20170812, 03:09  #34 
Nov 2016
2×5×223 Posts 
Searched up to b=260.

20170812, 15:23  #35 
Nov 2016
2×5×223 Posts 
Searched up to b=300.

20170815, 16:34  #36 
Nov 2016
2×5×223 Posts 
Searched up to b=432.
Last fiddled with by sweety439 on 20170815 at 16:35 
20170921, 16:21  #37 
Nov 2016
2·5·223 Posts 
Links for the full list for the n's <= 1000 such that (b+1)*b^n+1 is prime for bases b <= 1000:
(b1)*b^n1 case: http://www.bitman.name/math/table/484 (b1)*b^n+1 case: http://www.bitman.name/math/table/477 (b+1)*b^n1 case: http://www.bitman.name/math/table/471 (b+1)*b^n+1 case: http://www.bitman.name/math/table/474 Last fiddled with by sweety439 on 20170921 at 16:21 
20171017, 22:41  #38 
Nov 2016
2230_{10} Posts 
Searched the dual form (i.e. b^n+b+1) for bases 2<=b<=48.
Note 1: The name of the file is not right, it should be "numbers n such that b^n+b+1 is (probable) prime for b up to 48". Note 2: In this file, "b, +1, +1" means "b^n+b+1", e.g. "12, +1, 1" means "12^n+121", "19, 1, +1" means "19^n19+1". Note 3: If b = 1 (mod 3), then all numbers of the form b^n+b+1 are divisible by 3, thus "b, +1, +1" should not be searched for b = 1 (mod 3). Note 4: Some large terms may be only probable primes (i.e. not definite primes), since for these numbers N, neither N1 nor N+1 can be trivially written into a product. Last fiddled with by sweety439 on 20171017 at 22:48 
20171017, 23:08  #39  
Nov 2016
2×5×223 Posts 
Quote:
The dual of (b1)*b^n+1 (b+ for original form) is b^n+(b1) = b^n+b1 (b+ for dual form) The dual of (b+1)*b^n1 (b+ for original form) is b^n(b+1) = b^nb1 (b for dual form) The dual of (b+1)*b^n+1 (b++ for original form) is b^n+(b+1) = b^n+b+1 (b++ for dual form) A form and its dual form have the same Nash weight, thus, the possibility for them to have a prime in the given interval of n are the same. Last fiddled with by sweety439 on 20171019 at 04:18 

20171018, 01:31  #40 
Nov 2016
2×5×223 Posts 
Dual form searched up to b=160, up to n=1024.
Last fiddled with by sweety439 on 20171018 at 02:53 
20171018, 02:09  #42 
Nov 2016
2·5·223 Posts 
Also these sequences:
Least k>=1 such that n^kn1 is prime: http://oeis.org/A178250 Least k>=1 such that n^kn+1 is prime: http://oeis.org/A113516 Least k>=1 such that n^k+n1 is prime: http://oeis.org/A076845 Least k>=1 such that n^k+n+1 is prime: (sequence not in OEIS) Last fiddled with by sweety439 on 20171018 at 02:24 
20171018, 02:35  #43  
Nov 2016
2×5×223 Posts 
Quote:
(b1)*b^n1 case: http://oeis.org/A122396 (the "n" in this formula is one less than the number in the sequence) (b1)*b^n+1 case: http://oeis.org/A087139 (the "n" in this formula is one less than the number in the sequence) 

20171018, 02:42  #44  
Nov 2016
2·5·223 Posts 
Quote:
The dual of 11*12^n1 is 12^n11 The dual of 11*12^n+1 is 12^n+11 The dual of 13*12^n1 is 12^n13 The dual of 13*12^n+1 is 12^n+13 

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