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.

Files in post #62 updated again. :smile:

[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]

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[/CODE]

I will sieve and search the 4 sierpinski bases only searched to 25k(244, 560, 668, 758)

Here it was. [URL="https://www.mersenneforum.org/showthread.php?t=24576"]Link back[/URL].
With the [URL="https://www.mersenneforum.org/showthread.php?p=524789"]current found[/URL].

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.

I've found:
8*283^164768-1 is prime

Base 283 for k=8 tested to n=166k.

8*97^192335-1 is prime (382127 digits)
8*97^n-1 tested for 100000<n<200000

[url='https://primes.utm.edu/primes/page.php?id=130922']4*303^198357-1[/url] is prime, 492,213 digits

The web pages and the files in post 62 in this thread have been updated for the recent finds.

4*438^n-1 is tested through n=300k, no prime.

I have updated the files formerly attached to post #62 here.

The files are now attached to post #1 in this thread.