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2019-06-10, 13:07   #100
sweety439

Nov 2016

276410 Posts

Since all Sierp bases <= 1030 have a k=7 prime, thus I try to find the smallest Sierp base without known prime for k=7 and continue searched Sierp k=7 for larger bases (b>1030) and find such Sierp bases would be 1136....

Only list even bases, since for odd bases all the k=7 numbers are divisible by 2.
Attached Files
 Sierp k=7 for bases gt 1004.txt (541 Bytes, 158 views)

Last fiddled with by sweety439 on 2019-06-10 at 13:08

 2019-06-14, 23:06 #101 gd_barnes     May 2007 Kansas; USA 7×13×113 Posts Files in post #62 updated again.
2019-06-17, 10:32   #102
henryzz
Just call me Henry

"David"
Sep 2007
Cambridge (GMT/BST)

5·19·61 Posts

Code:
Riesel k=13:
b==(1 mod 2) has a factor of 2
b==(1 mod 3) has a factor of 3
b==(20 mod 21) has a covering set of [3, 7]
b==(38 or 302 mod 510) have a covering set of [3, 5, 17]
(This includes bases 38, 302, 548, 812.)
Proth k=13:
b==(1 mod 2) has a factor of 2
b==(1 mod 7) has a factor of 7
b==(20 mod 21) has a covering set of [3, 7]
b==(132 and 888) have a covering set of [5, 7, 17] // probably mod 1190
remaining at 25k:
Code:
13*422^n-1 - searched to 200k
13*446^n-1 - searched to 300k
13*542^n-1 - prime at 70447
13*698^n-1 - searched to 150k
13*842^n-1 - searched to 100k
13*962^n-1 - searched to 100k

13*244^n+1
13*326^n+1 - prime at 56864
13*338^n+1 - prime at 37612
13*422^n+1 - searched to 200k
13*458^n+1 - prime at 306196
13*536^n+1 - searched to 300k
13*542^n+1 - searched to 200k
13*560^n+1
13*620^n+1 - searched to 200k
13*656^n+1 - searched to 100k
13*668^n+1
13*720^n+1 - searched to 400k
13*740^n+1 - searched to 200k
13*748^n+1 - prime at 32635
13*758^n+1
13*808^n+1 - searched to 100k
13*842^n+1 - searched to 400k
13*872^n+1 - prime at 38782
13*878^n+1 - searched to 150k
13*920^n+1 - searched to 300k
13*926^n+1 - searched to 100k
13*958^n+1 - prime at 101751
13*992^n+1 - searched to 100k
I will sieve and search the 4 sierpinski bases only searched to 25k(244, 560, 668, 758)
Attached Files
 rieselk13.zip (1.6 KB, 137 views) prothk13.zip (1.9 KB, 142 views)

 2019-08-29, 13:25 #103 LaurV Romulan Interpreter     Jun 2011 Thailand 9,161 Posts Here it was. Link back. With the current found. Last fiddled with by LaurV on 2019-08-29 at 13:27
 2019-12-10, 02:43 #104 gd_barnes     May 2007 Kansas; USA 1028310 Posts I have searched all remaining k=2 thru 12 for bases <= 1030 to n=100K. There were 42 k/base combos that had previously only been searched to n=25K. Here are the combos that were searched for n=25K-100K: Riesel: k=4 b=303 k=4 b=921 k=6 b=768 k=8 b=283 k=8 b=374 k=8 b=432 k=8 b=721 k=8 b=728 k=9 b=566 k=9 b=570 k=10 b=284 k=10 b=899 k=11 b=804 k=12 b=263 Sierp: k=2 b=801 k=5 b=824 k=6 b=509 k=6 b=522 k=8 b=254 k=8 b=389 k=8 b=434 k=8 b=575 k=8 b=824 k=8 b=1014 k=9 b=884 k=10 b=432 k=10 b=614 k=10 b=668 k=10 b=786 k=10 b=863 k=10 b=986 k=11 b=560 k=12 b=230 k=12 b=359 k=12 b=362 k=12 b=481 k=12 b=593 k=12 b=692 k=12 b=700 k=12 b=923 k=12 b=1019 k=12 b=1022 Primes found: 4*921^98667-1 6*768^70213-1 6*522^52603+1 8*254^67715+1 10*786^68168+1 10*986^48278+1 12*230^94750+1 12*359^61294+1 12*481^45940+1 12*593^42778+1 12*700^91952+1 12*923^64364+1 All k<=12 for b<=1030 have now been searched to n>=100K. :-) The web pages and the files in post 62 in this thread have been updated accordingly. Last fiddled with by gd_barnes on 2019-12-10 at 02:46
 2020-02-18, 07:17 #105 kar_bon     Mar 2006 Germany 2×1,433 Posts I've found: 8*283^164768-1 is prime Base 283 for k=8 tested to n=166k.
 2020-05-05, 07:14 #106 kar_bon     Mar 2006 Germany B3216 Posts 8*97^192335-1 is prime (382127 digits) 8*97^n-1 tested for 100000
 2020-05-25, 11:30 #107 kar_bon     Mar 2006 Germany 1011001100102 Posts 4*303^198357-1 is prime, 492,213 digits
 2020-05-25, 20:55 #108 gd_barnes     May 2007 Kansas; USA 7×13×113 Posts The web pages and the files in post 62 in this thread have been updated for the recent finds.
 2020-08-03, 06:28 #109 kar_bon     Mar 2006 Germany 2×1,433 Posts 4*438^n-1 is tested through n=300k, no prime.
 2020-08-30, 11:37 #110 gd_barnes     May 2007 Kansas; USA 282B16 Posts I have updated the files formerly attached to post #62 here. The files are now attached to post #1 in this thread.