977425 4123 5984679 4124 4053885 4125 623499 4126 5819847 4127 55853139* 4128 3763035 4129 602079 4130 1883577 4131 7249989 4132 14967405 4133 3521175 4134 2434497 4135 7922469 4136 5506053 4137 2285895 4138 12862107 4139 1206465 4140 3288423 4141 10603671 4142 1526175 4143 3608019 4144 9183993 4145 5062821 4146 5324223 4147 11652549 4148 7213035 4149 5353701 4150 7994973 4151 9831891 4152 9932823 4153 793515 4154 10844163 4155 5034741 4156 2383257 4157 3500085 4158 11951205 4159 996735 4160 14606115 4161 24134451 4162 17500413 4163 320529 4164 111573 4165 4214799 4166 10678137 4167 13106685 4168 6658317 4169 1881741 4170 13800507 4171 1315461 4172 37843593 4173 2347095 4174 9794493 4175 1579431 4176 2855223 4177 9561711 4178 11135817 4179 4778295 4180 8928675 4181 5597595 4182 5621583 4183 1580535 4184 6985017 4185 449949 4186 12173085 4187 12751539 4188 7751607 4189 674235 4190 9015387 4191 18795459 4192 6787167 4193 3668211 4194 3570495 4195 449841 4196 19934715 4197 10339371 4198 34758087 4199 3062121 4200 23831535 4201 8191689 4202 4670277 4203 14047131 4204 12249897 4205 2703981 4206 11968623 4207 4260879 4208 8983635 4209 4561179 4210 3254517 4211 4763349 4212 9014493 4213 2011869 4214 2300367 4215 11868741 4216 2534475 4217 8219919 4218 5128893 4219 941421 4220 1328055 4221 5296389 4222 3006015 4223 4363281 4224 902883 4225 15034761 4226 490263 4227 2405079 4228 5595207 4229 5350275 4230 7985073 4231 1989009 4232 5872395 4233 7507665 4234 1443855 4235 13782111 4236 10167255 4237 4070361 4238 10651827 4239 138009 4240 3286257 4241 2819649 4242 491547 4243 3783519 4244 3233517 4245 6763335 4246 734193 4247 17920029 4248 7857363 4249 684291 4250 4690353 4251 8541375 4252 4221735 4253 1792431 4254 14364465 4255 1263771 4256 665763 4257 4611861 4258 2422365 4259 19933635 4260 3592017 4261 3091125 4262 957957 4263 4035705 4264 2415567 4265 27452691 4266 16480137 4267 5148171 4268 16075587 4269 257241 4270 3043467 4271 3833985 4272 10074993 4273 12296349 4274 8986233 4275 5226741 4276 16431303 4277 8013351 4278 12607257 4279 11052441 4280 5403153 4281 1014549 4282 977103 4283 878571 4284 5151975 4285 5956551 4286 1944837 4287 4141749 4288 3464043 4289 247065 4290 2056485 4291 38173815 4292 5202555 4293 2280561 4294 2474367 4295 5126421 4296 19057503 4297 22449621 4298 6859227 4299 1421535 4300 10365747 4301 5867091 4302 6584457 4303 440229 4304 10883715 4305 1485039 4306 21385155 4307 13705665 4308 4159227 4309 12113949 4310 3337653 4311 106131 4312 15493413 4313 2107305 4314 8822523 4315 1897905 4316 2672793 4317 9396009 4318 28262925 4319 7706091 4320 1446447 4321 15641001 4322 14597997 4323 3195591 4324 6721995 4325 3352131 4326 4382907 4327 9512475 4328 6042225 4329 7928751 4330 7132593 4331 2027631 4332 587277 4333 6590199 4334 50591937 4335 32721 4336 32976393 4337 17708079 4338 1701303 4339 1809435 4340 2802135 4341 2097219 4342 1387797 4343 574701 4344 7546725 4345 22526925 4346 1557555 4347 952305 4348 4064643 4349 12341049 4350 208887 4351 12564945 4352 2268675 4353 104241 4354 16815345 4355 1280415 4356 24151365 4357 543699 4358 865035 4359 2830839 4360 2309985 4361 3991215 4362 8421147 4363 22296339 4364 3132933 4365 2673891 4366 8549973 4367 4352079 4368 6146175 4369 7636725 4370 6608433 4371 2568081 4372 12767523 4373 2443125 4374 2438517 4375 119895 4376 5801025 4377 3375285 4378 2417847 4379 16317645 4380 12325887 4381 326115 4382 14899623 4383 5964345 4384 23140077 4385 1665045 4386 502953 4387 1184469 4388 2368797 4389 1290261 4390 12547527 4391 7195731 4392 2812773 4393 1322631 4394 14447115 4395 6289701 4396 4998957 4397 1475751 4398 4326345 4399 6280119 4400 7162623 4401 11912661 4402 4430475 4403 1491171 4404 3517803 4405 50143095 4406 6340473 4407 2067195 4408 4154295 4409 3698145 4410 14053875 4411 1501521 4412 12986583 4413 3457731 4414 6179745 4415 5092629 4416 668103 4417 3672165 4418 9048117 4419 34060065 4420 2864787 4421 6286029 4422 13699185 4423 7288671 4424 228477 4425 9349305 4426 1234875 4427 7029309 4428 13309587 4429 13686819 4430 395655 4431 402801 4432 11848377 4433 21385095 4434 34698843 4435 13259451 4436 6601797 4437 379269 4438 814605 4439 3960771 4440 4767495 4441 13650909 4442 3646803 4443 3469281 4444 3403317 4445 970785 4446 3855873 4447 7807059 4448 10377543 4449 3038871 4450 7373547 4451 3574395 4452 842307 4453 5856249 4454 5364327 4455 3213045 4456 5330457 4457 2229261 4458 227757 4459 23481015 4460 28485345 4461 13996815 4462 2054613 4463 15783111 4464 10158507 4465 2520579 4466 8478735 4467 2341299 4468 7463547 4469 1200711 4470 10794417 4471 7310421 4472 6715587 4473 4442139 4474 1762665 4475 5796651 4476 2650737 4477 5588535 4478 18120603 4479 29720421 4480 16043427 4481 37383291 4482 5716695 4483 1461711 4484 4246137 4485 4616169 4486 20749035 4487 8742285 4488 1172997 4489 2249505 4490 2302287 4491 702501 4492 5405583 4493 2972775 4494 14668215 4495 3375609 4496 3634275 4497 2720205 4498 8718855 4499 18231405 4500 1161615 4501 1178661 4502 10074933 4503 13096125 4504 887733 4505 4299159 4506 5578317 4507 4633839 4508 4300587 4509 5443125 4510 9742923 4511 4495575 4512 852927 4513 12113151 4514 2234193 4515 5462811 4516 7343313 4517 9926259 4518 4564527 4519 10684011 4520 18154275 4521 11430591 4522 4800633 4523 6909141 4524 5697363 4525 594165 4526 11545107 4527 5021289 4528 292143 4529 4062741 4530 2270205 4531 1705185 4532 877593 4533 4697361 4534 3804453 4535 4756251 4536 4153593 4537 17579571 4538 1285917 4539 5114445 4540 29486415 4541 2171961 4542 7361685 4543 1071075 4544 1726263 4545 9139035 4546 3212145 4547 290835 4548 3076533 4549 1309191 4550 10631043 4551 18137331 4552 238743 4553 2993535 4554 7959705 4555 16069611 4556 13019703 4557 6074871 4558 8136387 4559 10301661 4560 6983265 4561 9906855 4562 2622465 4563 6018051 4564 237903 4565 10525761 4566 6373437 4567 703341 4568 2559603 4569 5012499 4570 18235965 4571 1018731 4572 6225825 4573 11385729 4574 4184433 4575 7321521 4576 7490463 4577 2872485 4578 16817283 4579 2281341 4580 2347323 4581 9486591 4582 25494177 4583 10972389 4584 348747 4585 8892939 4586 314607 4587 11923851 4588 2410275 4589 7503705 4590 146787 4591 197595 4592 5185935 4593 6009519 4594 21133947 4595 22808649 4596 548067 4597 4112031 4598 3006213 4599 280569 4600 21490167 4601 1803669 4602 10967127 4603 1280655 4604 2881677 4605 2428389 4606 7146327 4607 3073935 4608 3506277 4609 8614479 4610 31193595 4611 211179 4612 1609713 4613 13070175 4614 4585845 4615 1718169 4616 3219315 4617 6736131 4618 9814695 4619 66969 4620 13406577 4621 5464989 4622 10128525 4623 15185835 4624 2413203 4625 623511 4626 1403787 4627 1820055 4628 17699475 4629 7434375 4630 8933127 4631 28597089 4632 546513 4633 12029451 4634 9803373 4635 4144131 4636 3518643 4637 618561 4638 456153 4639 3271605 4640 9476355 4641 16912905 4642 843513 4643 1731951 4644 10696527 4645 6674589 4646 4568985 4647 1770615 4648 6373395 4649 12272985 4650 3839943 4651 10306239 4652 1204413 4653 3015471 4654 1501695 4655 4660005 4656 2022153 4657 5488665 4658 27693627 4659 1974555 4660 2468793 4661 274485 4662 7936455 4663 671559 4664 16292997 4665 1568691 4666 29853837 4667 1767381 4668 3254925 4669 2587515 4670 9826197 4671 29267949 4672 2592765 4673 1610661 4674 364383 4675 5657511 4676 744087 4677 9793665 4678 2767773 4679 2435349 4680 3541767 4681 21542925 4682 4509945 4683 20813949 4684 5581557 4685 25355919 4686 2583765 4687 3273171 4688 6711765 4689 2079165 4690 2149413 4691 5378619 4692 14343543 4693 7119051 4694 8611383 4695 24459759 4696 7274517 4697 6030315 4698 66725397* 4699 1971459 4700 3345303 4701 19378215 4702 8215527 4703 27137481 4704 8067447 4705 413001 4706 2347887 4707 12500679 4708 7416597 4709 7331709 4710 1691193 4711 5119785 4712 7183785 4713 7160361 4714 2645565 4715 2847939 4716 20119953 4717 27154521 4718 13174755 4719 6193029 4720 10987347 4721 3224529 4722 3988467 4723 11775741 4724 8663823 4725 14309379 4726 3324375 4727 16026135 4728 1133517 4729 3920019 4730 14581893 4731 2763609 4732 906165 4733 12494985 4734 6378123 4735 2055711 4736 4940103 4737 16994625 4738 637155 4739 7695141 4740 12691245 4741 5735535 4742 9325557 4743 143439 4744 14714415 4745 6004929 4746 134433 4747 8525805 4748 1417275 4749 4257195 4750 14069277 4751 2299539 4752 8618823 4753 2975379 4754 203253 4755 8980125 4756 4798935 4757 1532691 4758 2070003 4759 6352995 4760 3991557 4761 1441095 4762 4768083 4763 1290405 4764 13029837 4765 7039881 4766 5765817 4767 11413689 4768 15722433 4769 1354581 4770 3297045 4771 11341899 4772 2357793 4773 2172261 4774 9267837 4775 2545341 4776 6984633 4777 5537049 4778 1284093 4779 12115569 4780 1597365 4781 2727585 4782 18460983 4783 4625469 4784 1025403 4785 6666051 4786 8765583 4787 74565 4788 26335185 4789 12161865 4790 2964297 4791 3379869 4792 991347 4793 1475919 4794 7784385 4795 25337691 4796 7295385 4797 2502735 4798 6126057 4799 4023261 4800 11252973 4801 1120701 4802 732327 4803 963039 4804 6481305 4805 3208845 4806 22019655 4807 8981469 4808 7942635 4809 10768179 4810 1577547 4811 6326685 4812 18641415 4813 3358509 4814 22625133 4815 19246995 4816 26440797 4817 3490155 4818 2107287 4819 11603031 4820 6648543 4821 2900691 4822 8791755 4823 20476011 4824 16484127 4825 2501799 4826 15078867 4827 1282755 4828 3638523 4829 10793049 4830 3742263 4831 7415541 4832 622497 4833 1024389 4834 1386357 4835 7787025 4836 429993 4837 144249 4838 12707073 4839 6552459 4840 4175715 4841 28587261 4842 3666075 4843 26010669 4844 26548563 4845 8656371 4846 15123837 4847 1440495 4848 24098343 4849 6213075 4850 866445 4851 2867559 4852 4038993 4853 5986551 4854 31056513 4855 7335585 4856 34814637 4857 17719305 4858 4574505 4859 4362975 4860 8067087 4861 10488015 4862 11986017 4863 1494729 4864 11661705 4865 5600241 4866 938565 4867 5065881 4868 13326825 4869 947229 4870 6740505 4871 2969739 4872 21553917 4873 9951669 4874 2882697 4875 36656655 4876 6549243 4877 7966575 4878 7465395 4879 4358019 4880 442593 4881 3123519 4882 3151407 4883 6706479 4884 22767 4885 1847511 4886 22505223 4887 800109 4888 13397595 4889 3926919 4890 13076373 4891 5602605 4892 15356907 4893 1445295 4894 3269007 4895 2834625 4896 5064003 4897 1433691 4898 11555667 4899 5602041 4900 5652675 4901 2565 4902 1243923 4903 7230669 4904 37819947 4905 9718371 4906 17463207 4907 15869811 4908 10184727 4909 12373941 4910 11616003 4911 111885 4912 42343545 4913 7248189 4914 7325685 4915 8774751 4916 3337683 4917 2763939 4918 13608603 4919 8808645 4920 18012753 4921 3451119 4922 514545 4923 4562481 4924 12797283 4925 14017119 4926 3407205 4927 5049735 4928 13078323 4929 13039455 4930 14661003 4931 1174485 4932 433983 4933 218325 4934 2202735 4935 730755 4936 10073517 4937 14903361 4938 3608973 4939 14440995 4940 3560817 4941 575601 4942 1229493 4943 13010409 4944 22354365 4945 5402601 4946 17615433 4947 2566245 4948 11933637 4949 2386209 4950 11668863 4951 2242011 4952 3527595 4953 903411 4954 7987455 4955 2346735 4956 3434685 4957 28524351 4958 7079163 4959 3698835 4960 23016237 4961 918765 4962 5027265 4963 16934049 4964 4950315 4965 5701215 4966 8250747 4967 4188279 4968 20488125 4969 1751919 4970 381273 4971 11855175 4972 9754107 4973 1807845 4974 2537505 4975 6104415 4976 718665 4977 33114849 4978 13417515 4979 6874809 4980 5286603 4981 5153391 4982 1898415 4983 6773505 4984 14809737 4985 2071551 4986 2672133 4987 4554615 4988 12744243 4989 12815919 4990 7486395 4991 1950675 4992 416343 4993 6694449 4994 5367237 4995 886461 4996 9677493 4997 31569 4998 2455005 4999 8130255 5000 5852235 [/CODE] |
Wow, I wish I had your computer farm :razz: I'm afraid I only have a single 2Gb laptop, but am running an the batch files on both cores. It's still going slowly, but picking up as I have increased the kmax and with the stoponsuccess. With kmax=50M, it looks like around 70-90% of n's have verified twins.
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cnewpgen
Hello, how I get the program cnewpgen ? You can also send this file to
[email]nluhn@yahoo.de[/email]. Perhaps I look for n between 10000 and 10200 Thanks! |
[QUOTE=Cybertronic;130338]Hello, how I get the program cnewpgen ?
Thanks![/QUOTE] Norman, see post #58 in this thread |
Thanks.. I will try n=10000 to 10200 . okay ?
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i updated the page with all results upto n=5000 and marked the champions too.
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[QUOTE=gd_barnes;130153]it makes more sense to search a much smaller range of k over a range of n instead of doing a fixed-n search[/QUOTE]
If you want TPS to abandon our fixed-n search after finding a prime for n=333333, you'll need to: 1.) Suggest the range of k and n that you think makes sense. 2.) Provide a program that can search the whole range of k and n at once. NewPGen won't work because either the k or the n value has to be fixed. [QUOTE] I thought TPS was going to do a fixed-n twin search on n=500K. [/QUOTE] That was the original plan, but I'm willing to change it even after doing some sieving on n=500K. |
Whatever "k" and "n" you look at, simultaneously searching with a "[URL="http://tech.groups.yahoo.com/group/primeform/message/8721"]quadruple sieve[/URL]" for [URL="http://primes.utm.edu/top20/"]archivable forms[/URL] "[URL="http://primes.utm.edu/top20/page.php?id=1"]twin primes[/URL]" and "[URL="http://primes.utm.edu/top20/page.php?id=2"]Sophie Germain primes[/URL]" is the right thing to do IMHO. :geek:
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I go back to my old project. Here the results.
n k 10000 10642317 10001 8590875 10002 2481813 10003 12176169 10004 10808517 10005 3257595 10006 12110457 10007 1374729 10008 227547 10009 14244069 10010 >33M 10011 >33M 10012 >33M |
1 Attachment(s)
I stitched the posts above into one excel chart and graphed them, with and without my data. I added a trendline, and the equations turned out to be (averages):
k=0.2973*n^1.9555 [for data of n=1->5000, no gaps] k=0.3823*n^1.9191 [for data of n=1->10000, with gaps] Attached is the excel file. |
[QUOTE=roger;130438]I stitched the posts above into one excel chart and graphed them, with and without my data. I added a trendline, and the equations turned out to be (averages):
k=0.2973*n^1.9555 [for data of n=1->5000, no gaps] k=0.3823*n^1.9191 [for data of n=1->10000, with gaps] Attached is the excel file.[/QUOTE] This accords with my findings, but Bob Silverman guided me to retrofit to theory, which deal with A*n^2, with A a variable or a constant, and it was also concluded that we should look at medians rather than averages - try to place the values in percentiles over a block of n and you will see that the rogue values have a large influence over the average. When you look at A constant, the data fits quite well to A=0.24. You might want to try to plot Norman's formula that he suggested a couple of days ago. |
[QUOTE=MooooMoo;130396]If you want TPS to abandon our fixed-n search after finding a prime for n=333333, you'll need to:
1.) Suggest the range of k and n that you think makes sense. 2.) Provide a program that can search the whole range of k and n at once. NewPGen won't work because either the k or the n value has to be fixed. That was the original plan, but I'm willing to change it even after doing some sieving on n=500K.[/QUOTE] MooooMoo I hope the work we are doing here will be persuasive, it is not our purpose to "want" you to abandon. My choice, to be further analysed was posted on 29th March in this thread, but before this approach could be adopted, then I would want (if I was you) some comfort that this bottom slicing approach would work, and I suggested a test at the 30000 level, in the same post. If we are able to find an twin in the very narrow bounds of k suggested, it might give you confidence in the approach. In terms of distributed effort, I don't know if there are sieves out there that can attack 1000 n at a time, over a fixed range of k. So the approach might be to sieve with a program that provides the maximum range of n, set up a series of parallel sieves, then start to prp the results. This is still in its infancy as an approach, and our objective is to provide a sound footing for any attack on the twin prime record. |
I'm working on finding the 90th or 95th percentile of where these twins fall on the graph. That should reduce the range of k's to search somewhat, or at least be of passing interest.
Will post the results in a few hours I think |
[QUOTE=roger;130510]I'm working on finding the 90th or 95th percentile of where these twins fall on the graph. That should reduce the range of k's to search somewhat, or at least be of passing interest.
Will post the results in a few hours I think[/QUOTE] Roger You may wish to look at message #12 on [url]http://www.mersenneforum.org/showthread.php?p=130510#post130510[/url] where I had analysed blocks of 100 by decile. |
Post #12 seems to be written by MooooMoo...
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[QUOTE=roger;130525]Post #12 seems to be written by MooooMoo...[/QUOTE]
Sorry Try this link [url]http://www.mersenneforum.org/showthread.php?t=10063[/url] |
[quote=MooooMoo;130396]If you want TPS to abandon our fixed-n search after finding a prime for n=333333, you'll need to:
1.) Suggest the range of k and n that you think makes sense. 2.) Provide a program that can search the whole range of k and n at once. NewPGen won't work because either the k or the n value has to be fixed. That was the original plan, but I'm willing to change it even after doing some sieving on n=500K.[/quote] First, I don't suggest waiting for n=333333 to find a twin. The chances of you finding a twin are no greater now than when you started regardless of what has already been tested. Interest will wane once the last n=333333 prime has dropped off of top-5000. I've seen it already waning. Essentially the same sized prime gets boring after a while. Suggestions: 1.) n=350K-450K 2.) k=3 to 2M (odd values only); that's a starting value of three, not three million. 3.) Sieving: NewPGen with the increment counter set on. In a distributed effort, have people reserve n-value ranges instead of P-values for sieving. Determine ahead of time what the optimum sieve depth is and have everyone sieve to the same depth; increasing moderately as you go up by n-value. Number of possible candidates: 100K * 1M = 100G. Number of candidates from your n=333333 search assuming a top k-value of 100G: 50G The above is exactly what I'm doing to create the 'all twin pages' that I've done so far to n=~36K. (I've temporarily stopped the effort for about the last 5-6 weeks but have sieved up to n=50K. Will start again in ~1-2 weeks.) Sieving 1 n-value at a time is far more effective than it looks at a glance. Low k-values LLR MUCH MUCH faster. IMHO, fixed-n searches should not be done in the future unless there is an improvement to LLRing high k-values. Despite this, if you still decide to do a fixed-n search, do EVEN AND ODD k's. That's what I did to find my 2 top-5 prime quadruplets; one which is for n=3800 and the other for n=3802. I sieved all n=3800 but one of the k's was divisible by 4 so it was reduced and n increased by 2. Once again, it's about efficiency. You may as well get twice the k-values within the same range. I can't think of a reason to limit it to odd k-values if you're doing a fixed-n search. The above quad search wasn't very efficient because I sieved something like k=3 to 5T!! I was still ignorant. I should have taken what I'm suggesting above and sieved across 1000n up to about k=5G. 10-digit k's would have been bad enough in that search but 13-digit k's that I ended up testing in the actual search are ridiculous when LLRing. NOW...all of this said, if you can convince people to search with no reward of top-5000 primes, I agree with what some others have suggested here: Do n=200K instead. Or to be consistent with what I suggested above, do n=200K-300K with an appropriate k-range that gives you ~90% chance of finding a twin. Gary |
I'll be willing to help TPS at n=333,333 once the dust settles, and all reported primes drop from the Top-5000 list. Moo-moo, can you remind us how far have you sieved, I assume at least to 1000T?
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[QUOTE=gd_barnes;130597]First, I don't suggest waiting for n=333333 to find a twin. The chances of you finding a twin are no greater now than when you started regardless of what has already been tested. Interest will wane once the last n=333333 prime has dropped off of top-5000. I've seen it already waning. Essentially the same sized prime gets boring after a while.
[/QUOTE] TPS/PG will be staying on n=333,333 as long as there are still some of those primes on the top 5000 list. I'll only consider switching to a broad n-range once all of the n=333,333 primes have dropped off the list. But it isn't likely that we'll be moving away from n=333,333 immediately after the last n=333,333 prime has dropped off. We've sieved a huge range for that n (1-100G), and I don't want to let most of it go to waste. [QUOTE] Suggestions: 1.) n=350K-450K 2.) k=3 to 2M (odd values only); that's a starting value of three, not three million. [/QUOTE] In a previous poll: [url]http://www.mersenneforum.org/showthread.php?t=69743[/url] most people said that they wanted to search n's between n=460K and n=520K after finding a twin for n=333333. Therefore, I'll probably pick the range n=430K-530K and a k range from 3 to 3M, to account for the higher n-range. [QUOTE] 3.) Sieving: NewPGen with the increment counter set on. In a distributed effort, have people reserve n-value ranges instead of P-values for sieving. Determine ahead of time what the optimum sieve depth is and have everyone sieve to the same depth; increasing moderately as you go up by n-value. [/QUOTE] Could you give us a quick guide on how to use NewPGen's increment counter? I'll see what a good sieve depth is after trying out some values. |
[QUOTE=Kosmaj;130674]Moo-moo, can you remind us how far have you sieved, I assume at least to 1000T?[/QUOTE]
We've sieved a total of 4752T. All ranges below 4000T have been sieved, but there are some gaps between 4000T to 5500T. |
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