20050316, 23:45  #13 
Jun 2003
Oxford, UK
3·5^{4} Posts 
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 p1. 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 44957544) 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 
20050316, 23:49  #14 
Jun 2003
Oxford, UK
3·5^{4} Posts 
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 
20050417, 09:06  #15 
Mar 2005
Internet; Ukraine, Kiev
11×37 Posts 
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 
20050421, 03:46  #16 
"Curtis"
Feb 2005
Riverside, CA
4,211 Posts 
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 lowweight number beyond 1M or this number to higher powers. What's the current cutoff for top5000 entry? n=220,000? Curtis 
20050421, 04:06  #17 
Nov 2004
California
2^{3}·3·71 Posts 
The top5000 cutoff is just below n=189,000 now.
Larry 
20050425, 18:47  #18 
Mar 2005
Internet; Ukraine, Kiev
110010111_{2} Posts 
Primes for 15k=187466565 with n from 100000 to 150000
The range 100000150000 was sieved by me, gribozavr, and LLR'ed mostly by my friend yasya. So, please, give us both a credit for theese primes (write something like gribozavr and yasya):
Code:
187466565 107376 187466565 109098 187466565 111081 187466565 127062 187466565 130833 187466565 134459 
20050916, 17:49  #19 
May 2005
2×809 Posts 
Attached see primes for k=736320585 for 1<n<250000 (total of 100 primes incl. 2 Sophie Germain).
Continuing sieving and testing. 
20050924, 20:10  #20 
Mar 2005
Internet; Ukraine, Kiev
407_{10} Posts 
I have finished testing k=187466565 for n=1200k. I have found some more primes:
Code:
187466565 160453 187466565 165138 187466565 178879 187466565 187871 Can any of theese primes go into Top5000? The biggest one is 56564 digits long. 
20050924, 20:31  #21  
Sep 2002
Database er0rr
5^{2}·131 Posts 
Quote:
http://primes.utm.edu/primes/submit.php which states: Quote:


20050928, 12:49  #22 
Sep 2005
Raleigh, North Carolina
337 Posts 
Please dont tell me I have been wasting my time I just noticed the posts from gribozavr and he has already been testing my reserved K187466565

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