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2021-03-03, 13:59
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#1 |
Jun 2003
Suva, Fiji
2×1,021 Posts |
Multithreading existing code
I am wondering if there are c programmers out there who could take a great piece of prime finding software and make it multi thread.
The software helps to find constant k such that the power series k*2*n+/-1, variable n, is very prime. The existing software was written by Robert Gerbicz and can be found at: https://sites.google.com/site/robertgerbicz/payam payam2.c |
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2021-03-03, 16:57
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#2 | |
Jul 2003
Behind BB
2×7×11×13 Posts |
Quote:
I have questions about the definition here. Is there a scientific definition for "very prime"? We know there is a set of k values for which the series, k*2^n+1, is never prime. Do we know that a k value (call it k_many) that produces many primes for say, n < 1000, will have have a higher probability of generating a prime for a large value of n = N (say N=10^6) than a k value (call it k_few) that produced few primes for n < 1000? Assume we trial factor both k_many*2^N+1 and k_few*2^N+1 up to F = 2^B, where B is some value greater than 50. Both terms "survive" trial factoring, which means no factors were found. [Maybe we should also assume that F>>max(k_many,k_few)] Does the k_many term have a greater probability of being prime? If so, that is what I would call a "very prime" sequence. My larger question is, does the software find k values that generate "dense-after-trial-factoring" sequences or "very prime" sequences? Last fiddled with by masser on 2021-03-03 at 17:00 |
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2021-03-03, 17:30
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#3 | ||
Feb 2017
Nowhere
640910 Posts |
Quote:
From the link in the OP, Quote:
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2021-03-03, 18:28
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#4 |
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Jun 2003
Suva, Fiji
2·1,021 Posts |
Thank you for clarifying Dr S.
Very prime sequences arise from "very prime numbers" also been referred to on this site as a VPN. All VPNs are a multiple of k (an integer) and M(p) where M(p) is the product of primes with primitive root 2 less than or equal to p see OEIS http://oeis.org/A001122 for a list of those primes. k are found through application of the Chinese Remainder Theorem. There was an active search for VPN on Mersenneforum which stopped in 2014 https://www.mersenneforum.org/showthread.php?t=9755 The definitions of k etc in the first post of that thread differ to those in this post. But the sentiment is the same. I was thinking with today's computer power, this maybe worth looking at again. Last fiddled with by robert44444uk on 2021-03-03 at 18:29 |
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2021-03-04, 10:37
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#5 | |
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Jun 2003
Suva, Fiji
111111110102 Posts |
Quote:
Code:
R 267710937687553 52 100/8531 100/10000 K=620472594867229918205535 iteration=93 I=29389 Sun Oct 19 12:37:40 2014 R 267494780038573 52 100/7065 106/10000 K=619971607128284591472435 iteration=93 I=31889 Sun Oct 19 12:52:54 2014 R 269332638364685 52 100/9216 105/10000 K=624231204193877610405075 iteration=93 I=40088 Sun Oct 19 13:41:49 2014 K= 267494780038573*M(53) where M(53) = 3*5*11*13*19*29*37*53 Last fiddled with by robert44444uk on 2021-03-04 at 10:40 |
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2021-03-04, 13:39
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#6 |
Mar 2006
Germany
2·1,531 Posts |
On my old Prime Database there's still a page with Payam numbers of the Riesel side.
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2021-03-04, 14:32
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#7 | |
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Jun 2003
Suva, Fiji
2·1,021 Posts |
Quote:
Here is (I think) a table of the most recent Riesel records at each level. First column is the cumulative number of primes, and the other columns represent the smallest n value where that number of primes has been found. Code:
Best m28 m36 m52 m58 m60 m66 m82 m100 m106 m130 m138 m148 m162 m172 m178 m180 m196 m210 m226 m268 m292 m316 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 7 11 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 8 11 17 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 15 19 22 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 19 20 27 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 9 24 26 47 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 11 11 39 34 124 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 10 11 13 17 40 49 135 9 9 9 9 9 9 9 9 9 9 9 9 10 10 12 11 12 11 15 16 19 59 56 176 10 10 10 10 10 10 10 10 10 10 11 11 12 12 15 16 14 17 17 19 27 74 57 200 11 11 11 11 11 11 11 12 11 12 12 13 13 14 18 17 17 20 22 23 38 78 64 231 12 12 12 12 12 13 14 13 12 14 15 14 17 19 21 22 22 24 26 25 46 91 65 273 13 13 14 14 13 15 15 15 16 18 17 18 19 22 23 25 26 27 28 34 47 98 72 276 14 16 16 17 16 18 17 18 19 19 20 22 23 24 24 30 27 30 39 37 53 110 77 284 15 17 17 18 20 20 20 20 20 21 22 27 27 30 32 32 38 37 45 44 60 134 79 300 16 19 19 20 21 22 23 22 22 25 25 31 33 33 38 35 39 41 48 46 72 135 85 320 17 23 23 24 24 25 27 23 26 31 29 36 35 36 39 36 40 44 56 47 77 183 88 419 18 26 26 27 27 29 28 28 29 34 33 40 38 41 40 49 49 46 65 55 83 192 100 444 19 28 28 29 29 31 33 33 33 38 34 46 44 45 53 54 59 54 73 71 94 222 115 465 20 30 30 32 32 34 34 36 36 39 41 49 51 52 55 55 65 61 76 78 105 237 136 483 21 34 34 37 35 38 37 40 37 47 47 53 54 61 67 68 68 67 82 90 115 241 144 490 22 35 35 39 41 43 44 41 42 48 52 56 57 66 74 70 84 77 96 99 119 250 203 506 23 41 43 41 47 48 50 45 43 56 57 58 58 73 81 78 90 89 98 114 133 271 229 651 24 45 45 46 48 53 54 50 54 60 64 72 78 76 88 81 94 100 100 122 151 315 280 653 25 49 51 49 56 57 57 55 56 63 70 81 79 81 94 83 100 104 101 130 153 320 324 670 26 55 55 57 60 59 59 59 62 70 74 85 86 86 106 102 108 115 114 150 185 389 413 710 27 58 61 58 65 63 63 62 64 76 76 86 89 92 114 117 116 138 136 153 188 405 464 739 28 64 64 67 68 73 73 69 80 84 87 87 91 102 122 122 120 141 145 170 193 410 489 804 29 68 68 70 75 77 83 72 83 89 90 93 103 105 129 142 133 145 152 178 216 418 497 874 30 74 74 75 80 83 85 76 92 94 92 94 112 114 137 149 147 146 169 201 225 460 606 995 31 79 79 82 87 88 88 83 102 107 99 113 120 126 140 156 148 159 184 233 265 497 631 1007 32 89 90 92 89 94 94 92 104 110 103 123 140 127 151 164 168 163 192 239 272 500 718 1068 33 91 94 94 91 97 97 100 106 118 109 130 149 146 163 180 175 168 203 244 280 520 724 1086 34 98 98 98 105 110 112 111 115 121 129 136 160 168 173 181 176 171 226 245 292 538 756 1192 35 101 101 101 109 116 122 124 123 146 130 152 167 179 196 201 212 229 245 289 351 607 802 1200 36 115 115 115 118 120 128 130 125 155 136 158 175 180 203 214 231 245 252 303 364 620 837 1333 37 118 118 121 124 124 135 135 159 161 139 160 176 181 224 217 251 260 269 316 393 629 1144 1339 38 125 125 131 129 136 143 147 163 164 142 175 187 220 229 232 259 276 304 330 402 649 1171 1454 39 131 131 146 140 141 153 161 169 169 150 184 207 227 255 254 286 289 329 338 454 689 1290 1466 40 137 137 152 152 146 154 162 171 172 160 196 210 232 263 281 310 290 337 354 489 798 1366 1526 41 141 141 158 162 160 160 183 191 173 169 208 219 250 278 285 321 296 386 385 502 818 1399 1532 42 163 163 163 173 167 167 187 200 179 185 215 226 267 290 302 325 302 407 419 529 828 1439 1850 43 171 171 172 187 180 180 205 224 182 194 234 265 271 316 333 363 357 430 445 546 929 1690 1939 44 176 176 183 193 182 182 223 230 202 220 240 272 274 334 360 383 373 447 502 547 982 1831 2057 45 188 198 213 213 188 188 228 240 237 235 264 296 277 339 366 394 376 477 553 608 1147 1839 2293 46 204 207 217 223 204 204 233 248 239 258 278 304 282 361 378 422 387 478 562 637 1160 1904 2370 47 218 218 226 230 249 249 237 249 243 291 329 316 323 382 422 439 447 480 585 653 1227 2151 2505 48 241 250 257 241 276 262 241 259 248 318 361 341 332 387 432 462 474 534 598 663 1231 2291 2509 49 251 265 261 259 278 275 269 289 251 327 375 351 351 411 466 476 502 571 605 694 1267 2323 2617 50 262 277 270 262 295 283 283 301 322 350 384 359 367 422 484 478 525 582 609 698 1286 2386 3226 51 273 290 273 287 304 290 321 329 350 352 397 407 445 431 504 495 533 646 612 759 1313 2425 3452 52 278 322 278 295 315 317 356 354 361 373 407 425 449 450 560 555 557 667 615 823 1330 2533 3837 53 296 328 296 309 318 348 362 384 392 389 410 452 463 454 587 570 611 710 647 854 1464 2535 3852 54 317 333 327 317 338 374 378 426 397 427 440 456 468 467 588 577 619 723 702 1000 1508 2567 3935 55 328 360 352 328 347 383 384 450 421 445 473 510 533 476 624 579 636 766 782 1037 1547 2581 4016 56 348 367 362 348 352 396 385 456 444 450 495 520 578 490 644 585 674 802 805 1070 1653 2847 4329 57 361 440 407 361 375 403 386 499 446 493 521 541 642 651 677 589 764 850 820 1118 1655 2869 4706 58 371 458 417 371 397 410 416 507 451 517 539 585 665 706 700 590 771 924 938 1220 1711 3260 5472 59 395 461 448 395 404 428 447 528 479 543 591 627 706 711 711 678 826 949 1023 1288 1820 3266 5601 60 411 492 457 462 411 506 455 579 491 551 626 628 763 712 712 725 897 998 1057 1369 1965 3375 5946 61 463 512 471 492 463 556 473 587 544 566 630 664 786 721 721 872 928 1086 1124 1402 2553 3431 6619 62 495 579 499 516 495 581 521 608 548 635 645 713 838 796 796 936 940 1087 1135 1416 2618 3586 7431 63 510 642 510 539 536 601 538 625 550 648 659 795 907 804 804 1004 962 1123 1148 1544 2718 3618 8478 64 519 657 519 571 541 615 563 634 553 693 706 825 934 809 809 1017 977 1133 1219 1545 2801 3698 8657 65 542 698 630 579 542 651 578 651 571 721 791 875 938 824 824 1028 1070 1139 1327 1621 3172 4360 9229 66 564 730 705 599 564 683 595 661 615 737 838 938 1048 884 884 1083 1101 1158 1328 1663 3203 4434 9970 67 565 732 722 628 565 689 615 716 616 794 908 1005 1059 893 893 1090 1127 1287 1348 1711 3329 4771 10372 68 581 745 777 634 581 758 628 755 690 840 950 1057 1089 967 967 1194 1134 1322 1403 1766 3439 5035 10674 69 637 783 795 650 676 772 637 806 719 849 975 1100 1128 1035 1035 1221 1276 1372 1431 1875 3537 5188 10930 70 682 893 864 721 692 789 682 813 749 910 1049 1119 1183 1096 1096 1250 1322 1550 1491 1895 3657 5223 11045 71 695 897 916 732 788 794 695 846 808 972 1156 1156 1289 1184 1184 1442 1382 1648 1518 1942 3919 5552 11734 72 717 967 987 736 832 836 717 867 839 1011 1216 1199 1312 1309 1309 1553 1400 1721 1723 2126 4229 5650 12053 73 720 1113 1065 754 834 863 720 951 867 1023 1221 1271 1422 1455 1635 1584 1450 1748 1796 2305 4295 6071 12833 74 764 1141 1121 764 851 945 783 954 880 1103 1348 1322 1478 1475 1778 1626 1507 1865 1977 2408 4914 6129 13756 75 813 1179 1165 851 938 1001 813 1060 1108 1108 1430 1346 1483 1562 1843 1748 1660 1913 2003 2551 4925 6380 13873 76 828 1284 1233 1046 957 1040 828 1066 1169 1157 1502 1348 1526 1597 1883 1852 1808 1955 2132 2697 5343 7357 13901 77 848 1382 1268 1056 976 1046 848 1127 1172 1239 1508 1356 1691 1670 1912 1964 1878 1975 2238 2965 5648 8159 13921 78 1032 1495 1318 1065 1032 1102 1084 1143 1175 1270 1600 1370 1744 1819 1950 2012 2050 2111 2305 3204 5887 9047 14867 79 1036 1541 1462 1117 1036 1130 1090 1245 1180 1409 1657 1417 1814 1863 2021 2064 2123 2132 2317 3344 6138 9358 16378 80 1040 1613 1501 1204 1040 1293 1175 1247 1190 1521 1702 1573 1821 1876 2092 2294 2216 2449 2367 3608 6362 9834 17123 81 1173 1707 1509 1210 1173 1319 1187 1264 1292 1538 1876 1846 1842 1915 2345 2425 2244 2617 2370 4050 6370 9928 17417 82 1180 1721 1711 1287 1180 1427 1212 1487 1360 1674 1889 1884 1864 1950 2416 2627 2391 2881 2588 4120 6395 9950 18578 83 1302 1757 1818 1382 1372 1465 1302 1493 1416 1698 2058 1887 2148 2321 2480 2639 2554 2921 2671 4243 6939 10529 20832 84 1303 2154 1879 1400 1483 1595 1303 1561 1459 1835 2158 2076 2281 2454 2524 2839 2716 3090 3107 4387 7615 10643 25571 85 1413 2248 1907 1413 1507 1633 1609 1723 1472 1898 2255 2158 2323 2547 2567 3062 2776 3258 3314 4426 7674 12082 27141 86 1421 2276 1987 1421 1628 1662 1784 1762 1525 1998 2360 2309 2439 2655 2709 3225 2813 3350 3322 4563 7741 13201 28935 87 1495 2284 1997 1495 1666 1677 1794 1844 1590 2099 2471 2333 2571 3162 2855 3397 2923 3633 4005 5118 8219 13220 30331 88 1659 2319 2093 1659 1713 1706 1933 1940 1680 2159 2512 2533 2713 3211 3200 3518 2928 3753 4955 5310 8732 13787 30777 89 1721 2353 2098 1884 1815 1815 2003 1945 1721 2191 2550 2634 2787 3236 3374 3797 3410 3771 5085 5398 8935 15024 30820 90 1740 2584 2369 2056 1818 1829 2144 1983 1740 2370 2726 2746 2861 3362 3474 3869 3454 4212 5212 5562 9716 15509 31838 91 1857 2819 2548 2186 1857 2045 2158 2020 1879 2464 2825 2812 3118 3392 3479 4025 3625 4480 5266 5720 10235 16290 33178 92 1917 3030 2658 2233 1930 2108 2170 2024 1917 2617 2921 3074 3258 3747 3591 4193 3649 4560 5391 5842 10291 18304 34444 93 1921 3145 2765 2342 2022 2210 2218 2295 1921 2669 2947 3185 3433 3839 3678 4351 3701 4633 5460 6090 10758 18777 38407 94 1931 3270 3096 2548 2315 2332 2460 2653 1931 2754 3113 3293 3570 4205 3708 4517 3730 4719 5524 7498 11114 19863 44354 95 2081 3583 3458 2615 2529 2378 2635 2744 2081 2851 3248 3349 3831 4314 4075 4849 4268 5494 5589 7629 11289 21699 44491 96 2102 3612 3812 2694 2622 2701 2701 3233 2102 3256 3461 3746 4128 4514 4595 5116 4339 5666 5793 7979 11926 22361 44744 97 2152 3680 3832 2912 2792 2792 2792 3324 2152 3354 3746 4205 4240 5164 4607 5178 4661 5901 6349 8292 12968 22617 46873 98 2185 3834 4282 3299 3228 2929 3839 3548 2185 3791 3877 4261 4656 5504 5016 5207 4926 6421 6360 9129 13676 27204 50741 99 2501 4203 4602 3503 3245 3076 4094 3619 2501 3902 4047 4375 4993 5627 5054 5309 4986 6517 6836 9171 16283 27206 51857 100 2570 4644 5162 3556 3810 3154 4114 3681 2570 3905 4275 4608 5255 5830 5431 5832 5295 7064 6885 9845 20603 27717 62843 101 3045 5840 5241 3943 3945 3158 4476 4063 3045 3950 4567 5134 5412 6052 5609 6249 5753 7601 7483 9915 23009 28071 62934 102 3222 5913 5557 4395 4158 3222 4792 4115 3280 4157 4847 5320 5498 6304 5789 6490 6028 7767 7536 10041 23206 29662 66755 103 3363 5983 5909 4481 4292 3461 5119 4860 3363 4293 5590 5395 5690 6682 6600 6514 6712 8012 7656 10274 27572 34554 68490 104 3429 6008 6480 4559 4299 3481 5361 5134 3429 4501 5886 5448 6263 6825 6765 6561 6934 8757 8532 10720 27752 34780 71484 105 3588 6975 6706 4976 4381 4023 5486 5437 3588 4689 6028 5459 6862 7902 7112 7197 8076 8979 13841 11218 28985 36653 76888 106 3659 7034 7228 4985 4505 4107 5597 5619 3659 5004 6378 6202 6902 8080 7162 7705 8100 9499 15516 11400 29174 38805 107 4195 7773 7646 5232 4628 4195 5806 5628 4574 5368 6848 7056 7080 8676 7414 7951 8604 9740 16142 12486 32980 39968 108 4731 7827 8312 5409 4731 4879 6466 5924 5013 5721 7021 7080 7324 8892 8120 8209 8789 10625 16670 13161 34044 43524 109 4899 8018 8592 5840 4899 5111 6777 5927 5032 6343 7079 7384 7655 9389 8180 8382 9273 11537 16921 14569 38589 44212 110 5246 8677 8691 5953 5628 5289 6845 6446 5246 6496 7082 8421 8169 9911 8270 8984 9579 13578 17482 14871 38807 48563 111 5411 9729 8968 5996 5776 5781 7297 6544 5411 7681 7104 8435 8206 10875 8740 9833 9762 14621 18411 15173 38852 50387 112 5459 10591 9965 6159 5880 6233 7414 6576 5459 7731 7514 9443 8747 11026 8970 9956 15478 15501 19248 16264 40067 53183 113 5528 10677 10035 6213 5949 6453 7659 6578 5528 8302 8279 9927 9104 11183 9547 13610 16181 16539 20238 18277 40343 55558 114 5668 10683 10041 6218 6042 6468 8322 7091 5668 8419 8372 11102 9423 12804 13914 14968 16282 16717 22978 18476 40546 57334 115 6072 11556 11028 6872 6072 6733 8326 7510 6132 8946 8568 11194 10124 13772 15543 15027 17552 17404 23571 19399 40974 60400 116 6131 15029 11387 7388 6131 6852 9031 8150 6609 9478 8677 12485 10632 13886 15928 15335 17769 18416 23597 21391 41284 64575 117 6824 16189 12053 7516 6824 6961 9611 8458 7105 9897 8917 13728 10936 14388 16812 15489 17886 19506 23913 22958 41969 65949 118 7535 24392 13166 7557 8928 7535 10003 9084 8086 10065 10574 14333 10951 14957 17010 15820 18744 20541 24163 24591 42812 67007 119 7618 26228 13242 7799 10679 7618 10153 9625 8444 10215 12163 14900 12947 16304 17580 16002 21044 21058 24904 24987 50939 68339 120 7680 29394 13359 8412 11741 7680 10528 9777 9540 11358 12360 15350 18043 19028 18371 16107 22907 21424 26282 27198 55233 77362 121 8169 39390 14536 9439 12061 8169 11112 9859 10940 11367 12362 15480 19929 19860 20710 16173 23078 30904 27210 55539 79234 122 8642 14625 10161 13594 8642 11650 10533 11359 12389 13210 15845 20279 22758 21597 17801 24472 33685 31589 58648 80278 123 9502 18104 11609 14154 9502 12357 11369 11360 13208 13652 17787 20771 23256 21933 17883 25559 35756 32008 59824 82629 124 9506 18282 13511 17304 9506 12837 13175 11716 13464 14583 18456 22269 23457 22556 18184 27015 36148 32894 62689 87285 125 9981 18509 13517 20192 9981 12916 13983 12639 15452 16088 18548 23016 24082 23618 18641 27504 38794 34533 64679 90402 126 10332 22830 13674 20483 10332 13025 14385 13274 15745 17688 20412 23901 25003 28160 20824 27755 41242 36982 65516 96978 127 10848 25111 14560 20775 10848 13162 14453 14251 17819 19114 21549 24189 27467 31383 22279 28424 41792 37789 68311 128 11198 27308 16051 24046 11198 14574 14462 14820 18113 20503 22879 25223 31517 32904 22969 34351 44196 38521 129 12577 28986 16472 24120 12577 15860 14842 14886 18700 22211 23528 29096 33759 33100 23555 36933 44544 41216 130 12672 30957 17532 24396 12672 18142 15008 14902 19066 22887 27752 30467 35268 37209 25025 37822 45020 42162 131 13073 32318 17587 26136 13073 20931 15303 15589 19096 25002 28208 35060 36504 38416 25042 38396 49873 43760 132 13080 33221 19262 26830 13080 26468 17653 15982 21543 26252 31110 36510 39798 41502 25696 39864 48083 133 15043 34078 20000 28753 15043 27535 18144 20811 22956 26523 31253 38082 40745 48724 27460 41950 50358 134 16900 44589 20662 28596 16900 29052 25142 20863 23497 27251 32497 43141 45401 28895 45468 52282 135 19531 48283 21701 28925 19531 31521 25761 21014 26273 28233 34641 44753 46293 29104 51450 57222 136 20218 22884 29636 20218 33242 29403 22161 27050 29803 35248 48641 46454 29143 57938 66413 137 21960 27779 37499 21960 33836 34122 22396 27750 30173 36506 49677 49851 29808 58446 68512 138 22541 32018 42575 22541 35402 35326 22670 29100 31212 40242 56391 53357 30293 63706 72754 139 23034 32220 47388 23034 35755 39155 24430 29788 31424 43575 59791 56237 33118 63953 75541 140 24154 32967 48448 24154 37270 40441 24679 30037 32583 45364 62726 56248 34523 65113 141 24871 33865 27402 38683 44138 24871 32456 33696 54698 78211 57066 38647 67517 142 25771 38148 30612 41094 44763 25771 34887 36106 63384 78815 57442 39807 143 29135 41037 32912 41490 50213 29135 36679 36320 71207 66230 41365 144 29319 42456 33475 41563 50893 29319 37472 40172 66821 44472 145 35119 43490 36373 42239 53950 35119 38388 42457 71819 45690 146 35510 45494 36973 47069 67234 35510 40418 44900 73893 49501 147 36069 47136 38026 48702 72873 36069 41490 46170 75107 51039 148 37768 40007 52730 76577 37768 50698 46787 77583 56904 149 39663 42601 53444 77861 39663 47920 82052 58549 150 42842 42842 57873 78115 42846 49784 90954 60146 151 44096 50904 63931 80326 44096 53246 61970 152 44497 51658 71270 82317 44497 55579 63970 153 46270 53909 77127 92273 46270 59638 64199 154 47433 60193 79950 96914 47433 60260 68059 155 48365 61232 79974 105955 48365 64574 69898 156 51853 65240 80445 108330 51853 67190 75331 157 52967 66052 97018 117837 52967 67470 76853 158 53035 95621 103177 124578 53035 71221 86023 159 58573 97411 103445 139973 58573 73142 102954 160 59598 100438 106295 143571 59598 77776 112308 161 67574 103309 158755 67574 80678 112904 162 68587 110902 159331 68587 84684 125556 163 69612 114094 160412 69612 87557 131807 164 74332 128237 74332 96045 143989 165 77853 136696 77853 102231 146713 166 78530 145204 78530 102651 150515 167 81716 147339 81716 104202 156736 168 87299 165044 87299 104655 165557 169 95077 172883 95077 111235 180017 170 99889 99889 111239 191950 171 118689 118983 118689 192926 172 119254 136499 119254 211703 173 129630 139691 129630 216995 174 134337 140555 134337 242980 175 134490 141834 134490 176 141805 145565 141805 177 146149 153125 146149 178 159874 160854 159874 179 163330 181539 163330 180 168072 190248 168072 181 174712 205078 174712 182 177119 212228 177119 183 177684 218973 177684 184 190958 232755 190958 185 193804 239683 193804 186 197942 245214 197942 187 210616 260978 210616 188 226559 264131 226559 189 227776 273212 227776 190 229069 229069 191 245288 245288 192 255530 255530 193 294807 294807 194 318934 318934 195 334623 334623 196 334645 334645 197 363020 363020 198 376732 376732 199 403709 403709 200 414907 414907 201 449150 449150 202 472040 472040 203 479697 479697 204 496187 496187 205 498496 498496 206 517692 517692 207 531133 531133 208 549598 549598 209 587833 587833 210 608207 608207 211 608462 608462 212 639888 639888 213 716611 716611 214 788439 788439 215 834442 834442 Last fiddled with by robert44444uk on 2021-03-04 at 14:33 |
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2021-03-12, 12:35
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#8 |
Aug 2020
79*6581e-4;3*2539e-3
2×5×73 Posts |
That sounds interesting, strange that it was just discontinued.
So apparently it's two parts, first computation of payam k and then doing the sieving/LLR with that k? I started payampentium using the supplied in.txt and it's doing something, but I have no clue what the values in in.txt mean. Will I just rediscover the k you already found 15 years ago? It created a recordtable.txt, which seems to contain the K(?) that is multiplied with 3*5*11*13*19*29*37*53 to yield the k and also says how many primes were found until which n. So now I have a list of good potential k-values, nice. Last fiddled with by bur on 2021-03-12 at 12:44 |
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2021-03-13, 08:30
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#9 | |
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Jun 2003
Suva, Fiji
2·1,021 Posts |
Quote:
Yes it will rediscover K that provide very prime series. To get new results you need to scan a different area. You will need to also set up a progress file where many variables are kept...progress.txt . The format can be downloaded at the software site. c - 1 for Sierpinski series and -1 for Riesel series. i.e. K*M*2^n+1 and K*M*2^n-1 The E value is one less than the product of primes with primitive root 2 that you want to search - so 52 means 3*5*11*13*19*29*37*53 iteration Start this at 100000 to be sure you are looking at a fresh range. If you want to look at rich VPS areas don't look smaller than E = 82. You would get 10-20 or so VPS results in a day. I this is a subcategory of iteration to ensure the program can pick up where it left off I'm using payam2.exe as it allows for smaller E to be used and is faster. In the in.txt file you will see any number of variables, but you don't need to change them for smaller M. You can switch off the smith_check indicator by using 0 as the flag for larger M, which will provide a more detailed search but perhaps not pick up the better values as quickly. For very large M, say 268 onwards, then you also need to reduce vps count to say 10, as candidates only pop up twice a day for 268 and once in a blue moon for higher numbers. I have found 1 payam number at 316 and 1 at 292 after 5 days of searching, but the 316 is a fluke - you could go months without finding a payam number. No-one ever found a 346 in the years of searching. I've decided to look at the Sierpinski side starting everything from 100000. My best result after 2 days of searching is 114 primes in 10000 n. The reason I wanted to make this multithread is to really speed up the search. |
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2021-03-14, 17:15
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#10 |
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Aug 2020
79*6581e-4;3*2539e-3
2×5×73 Posts |
Ok, so the goal was finding k that produced a large number of primes for small n and not so much identifying one or two such k and then doing a thorough search for n up to a few million?
I wonder if the prime density remains that high even when n ~ 1e6. And more importantly, if even after sieving the prime density would remain higher than for other k. |
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2021-03-15, 18:13
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#11 | |
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Jun 2003
Suva, Fiji
111111110102 Posts |
Quote:
Checking is quite slow for these k, because there is no really superfast sieve (although one could be constructed!), newpgen is not really geared from today's computers. Also, because there are no small factors for any of the k*2^n+ or -1, a significantly greater number of n need a prp test. Hence a payam k series will remain, on average, more prime at any level of n compared to a random k because of this. |
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