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 2018-06-10, 07:17 #89 kar_bon     Mar 2006 Germany 1011101001102 Posts 4*513^38031-1 is prime
 2018-06-20, 18:48 #90 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 3×1,217 Posts 8*728^7399+1 is prime.
2019-04-11, 16:52   #91
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

3·1,217 Posts

Quote:
 Originally Posted by gd_barnes I have now searched k=11 and 12 for all bases <= 1030. Therefore all k=2 thru 12 for all bases <= 1030 have been completed. All k=2 thru 7 have been searched to n=25K for all bases and k=8 thru k=12 have been searched to n=5K for all bases. Attached are all primes for n<=5K found by my effort, n>5K found by CRUS, and bases remaining for each k. There have been some updates for k=2 thru 10 so all of k=2 thru 12 are included. Below are all exclusions including bases with trivial factors, algebraic factors, and covering sets for k=11 and 12. Exclusions for k<=10 were previously posted. Code: Riesel k=11: b==(1 mod 2) has a factor of 2 b==(1 mod 5) has a factor of 5 b==(14 mod 15) has a covering set of [3, 5] Riesel k=12: b==(1 mod 11) has a factor of 11 b==(142 mod 143) has a covering set of [11, 13] base 307 has a covering set of [5, 11, 29] base 901 has a covering set of [7, 11, 13, 19] Sierp k=11: b==(1 mod 2) has a factor of 2 b==(1 mod 3) has a factor of 3 b==(14 mod 15) has a covering set of [3, 5] Sierp k=12: b==(1 mod 13) has a factor of 13 b==(142 mod 143) has a covering set of [11, 13] bases 562, 828, and 900 have a covering set of [7, 13, 19] base 563 has a covering set of [5, 7, 13, 19, 29] base 597 has a covering set of [5, 13, 29] bases 296 and 901 have a covering set of [7, 11, 13, 19] base 12 is a GFN with no known prime I am done with this effort. As the k's get higher, the exclusions get much more complex. Many of the bases for k>=8 are only searched to n=5K. That would be a good starting point for people to do some additional searching if they are interested in this effort.
Are there any update of these files? e.g. recently the prime 8*410^279991+1 (for Sierpinski k=8) was found.

 2019-04-12, 22:41 #92 gd_barnes     May 2007 Kansas; USA 71·163 Posts The files in post #62 have been updated.
 2019-06-07, 02:49 #93 gd_barnes     May 2007 Kansas; USA 1157310 Posts I searched all remaining k<=12 and b<=1030 up to n=25K. There were 45 k/base combos for k=8 thru 12 that needed to be searched for n=5K-25K. I found the following 11 primes: 8*997^15814-1 9*990^23031-1 10*599^11775-1 12*593^16063-1 10*537^7117+1 10*827^9894+1 10*929^13064+1 10*1004^10644+1 12*600^11241+1 12*607^7582+1 12*673^7789+1 The files in post #62 have been updated accordingly.
2019-06-07, 21:24   #94
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

E4316 Posts

Quote:
 Originally Posted by gd_barnes I searched all remaining k<=12 and b<=1030 up to n=25K. There were 45 k/base combos for k=8 thru 12 that needed to be searched for n=5K-25K. I found the following 11 primes: 8*997^15814-1 9*990^23031-1 10*599^11775-1 12*593^16063-1 10*537^7117+1 10*827^9894+1 10*929^13064+1 10*1004^10644+1 12*600^11241+1 12*607^7582+1 12*673^7789+1 The files in post #62 have been updated accordingly.
So you can add the prime 8*997^15814-1 in the CRUS page, currently R997 is only tested to n=10K.

Last fiddled with by sweety439 on 2019-06-07 at 21:24

 2019-06-08, 12:50 #95 kar_bon     Mar 2006 Germany 2×3×7×71 Posts I've included two pages in the Prime-Wiki for these values: - Riesel type - Proth type I took the data from post #62, compiled as CSV (link for download given) for all 2 ≤ k ≤ 12 and displayed all wanted values. The table columns are sortable.
 2019-06-08, 18:18 #96 Dylan14     "Dylan" Mar 2017 2·33·11 Posts I am presently working on trying to find a prime for 7*1004^n+1, currently past 50k, will take to n = 100k.
 2019-06-08, 20:33 #97 Dylan14     "Dylan" Mar 2017 2×33×11 Posts And we have a prime: Code: 7*1004^54848+1 is 3-PRP! (97.6687s+0.0034s) C:\Users\Dylan\Desktop\prime finding\prime testing\pfgw>pfgw64 -t -q"7*1004^54848+1" PFGW Version 3.8.3.64BIT.20161203.Win_Dev [GWNUM 28.6] Primality testing 7*1004^54848+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 7*1004^54848+1 is prime! (93.6171s+0.0033s) With this, all bases within CRUS limits (b <= 1030) have a prime for k = 7 on the Sierpinski side. (*) (*) if they are not excluded by covering sets.
2019-06-09, 01:14   #98
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

3×1,217 Posts

Quote:
 Originally Posted by Dylan14 And we have a prime: Code: 7*1004^54848+1 is 3-PRP! (97.6687s+0.0034s) C:\Users\Dylan\Desktop\prime finding\prime testing\pfgw>pfgw64 -t -q"7*1004^54848+1" PFGW Version 3.8.3.64BIT.20161203.Win_Dev [GWNUM 28.6] Primality testing 7*1004^54848+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 7*1004^54848+1 is prime! (93.6171s+0.0033s) With this, all bases within CRUS limits (b <= 1030) have a prime for k = 7 on the Sierpinski side. (*) (*) if they are not excluded by covering sets.
Great!!! Now there are no remain bases for Sierp k=7!!! Besides, how about reserving 2*801^n+1, the only form only searched to n=25K for Sierp k=2.

Last fiddled with by sweety439 on 2019-06-09 at 01:17

 2019-06-10, 07:38 #99 kar_bon     Mar 2006 Germany 2·3·7·71 Posts Checked 6*299^n-1 from n=25k (up to 65k) and found: 6*299^64897-1 is prime!

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