20170821, 01:58  #78 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
3651_{10} Posts 
12*312^21162+1 is prime.
Result text file attached. 
20170821, 02:04  #79 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
3×1,217 Posts 
2*801^n+1 is currently at n=28661, and 7*1004^n+1 is currently at n=31030, both no primes found.
Many of the bases for 8<=k<=12 are only searched to n=5K, I will reserve all such bases to n=25K. 
20171030, 14:21  #80 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
3·1,217 Posts 
Update current file.

20171030, 19:32  #81 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
3×1,217 Posts 
The exclusions are:
Code:
Riesel k=2: none Riesel k=3: b==(1 mod 2); factor of 2 Riesel k=4: b==(1 mod 3); factor of 3 b==(4 mod 5): odd n, factor of 5; even n, algebraic factors b=m^2 proven composite by full algebraic factors Riesel k=5: b==(1 mod 2); factor of 2 Riesel k=6: b==(1 mod 5); factor of 5 b==(34 mod 35); covering set [5, 7] b=6*m^2 with m==(2, 3 mod 5): even n, factor of 5; odd n, algebraic factors (This includes bases 24, 54, 294, 384, 864, 1014.) Riesel k=7: b==(1 mod 2); factor of 2 b==(1 mod 3); factor of 3 Riesel k=8: b==(1 mod 7) has a factor of 7 b==(20 mod 21) has a covering set of [3, 7] b==(83, 307 mod 455) has a covering set of [5, 7, 13] (This includes bases 83, 307, 538, 762, 993.) b=m^3 proven composite by full algebraic factors Riesel k=9: b==(1 mod 2) has a factor of 2 b==(4 mod 5): odd n has a factor of 5; even n has algebraic factors b=m^2 proven composite by full algebraic factors Riesel k=10: b==(1 mod 3) has a factor of 3 b==(32 mod 33) has a covering set of [3, 11] 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=2: b==(1 mod 3); factor of 3 base 512 is a GFN with no known prime Sierp k=3: b==(1 mod 2); factor of 2 Sierp k=4: b==(1 mod 5); factor of 5 b==(14 mod 15); covering set [3, 5] base 625 proven composite by full algebraic factors bases 32, 512, and 1024 are GFN's with no known prime Sierp k=5: b==(1 mod 2); factor of 2 b==(1 mod 3); factor of 3 Sierp k=6: b==(1 mod 7); factor of 7 b==(34 mod 35); covering set [5, 7] Sierp k=7: b==(1 mod 2); factor of 2 Sierp k=8: b==(1 mod 3) has a factor of 3 b==(20 mod 21) has a covering set of [3, 7] b==(47 or 83 mod 195) has a covering set of [3, 5, 13] (This includes bases 47, 83, 242, 278, 437, 473, 632, 668, 827, 863, 1022.) base 467 has a covering set of [3, 5, 7, 19, 37] base 722 has a covering set of [3, 5, 13, 73, 109] b=m^3 proven composite by full algebraic factors base 128 is a GFN with no possible prime Sierp k=9: b==(1 mod 2) has a factor of 2 b==(1 mod 5) has a factor of 5 Sierp k=10: b==(1 mod 11) has a factor of 11 b==(32 mod 33) has a covering set of [3, 11] base 1000 is a GFN with no known prime 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 296 and 901 have a covering set of [7, 11, 13, 19] 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] base 12 is a GFN with no known prime 
20171031, 01:45  #82 
May 2007
Kansas; USA
10110100110101_{2} Posts 
I have updated the files in post 62.

20180605, 21:32  #83 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
3×1,217 Posts 
Now I reserve all bases for k = 8 to 12 that are at n<25K to n=25K and found that 8*284^52661 and 10*1020^69441 are primes. (using pfgw)
Current at: Riesel k=8: n=6144 Riesel k=9: n=7445 Riesel k=10: n=7025 Riesel k=11: n=9679 Riesel k=12: n=8690 Sierp k=8: n=6135 Sierp k=9: n=9541 Sierp k=10: n=5828 Sierp k=11: n=9568 Sierp k=12: n=5631 Only found the above two primes. Last fiddled with by sweety439 on 20180605 at 21:33 
20180606, 17:41  #84  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
3·1,217 Posts 
Quote:


20180607, 03:02  #85 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
E43_{16} Posts 
8*854^65001 is prime.

20180607, 03:06  #86 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
3×1,217 Posts 
Currently at:
Riesel k=8: n=6632 Riesel k=9: n=8346 Riesel k=10: n=7750 Riesel k=11: n=11009 Riesel k=12: n=9840 Sierp k=8: n=6599 Sierp k=9: n=10619 Sierp k=10: n=6196 Sierp k=11: n=11120 Sierp k=12: n=5915 
20180608, 07:16  #87 
Mar 2006
Germany
2·3·7·71 Posts 
8*194^383601 is prime

20180609, 09:23  #88 
Mar 2006
Germany
BA6_{16} Posts 
4*312^515651 is prime!
