20170121, 11:43  #45 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
6460_{8} Posts 
I checked (b1)*b^n+1 for 2<=b<=500, (b+1)*b^n1 for 2<=b<=300 and (b+1)*b^n+1 for 2<=b<=200.
For the primes of the form (b+1)*b^n+1 with integer b>=2 and integer n>=1: For (b1)*b^n1, it is already searched in http://harvey563.tripod.com/wills.txt for b<=2049, but one prime is missing in this website: (911)*91^5191, and the exponent of b=38 is wrong, it should be (381)*38^1362111, not (381)*38^1362211. Besides, (1281)*128^n1 has been reserved by Cruelty. The known primes with b<=500 and n>1000 are (381)*38^1362111, (831)*83^214951, (981)*98^49831, (1131)*113^2866431, (1251)*125^87391, (1881)*188^135071, (2281)*228^36951, (3471)*347^44611, (3571)*357^13191, (4011)*401^1036691, (4171)*417^210021, (4431)*443^16911, (4581)*458^468991, (4941)*494^215791. The bases b<=500 without known prime are 128 (n>1700000), 233, 268, 293, 383, 478, 488, all are checked to at least n=200000. For (b1)*b^n+1, the known primes with b<=500 and n>500 are (531)*53^960+1, (651)*65^946+1, (771)*77^828+1, (881)*88^3022+1, (1221)*122^6216+1, (1581)*158^1620+1, (1801)*180^2484+1, (1971)*197^520+1, (2481)*248^604+1, (2491)*249^1851+1, (2571)*257^1344+1, (2691)*269^1436+1, (2751)*275^980+1, (3191)*319^564+1, (3561)*356^528+1, (4341)*434^882+1. The bases b<=500 without known prime are 123 (n>100000), 202 (reserving, n>1024), 251 (n>73000), 272 (reserving, n>1024), 297 (CRUS prime), 298, 326, 328, 342 (n>100000), 347, 362, 363, 419, 422, 438 (n>100000), 452, 455, 479, 487 (n>100000), 497, 498 (CRUS prime), all are checked to at least n=1024. For (b+1)*b^n1, the known primes with b<=300 and n>500 are (63+1)*63^14831, (88+1)*88^17041, (143+1)*143^9211. The bases b<=300 without known primes are 208, 232, 282, 292, all are checked to at least n=1024. (except the case b=208, all of them are CRUS primes) For (b+1)*b^n+1, in this case this b should not = 1 (mod 3), or all numbers of the form (b+1)*b^n+1 are divisible by 3, the known primes with b<=200 (b != 1 mod 3) and n>500 are (171+1)*171^1851+1, there is no such prime with b=201 and n<=1024. 
20181214, 22:20  #47  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
D30_{16} Posts 
Quote:


20181214, 23:43  #48  
Sep 2003
5·11·47 Posts 
Quote:
Is it confirmed that there are no intervening terms between 15393 and 282989? If so, 282989 can be added, but if not, then you should add a comment instead: "282989 is also a member of this sequence". 

20181215, 10:45  #49 
Mar 2006
Germany
13·227 Posts 
Edits confirmed and I've checked the whole range again, continuing.

20181215, 17:15  #50 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
23135_{8} Posts 
Always press 'these edits are ready for review'. It's a gotcha in the OEIS Wiki.
(It was not always on the Wiki engine, actually.) 
20181215, 20:30  #51 
Mar 2006
Germany
13×227 Posts 

20190117, 09:21  #52 
Mar 2006
Germany
13·227 Posts 
Found:
4*5^4984831 is prime! (348426 decimal digits) 4*5^5042211 is prime! (352436 decimal digits) Currently at n=695k, OEIS updated. 
20190128, 09:23  #53 
Mar 2006
Germany
13·227 Posts 
4*5^7546111 is prime: 527452 decimal digits.

20190225, 15:32  #54 
Mar 2006
Germany
13·227 Posts 
4*5^8647511 is prime: 604436 decimal digits.
I've not updated the OEIS seq with the last two primes, will do after reaching n=1M. 
20190404, 10:01  #55 
Mar 2006
Germany
13·227 Posts 
4*5^n1 completed to n=1M and releasing
 no more primes found  OEIS / Wiki updated  S.Harvey informed 
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