20190610, 13:07  #100 
Nov 2016
9C2_{16} 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. Last fiddled with by sweety439 on 20190610 at 13:08 
20190614, 23:06  #101 
May 2007
Kansas; USA
7^{2}×11×19 Posts 
Files in post #62 updated again.

20190617, 10:32  #102 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
3^{4}×71 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 Code:
13*422^n1  searched to 200k 13*446^n1  searched to 300k 13*542^n1  prime at 70447 13*698^n1  searched to 150k 13*842^n1  searched to 100k 13*962^n1  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 
20190829, 13:25  #103 
Romulan Interpreter
Jun 2011
Thailand
2^{2}·7·11·29 Posts 
Last fiddled with by LaurV on 20190829 at 13:27 
20191210, 02:43  #104 
May 2007
Kansas; USA
2801_{16} 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=25K100K: 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*921^986671 6*768^702131 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 20191210 at 02:46 
20200218, 07:17  #105 
Mar 2006
Germany
2×1,427 Posts 
I've found:
8*283^1647681 is prime Base 283 for k=8 tested to n=166k. 
20200505, 07:14  #106 
Mar 2006
Germany
2·1,427 Posts 
8*97^1923351 is prime (382127 digits)
8*97^n1 tested for 100000<n<200000 
20200525, 11:30  #107 
Mar 2006
Germany
2×1,427 Posts 
4*303^1983571 is prime, 492,213 digits

20200525, 20:55  #108 
May 2007
Kansas; USA
10100000000001_{2} Posts 
The web pages and the files in post 62 in this thread have been updated for the recent finds.

20200803, 06:28  #109 
Mar 2006
Germany
2×1,427 Posts 
4*438^n1 is tested through n=300k, no prime.

20200830, 11:37  #110 
May 2007
Kansas; USA
10100000000001_{2} Posts 
I have updated the files formerly attached to post #62 here.
The files are now attached to post #1 in this thread. 