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Post small primes and tell us about your progress here
Well, there is no thread to post small primes of reserved k's
so I decided to create a new thread. For my k=3611911875 up to n=100800 I found additional small primes for following n's: 75088 90363 91405 93732 <-- 100th prime 97888 There are now 101 primes to 100k and 6 primes in the 134-200k range. I'll continue the work in the 100-134k range and I just began tests in the 200-220 range. I sieved candidates in the 200-400 range to 800 bn using ksieve. |
Ok, I searched up my k=158823815 up to n=85000 (and a little beyond this moment). While doing this I found 110 primes:
1, 3, 4, 7, 11, 12, 16, 19, 21, 28, 31, 40, 47, 53, 62, 69, 75, 76, 82, 98, 103, 104, 115, 118, 134, 151, 152, 154, 163, 177, 257, 261, 271, 274, 309, 328, 331, 349, 410, 452, 526, 573, 597, 616, 700, 714, 738, 862, 922, 923, 1009, 1025, 1306, 1564, 1848, 1936, 2032, 2061, 2074, 2212, 2255, 2467, 2522, 2627, 2678, 2753, 2788, 3011, 3979, 4185, 4983, 5189, 5494, 5850, 6838, 7076, 7469, 7816, 8048, 8226, 8396, 8624, 8738, 12933, 13540, 15779, 17388, 18792, 20849, 21382, 21446, 22330, 23681, 24527, 27299, 28409, 32634, 33558, 35264, 38374, 45234, 52257, 55111, 56096, 64593, 70900, 73506, 75326, 75617, 85535 With the other prime for n=336542 this makes 111 primes found for this k. Cyrix |
Oh, a typing error: Actual k=1581823815.
Cyrix |
Then this is now our "best [I]k[/I]" since the 100th prime occured for n=38374. The previous best was k=2995125705, and i(100)=60190.
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I tested the 15k = 968911515 from n=2 to n=50000 and found the following primes. I will [b]not[/b] continue testing this 15k.
[code] 968911515 3 968911515 6 968911515 13 968911515 15 968911515 16 968911515 18 968911515 21 968911515 23 968911515 28 968911515 31 968911515 32 968911515 39 968911515 40 968911515 43 968911515 54 968911515 63 968911515 70 968911515 71 968911515 74 968911515 84 968911515 88 968911515 92 968911515 100 968911515 110 968911515 128 968911515 136 968911515 139 968911515 151 968911515 203 968911515 218 968911515 223 968911515 238 968911515 248 968911515 253 968911515 321 968911515 349 968911515 356 968911515 362 968911515 374 968911515 507 968911515 533 968911515 572 968911515 952 968911515 970 968911515 993 968911515 1037 968911515 1262 968911515 1373 968911515 1378 968911515 1408 968911515 1601 968911515 1602 968911515 1615 968911515 1985 968911515 2338 968911515 2955 968911515 3111 968911515 3170 968911515 3828 968911515 4171 968911515 4857 968911515 5646 968911515 7035 968911515 8861 968911515 9331 968911515 11432 968911515 13846 968911515 15273 968911515 15638 968911515 27221 968911515 28197 968911515 34579 968911515 40628 968911515 42459 968911515 45364 968911515 46492 968911515 46632 [/code] |
I also tested the 15k = 475977645 from n=2 to n=50000 and found the following primes. I will [b]not[/b] continue testing this 15k.
[code] 475977645 3 475977645 6 475977645 7 475977645 21 475977645 23 475977645 28 475977645 34 475977645 37 475977645 46 475977645 54 475977645 59 475977645 67 475977645 75 475977645 81 475977645 96 475977645 99 475977645 101 475977645 107 475977645 112 475977645 114 475977645 123 475977645 138 475977645 153 475977645 171 475977645 215 475977645 233 475977645 389 475977645 421 475977645 463 475977645 595 475977645 652 475977645 793 475977645 821 475977645 952 475977645 970 475977645 1167 475977645 1669 475977645 1899 475977645 1967 475977645 2025 475977645 2217 475977645 2254 475977645 2260 475977645 3059 475977645 3118 475977645 3787 475977645 4828 475977645 5352 475977645 6049 475977645 6544 475977645 6675 475977645 6676 475977645 6685 475977645 6915 475977645 7266 475977645 7868 475977645 8659 475977645 9040 475977645 9382 475977645 9584 475977645 9990 475977645 10146 475977645 10192 475977645 10757 475977645 11492 475977645 11788 475977645 12181 475977645 12430 475977645 12838 475977645 13878 475977645 14478 475977645 14691 475977645 14754 475977645 15460 475977645 16729 475977645 17037 475977645 18310 475977645 22465 475977645 23662 475977645 37615 475977645 41087 475977645 41827 475977645 43860 475977645 44640 [/code] |
Here are the first 79 primes for 515106735. I'll continue searching to
see where the 100th prime occurs. 515106735 4 515106735 5 515106735 27 515106735 38 515106735 40 515106735 62 515106735 63 515106735 66 515106735 67 515106735 70 515106735 89 515106735 99 515106735 114 515106735 139 515106735 152 515106735 158 515106735 185 515106735 189 515106735 222 515106735 269 515106735 272 515106735 297 515106735 341 515106735 387 515106735 394 515106735 483 515106735 534 515106735 559 515106735 640 515106735 659 515106735 683 515106735 686 515106735 724 515106735 760 515106735 794 515106735 830 515106735 854 515106735 1121 515106735 1183 515106735 1314 515106735 1383 515106735 1427 515106735 1474 515106735 1521 515106735 1806 515106735 1896 515106735 2001 515106735 2092 515106735 2111 515106735 2282 515106735 2634 515106735 2737 515106735 3221 515106735 3343 515106735 4079 515106735 4137 515106735 4963 515106735 5086 515106735 5279 515106735 5567 515106735 6171 515106735 6623 515106735 10702 515106735 13178 515106735 14129 515106735 16075 515106735 16110 515106735 17041 515106735 18006 515106735 19518 515106735 21961 515106735 23612 515106735 26781 515106735 27811 515106735 29367 515106735 47173 515106735 58301 515106735 58722 515106735 61684 |
First hundred primes for 860541825
Here are the first hundred primes for 860541825.
The 100th occurs at n=54696 [QUOTE] 860541825 1 860541825 2 860541825 3 860541825 7 860541825 8 860541825 16 860541825 19 860541825 24 860541825 41 860541825 43 860541825 44 860541825 47 860541825 48 860541825 53 860541825 76 860541825 87 860541825 89 860541825 108 860541825 114 860541825 128 860541825 131 860541825 141 860541825 145 860541825 148 860541825 155 860541825 173 860541825 180 860541825 197 860541825 213 860541825 220 860541825 241 860541825 243 860541825 277 860541825 286 860541825 302 860541825 331 860541825 341 860541825 447 860541825 467 860541825 509 860541825 574 860541825 598 860541825 628 860541825 684 860541825 734 860541825 786 860541825 820 860541825 823 860541825 827 860541825 872 860541825 929 860541825 946 860541825 950 860541825 976 860541825 1067 860541825 1246 860541825 1405 860541825 1613 860541825 1712 860541825 1890 860541825 1939 860541825 2036 860541825 2105 860541825 2226 860541825 2630 860541825 2936 860541825 3151 860541825 3905 860541825 4324 860541825 4595 860541825 4891 860541825 5802 860541825 7355 860541825 7754 860541825 7805 860541825 8167 860541825 8915 860541825 11184 860541825 11755 860541825 12043 860541825 12999 860541825 13004 860541825 14180 860541825 15044 860541825 16155 860541825 16664 860541825 17447 860541825 18042 860541825 18811 860541825 21810 860541825 26177 860541825 27377 860541825 27632 860541825 30495 860541825 30498 860541825 34180 860541825 34347 860541825 40104 860541825 54696 [/QUOTE] |
[FONT=Arial]After looking at Primoproths and Payam numbers, I'm now running a script
to see how many primes are generated for k's constructed by multiplying all combinations of the first 11 primes. The top 20 so far are listed below and ALL fall into the 15*k category. Some have primes listed on the top-5000 site but some do not. Was something like this run to generate the original 15k candidate list? Format: #primes for n=1-10000, k 60 29058315 60 842691135 61 19635 61 25935 61 102765 61 15935205 61 3457939485 61 47912205 61 8580495 62 10015005 62 10555545 62 16545165 62 2330445 62 373065 63 111546435 64 14637315 64 25634895 65 190285095 66 26565 68 49335 thanks, Larry |
I believe the original 15k candidate list was produced by calculating the weights of all k divisible by 15 up to a certain limit and removing all of those k's with a weight lower than some cutoff.
There is a program available online called psieve that will compute the weights of a sequence of k values. You should check it out... regards, masser |
Here are the first 100 primes for 8331405
8331405 9 8331405 11 8331405 17 8331405 21 8331405 31 8331405 32 8331405 33 8331405 45 8331405 57 8331405 61 8331405 64 8331405 67 8331405 69 8331405 77 8331405 80 8331405 85 8331405 88 8331405 107 8331405 115 8331405 117 8331405 120 8331405 121 8331405 124 8331405 147 8331405 155 8331405 161 8331405 164 8331405 168 8331405 177 8331405 179 8331405 221 8331405 232 8331405 258 8331405 261 8331405 264 8331405 281 8331405 282 8331405 299 8331405 308 8331405 342 8331405 415 8331405 471 8331405 503 8331405 504 8331405 505 8331405 537 8331405 572 8331405 680 8331405 989 8331405 1328 8331405 1565 8331405 1607 8331405 1613 8331405 1841 8331405 1953 8331405 2509 8331405 2692 8331405 2739 8331405 2834 8331405 3627 8331405 3735 8331405 3870 8331405 3960 8331405 4083 8331405 4682 8331405 4788 8331405 5187 8331405 5247 8331405 5623 8331405 5804 8331405 6015 8331405 6020 8331405 6405 8331405 6569 8331405 7052 8331405 7315 8331405 7477 8331405 7489 8331405 8389 8331405 8800 8331405 10407 8331405 10512 8331405 12035 8331405 13015 8331405 14634 8331405 14941 8331405 16339 8331405 16367 8331405 16554 8331405 26533 8331405 28153 8331405 29081 8331405 30222 8331405 32391 8331405 36371 8331405 37323 8331405 39251 8331405 43935 8331405 45052 8331405 45773 |
Larry,
8331405*2-1 = 16662809 is also prime. Thus, the 100th prime occurs for n=45052 while in this respect the best among "old" candidates is k=1581823815 where the 100th prime occurs for n=38374. Very close! More such results can be found [URL=http://www.15k.org/stats.htm]here[/URL]. |
100 primes
For the groups interest, the best +1 number to get to a hundred primes got there with n=3258 with k = 1108828374241*M(59), where M(59) is a certain multiple of small primes p up to 59, excluding those with order base 2 of less than p-1. This is a Payam number, par excellence.
It may well be that the - series produced better, but I don't know for sure. In any case there are better numbers out there, although Phil Carmody thought that this was close to the ideal number at to that (i.e. 100 primes) range. For your interest, this number was checked up to n=100000 with "only" 140 primes, so we stopped checking it in earnest - ther are plenty with greater than that at that level, but software does not allow for fast checking of theses k, because k is rather large. Regards Robert Smith Ps this series is prime at n= (note the huge gap at 4495-7544) 3 11 13 14 18 19 23 25 26 29 31 42 45 50 64 65 71 86 98 101 116 119 134 191 194 195 212 257 259 269 276 284 285 294 307 324 396 403 406 420 447 449 459 480 486 540 545 602 607 625 654 659 703 742 780 827 828 838 848 867 923 960 976 982 1005 1011 1021 1037 1049 1081 1100 1130 1145 1192 1254 1327 1427 1488 1548 1599 1647 1663 1684 1818 1844 1861 1880 1892 1946 1951 1971 2044 2130 2150 2227 2328 2393 3215 3224 3258 no 100 3289 3405 3436 3450 3722 3833 4172 4227 4337 4495 7544 8666 9037 9263 9758 10493 10628 12817 12959 15351 15762 16529 18995 19249 21117 22601 25769 27486 32648 33107 38099 40751 52586 53046 53060 53105 54241 60535 75013 85111 102912 126708 |
n=10000
PS A good count for primes at 10000, on the + side would be greater than 116. The candidate at that level was 2158430601663 *M(67), whose 116th prime is at n=9971
Regards Robert Smith |
Primes for 15k=187466565 with n from 1 to 100000
Here are primes I've found for 15k=187466565 with n from 1 to 100000:
[CODE]187466565 7 187466565 8 187466565 11 187466565 13 187466565 25 187466565 26 187466565 36 187466565 42 187466565 43 187466565 44 187466565 49 187466565 54 187466565 57 187466565 61 187466565 73 187466565 78 187466565 81 187466565 95 187466565 97 187466565 99 187466565 125 187466565 128 187466565 129 187466565 137 187466565 159 187466565 167 187466565 187 187466565 189 187466565 224 187466565 234 187466565 235 187466565 320 187466565 395 187466565 440 187466565 491 187466565 546 187466565 561 187466565 602 187466565 621 187466565 684 187466565 694 187466565 703 187466565 788 187466565 803 187466565 1158 187466565 1298 187466565 1422 187466565 1561 187466565 1727 187466565 1920 187466565 1946 187466565 2265 187466565 2675 187466565 2990 187466565 2994 187466565 3150 187466565 3296 187466565 3453 187466565 3525 187466565 3608 187466565 4006 187466565 4391 187466565 4688 187466565 4866 187466565 6842 187466565 6996 187466565 7014 187466565 7115 187466565 7393 187466565 7796 187466565 8505 187466565 9722 187466565 10587 187466565 11144 187466565 13574 187466565 13629 187466565 13793 187466565 13837 187466565 14678 187466565 15213 187466565 16210 187466565 16578 187466565 17355 187466565 19121 187466565 20215 187466565 21542 187466565 22635 187466565 28375 187466565 37256 187466565 41362 187466565 41785 187466565 41888 187466565 63163 187466565 65203 187466565 74889 187466565 78879 187466565 80097 187466565 92598[/CODE] I will continue testing this 15k with n up to 200000. |
Primes for k=3803443215:
n=1 through n=9 already on 15k.org site. 19,20,28 (PRPs), 53,56,58,112,235,313,339,367,372,376,397,413,454,525,543,576, 847,850,1027,1048,1061,1125,1160,1301, 1318, 1329,1503,1874, 2033,2536,2544,2553,2709,2953,3352,3649,3726,3887,4709,5075, 5167,5175,7092,10902,11933,12333,19168,19822,20276,21919, 22792,23567,24845,25793,39906,40936,42092,42258,51165,66033, 71287,72993,85641,90943,119027,159420,161247,167492,169409, 178053. 82 primes so far. I'm at roughly n=188000 currently, planning to process to n=250,000, then decide whether to push the low-weight number beyond 1M or this number to higher powers. What's the current cutoff for top-5000 entry? n=220,000? -Curtis |
The top-5000 cutoff is just below n=189,000 now.
-Larry |
Primes for 15k=187466565 with n from 100000 to 150000
The range 100000-150000 was sieved by me, gribozavr, and LLR'ed mostly by my friend yasya. :bow: So, please, give us both a credit for theese primes (write something like gribozavr and yasya): :banana:
[CODE]187466565 107376 187466565 109098 187466565 111081 187466565 127062 187466565 130833 187466565 134459[/CODE] n=150000-200000 in progress :showoff: |
1 Attachment(s)
Attached see primes for k=736320585 for 1<n<250000 (total of 100 primes incl. 2 Sophie Germain).
Continuing sieving and testing. |
I have finished testing k=187466565 for n=1-200k. I have found some more primes:
[CODE]187466565 160453 187466565 165138 187466565 178879 187466565 187871[/CODE] Whom do I send the lresults.txt? Can any of theese primes go into Top-5000? The biggest one is 56564 digits long. |
[QUOTE]Can any of theese primes go into Top-5000? The biggest one is 56564 digits long.[/QUOTE]
:no: because they are too small according to: [url]http://primes.utm.edu/primes/submit.php[/url] which states: [QUOTE]Currently primes must have 60222 or more digits to make the list[/QUOTE] In a years time the bar will have been raised to 70k :mad: |
Please dont tell me I have been wasting my time :censored: I just noticed the posts from gribozavr and he has already been testing my reserved K-187466565 :rant:
|
Back-filling 15k=355424355
15k.org lists a gap for 15k=355424355 between n=10000 and 170000.
In that gap you will find: 10982, 14779, 14852, 15331, 15434, 16202, 16303, 16831, 16923, 19875, 21161, 23702, 28127, 29972, 33404 Ongoing... |
[QUOTE=fatphil]15k.org lists a gap for 15k=355424355 between n=10000 and 170000.
In that gap you will find: 10982, 14779, 14852, 15331, 15434, 16202, 16303, 16831, 16923, 19875, 21161, 23702, 28127, 29972, 33404 Ongoing...[/QUOTE] Beginning to slow down a little, but still progress is good. 39315, 41043, 41592, 51211, 59238, 59772, 60612, 66268 Which, if I'm not mistaken, brings that k to 100 primes. Should I insert a dancing banana here? It appears to roughly have a density of 7 per n doubling, so another 7-10 in the 70000-170000 range is likely. |
[QUOTE=fatphil]
15k.org lists a gap for 15k=355424355 between n=10000 and 170000. In that gap you will find: 10982, 14779, 14852, 15331, 15434, 16202, 16303, 16831, 16923, 19875, 21161, 23702, 28127, 29972, 33404, 39315, 41043, 41592, 51211, 59238, 59772, 60612, 66268 Which, if I'm not mistaken, brings that k to 100 primes. Should I insert a dancing banana here? It appears to roughly have a density of 7 per n doubling, so another 7-10 in the 70000-170000 range is likely.[/QUOTE] 7 more was comparatively easy: 79481, 87840, 91514, 103375, 104433, 106609, 108981 ongoing... |
K-55951335
I am done with this K untill forum issues are cleared up, or new project starts.
Here are all primes for K-55951335 up to n=100K n=0 to 10k = 73 primes 55951335 11289 55951335 11578 55951335 11758 55951335 12712 55951335 12844 55951335 13428 55951335 14182 55951335 15692 55951335 16398 55951335 16549 55951335 17906 55951335 31544 55951335 33250 55951335 33904 55951335 43090 55951335 48710 55951335 50294 55951335 50382 55951335 55884 55951335 59910 55951335 72804 55951335 76902 55951335 81033 55951335 92671 55951335 94435 55951335 98733 (99) |
[QUOTE=grobie]I am done with this K untill forum issues are cleared up, or new project starts.
[/QUOTE] The prime-hunting task, and its worth, should be independent of the website/mailing-list/fora that its participants use to discuss things. |
[QUOTE=fatphil]The prime-hunting task, and its worth, should be independent of the website/mailing-list/fora that its participants use to discuss things.[/QUOTE]Well said!
Paul |
3 more for 15k=355424355; now the 15k.org gap looks like this:
10982, 14779, 14852, 15331, 15434, 16202, 16303, 16831, 16923, 19875, 21161, 23702, 28127, 29972, 33404, 39315, 41043, 41592, 51211, 59238, 59772, 60612, 66268, 79481, 87840, 91514, 103375, 104433, 106609, 108981, 129800, 136851, 139247 It should be less than a week before I reach the 170000 where the 15k project started searching for bigger primes. I'm prepared to take on another similar sized gap if there are any other dense candidates deserving of a complete investigation. |
k=8331405 is anther one that may be of interest. It's hundredth
prime occurs at n=45773 (#101 at 47239). It has also yielded 20 primes in the range n=186251-616479 The missing gap is from n=48181-181000 -Larry |
[QUOTE=lsoule]k=8331405 is anther one that may be of interest. It's hundredth
prime occurs at n=45773 (#101 at 47239). It has also yielded 20 primes in the range n=186251-616479 The missing gap is from n=48181-181000 -Larry[/QUOTE] Thanks Larry! I shall do that next. I'll start in about 5 days, I guess, and it will take about 2 weeks. Cheers, Phil |
[QUOTE=fatphil]Thanks Larry!
I shall do that next. I'll start in about 5 days, I guess, and it will take about 2 weeks.[/QUOTE] I have seriously overerestimated the speed of my CPU... Nevertheless, I shall do it as soon as this current batch is done (having a dry patch presently). |
[QUOTE=fatphil]15k=355424355
10982, 14779, 14852, 15331, 15434, 16202, 16303, 16831, 16923, 19875, 21161, 23702, 28127, 29972, 33404, 39315, 41043, 41592, 51211, 59238, 59772, 60612, 66268, 79481, 87840, 91514, 103375, 104433, 106609, 108981, 129800, 136851, 139247[/QUOTE] that's all folks -- that k is now without n gaps. The first few small primes have started on my next k too, but I'll wait until I have a whole bunch before starting to post them to keep the noise down. |
I'm nearly half of the way through the hole
k=8331405: 49415 50445 52637 56391 64400 84059 85434 132909 Nice start, shame about the latter dearth. Phil |
For k=736320585 I have reached n=410k... so far 99 primes have been discovered, I am still looking for #100 :showoff:
BTW: Maybe we should move this thread to "RPS - forum" :question: |
[QUOTE=Cruelty]For k=736320585 I have reached n=410k... so far 99 primes have been discovered, I am still looking for #100 :showoff:
BTW: Maybe we should move this thread to "RPS - forum" :question:[/QUOTE] Brave chappy! It'll be there eventually, of course, and it will hopefully be worth the wait. Good luck with that. Regarding thread location - I have no strong opinion. On a side note, due to a catastrophic machine failure last week, I'll not be able to do any more small prime back-filling for a while, as I need to move the machine I was using onto sieving. However, it did appear that there weren't any obvious holes in the absolute densest (appearing) candidates. |
Should I move it?
Alex |
[QUOTE=akruppa]Should I move it?
Alex[/QUOTE] IMO, that would be cool :smile: |
First batch of results for K 3250995
from 10k to 50k: 3250995 12665 3250995 13757 3250995 14730 3250995 18772 3250995 18986 3250995 23930 3250995 26026 3250995 27348 3250995 28051 3250995 31445 3250995 34123 3250995 36262 3250995 38799 3250995 40595 3250995 41002 3250995 42615 3250995 45965 3250995 47757 3250995 48509 3250995 48859 |
Tested to k=80k
3250995*2^53311 - 1 is prime! 16055 digits 3250995*2^60917 - 1 is prime! 18345 digits 3250995*2^71729 - 1 is prime! 21600 digits 3250995*2^76722 - 1 is prime! 23103 digits -- Repasting the other primes with their lenght: [code] 3250995*2^12665 - 1 is prime! 3820 digits 3250995*2^13757 - 1 is prime! 4148 digits 3250995*2^14730 - 1 is prime! 4441 digits 3250995*2^18772 - 1 is prime! 5658 digits 3250995*2^18986 - 1 is prime! 5722 digits 3250995*2^23930 - 1 is prime! 7211 digits 3250995*2^26026 - 1 is prime! 7842 digits 3250995*2^27348 - 1 is prime! 8240 digits 3250995*2^28051 - 1 is prime! 8451 digits 3250995*2^31445 - 1 is prime! 9473 digits 3250995*2^34123 - 1 is prime! 10279 digits 3250995*2^36262 - 1 is prime! 10923 digits 3250995*2^38799 - 1 is prime! 11687 digits 3250995*2^40595 - 1 is prime! 12227 digits 3250995*2^41002 - 1 is prime! 12350 digits 3250995*2^42615 - 1 is prime! 12835 digits 3250995*2^45965 - 1 is prime! 13844 digits 3250995*2^47757 - 1 is prime! 14383 digits 3250995*2^48509 - 1 is prime! 14610 digits 3250995*2^48859 - 1 is prime! 14715 digits [/code] |
Primes of 869688105 < n=200000
For the record here are all the primes of k=869688105 less than n=200000. All of the larger primes are currently on the Top 5000 list.
[CODE]1, 3, 7, 10, 16, 17, 18, 19, 21, 26, 37, 45, 57, 58, 76, 84, 90, 104, 105, 107, 137, 145, 155, 190, 235, 251, 254, 286, 298, 421, 492, 502, 507, 540 597, 606, 641, 661, 738, 765, 999, 1397, 1487, 1659, 1699, 1815, 2019, 2128, 2326, 2401, 2523, 2736, 2819, 2859, 2898, 2997, 3150, 4084, 4411, 4690, 4842, 6466, 6614, 6632, 8471, 8755, 9067, 9899, 10872, 11862, 12130, 12158, 12264, 12842, 13205, 16257, 18968, 20107, 21783, 24333, 27102, 30777, 31224, 31527, 32235, 32872, 35314, 43604, 48078, 53391, 59191, 64124, 67464, 87768, 88497, 89458, 96851, 115483, 116955, 124675, 131943, 141817, 144768, 153564, 159318, 160002, 165964, 170562[/CODE] |
8331405 back-filled completely
15k=8331405's hole contained 9 primes:
49415, 50445, 52637, 56391, 64400, 84059, 85434, 132909, 163192 (I had a few problems with LLR in the middle of that, if anyone would like to have my lresults.txt file, and perhaps double-check the 85434-132909 region, then just ask.) Can somebody ensure 15k.org is updated? The full list now stands at 132: 1, 9, 11, 17, 21, 31, 32, 33, 45, 57, 61, 64, 67, 69, 77, 80, 85, 88, 107, 115, 117, 120, 121, 124, 147, 155, 161, 164, 168, 177, 179, 221, 232, 258, 261, 264, 281, 282, 299, 308, 342, 415, 471, 503, 504, 505, 537, 572, 680, 989, 1328, 1565, 1607, 1613, 1841, 1953, 2509, 2692, 2739, 2834, 3627, 3735, 3870, 3960, 4083, 4682, 4788, 5187, 5247, 5623, 5804, 6015, 6020, 6405, 6569, 7052, 7315, 7477, 7489, 8389, 8800, 10407, 10512, 12035, 13015, 14634, 14941, 16339, 16367, 16554, 26533, 28153, 29081, 30222, 32391, 36371, 37323, 39251, 43935, 45052, 45773, 47239, 49415, 50445, 52637, 56391, 64400, 84059, 85434, 132909, 163192, 186251, 198122, 199127, 200363, 205885, 207555, 220532, 222399, 264459, 269433, 274141, 309331, 317435, 359692, 371488, 377268, 383323, 422243, 433420, 585714, 616479 As I'm a machine down for my own project, I'm bowing out of this 15k/RPS back-filling task for the moment, but may rejoin later. Good luck all! |
[QUOTE=fatphil]15k=8331405's hole contained 9 primes:
... The full list now stands at 132: [/QUOTE] I've just noticed that 2995125705 is at 132 too, at roughly the same n level. Still 10 short of your leader, which is 20 short of my drag race leader. |
[code]
3250995*2^80610 - 1 is prime! 24273 digits 3250995*2^96176 - 1 is prime! 28959 digits [/code] Regards, C. |
Backfilling 15k=25935
I noticed that 25935 had a criminally small low hole, so decided to fill it last night:
11476, 12448, 13205, 16282, 19583, 22209, 26443, 28532, 29326, 32689, 34226, 42832, 44325, 46144 already known, 47396 already known, 54956, ... (67364) No point leaving a hole, so I'll finish this one off too. |
1 more prime to 100k:
[code] 3250995*2^97731-1 is prime! 29427 digits [/code] |
15k=25935 backfilled completely
11476, 12448, 13205, 16282, 19583,
22209, 26443, 28532, 29326, 32689, 34226, 42832, 44325, (46144 already known, 47396 already known,) 54956, 67599, 69182, 69625, 75563, 81684, 83898, 84676, 91943, 92016, 101560 This brings the total known list to: 1, 3, 4, 9, 10, 11, 12, 16, 19, 21, 23, 25, 29, 32, 33, 35, 44, 48, 64, 80, 82, 99, 100, 101, 128, 132, 141, 155, 170, 201, 213, 339, 570, 573, 623, 698, 721, 811, 826, 964, 1120, 1173, 1185, 1225, 1324, 1329, 1392, 1775, 2056, 2576, 2631, 3045, 3488, 3609, 3803, 4653, 4902, 5064, 5210, 5931, 6013, 6978, 7429, 8163, 8316, 9460, 11476, 12448, 13205, 16282, 19583, 22209, 26443, 28532, 29326, 32689, 34226, 42832, 44325, 46144, 47396, 54956, 67599, 69182, 69625, 75563, 81684, 83898, 84676, 91943, 92016, 101560 117344, 121855, 139225, 152803, 173518, 219995 (220000) Bugger, that's 98. Really stopping this time - factorial prime sieving is my next job... Good luck all. |
The [URL=http://www.15k.org/stats.htm]stats page[/URL] updated with small primes found by Phil and Amphoria. Will add those found by Cedric later (cannot locate primes for n<10k for his [I]k[/I]...).
BTW a historic remark on two [I]k[/I]'s included above. [B]k=25935[/B] > (46144 already known, 47396 already known,) These two primes were found in Engelsma (g174) in summer 2000. [B]k=869688105[/B] Primes for 27102 <= n <= 48078 were found by Herranen (g78) in November-December 1998. |
Last year I posted the first hundred primes for k=860541825
(The 100th is at n=54696). I have filled in the gaps and taken this k up to 260k so far. Here are the new primes for a total of 113 primes so far: 860541825 66286 860541825 67056 860541825 78227 860541825 86092 860541825 95583 860541825 100597 860541825 101104 860541825 102606 860541825 105210 860541825 153367 860541825 170189 860541825 187934 860541825 242559 -Larry |
1 Attachment(s)
I have started working on k=151515, just for fun :smile: So far 73 primes have been discovered for n<210000, continuing sieving and testing for 210000<n<400000.
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k=850612425
From Choose your own K, k=850612425 sieved to 312G 10K to 300K, currently at n=244600, Total 100 Primes :down: Will continue to 300k
Primes from n=1 to 10k =77 850612425 10649 850612425 11025 850612425 12050 850612425 12636 850612425 12654 850612425 13294 850612425 23950 850612425 25304 850612425 35537 850612425 46316 850612425 48793 850612425 64345 850612425 78208 850612425 91844 850612425 98819 850612425 107606 850612425 135696 850612425 143231 850612425 153594 850612425 167265 850612425 179716 850612425 219429 850612425 239205 (100th Prime) |
k=234686595
From choose your own K
234686595*2^11442 - 1 is prime! 3453 digits 234686595*2^18824 - 1 is prime! 5675 digits 234686595*2^23205 - 1 is prime! 6994 digits 234686595*2^26353 - 1 is prime! 7942 digits 234686595*2^27268 - 1 is prime! 8217 digits 234686595*2^27600 - 1 is prime! 8317 digits 234686595*2^27607 - 1 is prime! 8319 digits 234686595*2^29745 - 1 is prime! 8963 digits 234686595*2^32882 - 1 is prime! 9907 digits 234686595*2^33072 - 1 is prime! 9965 digits Makes 84 primes! Up to ?? :showoff: |
k=234686595
234686595*2^35503 - 1 is prime! 10696 digits
234686595*2^36492 - 1 is prime! 10994 digits 234686595*2^36752 - 1 is prime! 11072 digits 234686595*2^37128 - 1 is prime! 11186 digits 234686595*2^37376 - 1 is prime! 11260 digits 234686595*2^37694 - 1 is prime! 11356 digits 234686595*2^39137 - 1 is prime! 11790 digits 234686595*2^43606 - 1 is prime! 13136 digits 234686595*2^48861 - 1 is prime! 14717 digits 234686595*2^49489 - 1 is prime! 14907 digits Makes 94 primes! |
234686595*2^50913 - 1 is prime! 15335 digits
234686595*2^62127 - 1 is prime! 18711 digits Makes 96 |
From choose you own
k=1222853775
Primes from n=1 to 10k = 81 1222853775 12582 1222853775 15111 1222853775 15562 1222853775 17039 1222853775 20909 1222853775 25721 1222853775 27435 1222853775 29005 1222853775 29499 1222853775 29511 1222853775 30871 1222853775 32373 1222853775 32798 1222853775 36441 1222853775 37700 1222853775 45789 1222853775 46062 1222853775 48302 1222853775 52094 (100th Prime) :banana: 1222853775 53967 1222853775 54089 1222853775 55766 |
[QUOTE=grobie]k=1222853775
Primes from n=1 to 10k = 81 1222853775 12582 1222853775 15111 1222853775 15562 1222853775 17039 1222853775 20909 1222853775 25721 1222853775 27435 1222853775 29005 1222853775 29499 1222853775 29511 1222853775 30871 1222853775 32373 1222853775 32798 1222853775 36441 1222853775 37700 1222853775 45789 1222853775 46062 1222853775 48302 1222853775 52094 (100th Prime) :banana: 1222853775 53967 1222853775 54089 1222853775 55766[/QUOTE] Finished to 100k, this makes 114 Primes:smile: 1222853775 59546 1222853775 63546 1222853775 71758 1222853775 73031 1222853775 73453 1222853775 76219 1222853775 81370 1222853775 86500 1222853775 86716 1222853775 94574 1222853775 99938 |
2 more:
234686595*2^90940 - 1 is prime! 27385 digits 234686595*2^92990 - 1 is prime! 28002 digits Makes: 98 primes ! |
Grobie
Your [I]k[/I] looks very promissing since the 100th prime occurs early. If you can, keep on testing it to 250 or 300k.
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[QUOTE=Kosmaj]Your [I]k[/I] looks very promissing since the 100th prime occurs early. If you can, keep on testing it to 250 or 300k.[/QUOTE]
Yep! As a min to 300k but plan so far to go beyond that. My other k I will drop at 300 k, testing is at 273k now with only 100 primes so far, I just might just drop that one early, what do you think. |
Choose your own k:
k=1222853775 This makes 119 primes 1222853775 100189 1222853775 103325 1222853775 105875 1222853775 111050 1222853775 154362 |
Grobie
Cool, IMO it was a good decision to concentrate on this [I]k[/I]. Only the gap between the last two primes is a little bit too large. But let's hope there will be many primes from now on. Just keep on going! :cool:
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Choose your own k:
k=1222853775 This makes 122 primes 1222853775 164775 1222853775 169421 1222853775 171257 |
Choose your own K:
234686595*2^98272 - 1 is prime! 29592 digits 234686595*2^111766 - 1 is prime! 33654 digits Makes 100 primes!! |
Choose your own K:
360949875*2^11382-1 3435 digits 360949875*2^12646-1 3816 digits 360949875*2^14164-1 4273 digits 360949875*2^14856-1 4481 digits 360949875*2^16207-1 4888 digits 360949875*2^17228-1 5195 digits 360949875*2^18825-1 5676 digits 360949875*2^19113-1 5763 digits 360949875*2^32748-1 9867 digits 360949875*2^37252-1 11223 digits Makes 90 primes!!! |
Here are the first 106 primes for k=1952775825. This is one of the k's
in the first RPS drive 1952775825 4 1952775825 5 1952775825 16 1952775825 19 1952775825 23 1952775825 28 1952775825 36 1952775825 47 1952775825 55 1952775825 62 1952775825 64 1952775825 75 1952775825 82 1952775825 90 1952775825 96 1952775825 101 1952775825 111 1952775825 124 1952775825 130 1952775825 132 1952775825 144 1952775825 163 1952775825 169 1952775825 249 1952775825 251 1952775825 254 1952775825 279 1952775825 292 1952775825 296 1952775825 298 1952775825 309 1952775825 318 1952775825 325 1952775825 348 1952775825 364 1952775825 383 1952775825 391 1952775825 396 1952775825 420 1952775825 438 1952775825 444 1952775825 447 1952775825 457 1952775825 491 1952775825 532 1952775825 558 1952775825 560 1952775825 620 1952775825 691 1952775825 850 1952775825 899 1952775825 980 1952775825 1053 1952775825 1058 1952775825 1123 1952775825 1159 1952775825 1254 1952775825 1441 1952775825 1580 1952775825 1927 1952775825 2044 1952775825 2164 1952775825 2228 1952775825 2315 1952775825 2396 1952775825 2449 1952775825 2565 1952775825 3664 1952775825 4147 1952775825 4408 1952775825 4597 1952775825 4765 1952775825 4895 1952775825 4909 1952775825 5191 1952775825 5712 1952775825 6665 1952775825 6740 1952775825 7390 1952775825 8602 1952775825 11123 1952775825 11329 1952775825 12554 1952775825 15120 1952775825 16001 1952775825 16952 1952775825 19804 1952775825 21598 1952775825 22360 1952775825 22692 1952775825 24144 1952775825 27675 1952775825 28058 1952775825 28066 1952775825 29132 1952775825 33297 1952775825 35458 1952775825 44266 1952775825 46850 1952775825 48607 1952775825 55149 1952775825 73821 1952775825 81029 1952775825 83559 1952775825 90765 1952775825 100239 Tested up to n=117419 |
360949875*2^46142 - 1 is prime! 13899 digits
360949875*2^48976 - 1 is prime! 14752 digits 360949875*2^60759 - 1 is prime! 18299 digits Makes 93 primes! |
Choose your own k:
k=1222853775 This makes 124 primes < 200k 1222853775 184373 1222853775 184993 progress: box#1 testing n=o to 250k currently at 197277 with 124 primes box#2 testing n=250 to 300k currently at 270553 with 2 primes Total 126 Primes |
360949875*2^69027 - 1 is prime! 20788 digits
360949875*2^70726 - 1 is prime! 21300 digits 360949875*2^79219 - 1 is prime! 23856 digits Makes 96 primes! :showoff: |
360949875*2^107774 - 1 is prime! 32452 digits
360949875*2^111307 - 1 is prime! 33516 digits Makes 98 primes! |
Primes of k=5169615 < n=210000
All the primes of k=5169615 less than n=210000. This k is interesting in that primes are relatively sparse between n=10k and n=100k, but there are quite a few between n=100k and n=200k.
[CODE]5169615 1 5169615 5 5169615 9 5169615 14 5169615 21 5169615 24 5169615 26 5169615 27 5169615 32 5169615 41 5169615 48 5169615 51 5169615 55 5169615 56 5169615 59 5169615 65 5169615 68 5169615 85 5169615 97 5169615 99 5169615 127 5169615 149 5169615 174 5169615 199 5169615 207 5169615 270 5169615 275 5169615 336 5169615 346 5169615 351 5169615 420 5169615 525 5169615 526 5169615 537 5169615 564 5169615 598 5169615 627 5169615 631 5169615 659 5169615 701 5169615 822 5169615 900 5169615 982 5169615 1182 5169615 1289 5169615 1398 5169615 1417 5169615 1466 5169615 1478 5169615 1522 5169615 1776 5169615 2033 5169615 2108 5169615 2144 5169615 2435 5169615 2511 5169615 3471 5169615 3649 5169615 3705 5169615 3786 5169615 3910 5169615 4181 5169615 4618 5169615 5225 5169615 5281 5169615 5285 5169615 5451 5169615 6199 5169615 7112 5169615 7163 5169615 8026 5169615 8677 5169615 11093 5169615 12178 5169615 12582 5169615 15567 5169615 18234 5169615 19368 5169615 24761 5169615 31441 5169615 34229 5169615 39920 5169615 49932 5169615 62435 5169615 86969 5169615 109368 5169615 114065 5169615 121166 5169615 122409 5169615 122865 5169615 131241 5169615 134948 5169615 138531 5169615 146297 5169615 146505 5169615 154275 5169615 158790 5169615 158802 5169615 175677 5169615 183408 5169615 186027 5169615 186357 5169615 199712 5169615 207884 [/CODE] |
This one is not so small, but it was not enough for Top-5000.
445419975*2^203536-1 (61280 digits) I found it back in October but I think I never told anybody about it :smile: |
k=1222853775
Choose your own k:
k=1222853775 This makes 129 primes 1222853775 210992 progress: box#1 testing n=o to 250k currently at 231177 with 126 primes box#2 testing n=250 to 300k currently at 293245 with 3 primes Total 129 Primes |
k=317372055
From choose your own k:
317372055 53955 317372055 62185 317372055 63635 317372055 84815 This makes 100 primes for this k. The other 96 for n < 50k were found by Larry. |
k = 360949875
360949875*2^114960 - 1 is prime! 34615 digits
Makes 99 primes! |
k = 234686595
234686595*2^119958 - 1 is prime! 36120 digits
234686595*2^123788 - 1 is prime! 37273 digits Makes 102 primes! |
k= 360949875
360949875*2^132482 - 1 is prime! 39890 digits
Makes 100 primes! |
k=317372055
The remaining primes for this k that did not make it into the Top-5000.
317372055 91950 317372055 94270 317372055 139077 317372055 144290 317372055 149461 317372055 159253 317372055 168581 317372055 181167 317372055 185656 317372055 191704 That makes 110 primes less than 200k, but only two found between 200k and 300k. |
k=234686595
234686595*2^143007-1 is primel 43058 digits
Makes 103 primes! |
k= 2028893625
2028893625*2^50419-1 is prime! 15187 digits
2028893625*2^53384-1 is prime! 16080 digits 2028893625*2^54248-1 is prime! 16340 digits 2028893625*2^57544-1 is prime! 17332 digits Makes 102 primes |
2028893625*2^66796 - 1 is prime! 20117 digits
2028893625*2^85724 - 1 is prime! 25815 digits Makes 104 primes! |
2028893625*2^104208 - 1 is prime! 31380 digits
2028893625*2^109300 - 1 is prime! 32912 digits Makes 106 primes! |
2028893625*2^128161 - 1 is prime! 38590 digits
2028893625*2^128776 - 1 is prime! 38775 digits Makes 108 primes. |
1 Attachment(s)
Attached is a list of primes for k=12345 and n<240000 - none reportable to TOP-5000 list yet.
I will continue testing this "k". |
1 Attachment(s)
Attached is a list of primes for k=617 and n<240000 - none reportable to TOP-5000 list yet.
I will continue testing this "k". |
I have reached n=500000 for k=736320585. So far I have found 101 primes for this "k"... I'm still on it :flex:
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Two milestones to report:
k=617 tested till n=600000 (it's not a part of RPS) k=12345 tested till n=400000 I'm still working on both "k" :smile: |
1 Attachment(s)
Attached is a list of primes for k=1515 and n<240000 - none reportable to TOP-5000 list yet.
I will continue testing this "k". |
k=151515 tested till n=600000 - no primes to report in range 400000<n<600000.
I am still testing this "k" :smile: |
k=686701125
686701125*2^59037 - 1 is prime! 17781 digits
686701125*2^61564 - 1 is prime! 18542 digits 686701125*2^61743 - 1 is prime! 18596 digits 686701125*2^71904 - 1 is prime! 21655 digits |
[code]
686701125*2^77984 - 1 is prime! 23485 digits 686701125*2^82487 - 1 is prime! 24840 digits [/code] |
k=686701125
[CODE] 686701125*2^85355 -1 is prime! 25704 digits
686701125*2^86208 -1 is prime! 25961 digits 686701125*2^92474 -1 is prime! 27847 digits 686701125*2^101321 -1 is prime! 30510 digits[/CODE] |
475977645 199782 is prime (60150 digits)
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new best k found...
For [B]k=37850187375[/B] (Nash weight: 7261) the 100th prime appeared at [B]n=13719[/B] :w00t:
Here is the list of n which yield primes up to n=24000: [CODE]2, 5, 13, 16, 19, 20, 41, 56, 57, 64, 66, 74, 90, 97, 100, 107, 130, 137, 145, 147, 149, 171, 172, 178, 208, 241, 258, 301, 302, 318, 330, 331, 386, 439, 460, 462, 526, 529, 556, 558, 563, 625, 626, 628, 666, 699, 797, 804, 890, 907, 928, 968, 1050, 1117, 1247, 1304, 1453, 1584, 1782, 1788, 2115, 2193, 2239, 2371, 2439, 2533, 2789, 2827, 2984, 3044, 3382, 3568, 3633, 3884, 3900, 3909, 4406, 4426, 5833, 6241, 6283, 6325, 6580, 6596, 6714, 7621, 7727, 7968, 8323, 8817, 9002, 9258, 9833, 11742, 11868, 12248, 12294, 12754, 13340, 13719, 15527, 15913, 16323, 16554, 19362, 19802, 20013, 22376[/CODE] |
475977645*2^207784-1 (62558 digits)
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k=19217385 tested from 50k to 70k.
There are primes for the following n: 60121 62263 64849 66746 <----- 100th prime |
k=228461805
I decided to sieve and LLR some smaller N's for my K, which is already being sieved and LLR'd from 300k-500k.
228461805*2^102923-1 is prime! (30992 digits) |
I am currently working on 2 k's :
11069*2^n-1 : (on other machine) done until 450k 21879*2^n-1 : 28, 232, 244, 292, 448, 2068, 17548, 64288 ; done until 300k |
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