A319217 Integers k such that (13*2^k)^8 + 1 is prime.

4, 9, 13, 38, 42, 67, 133, 134, 142, 155, 167, 226, 654, 5787, 6703, 12704, 25969, 70198, 78060, 235304

Offset: 1

Author

Lei Zhou, Sep 13 2018

Keywords

• nonn
• hard
• more

Comments

These numbers are a subset of Generalized Fermat Primes power 8.

All numbers from 1 to 235763 has been checked by LLR, no other primes found.

k is not congruent to 6 mod 25 because otherwise (13*2^k)^8+1 would be divisible by 401. - Bruno Berselli, Sep 21 2018

Examples

			4 is a term because (13*2^4)^8+1 = 3503536769037500417 is a prime number.
		

Links

• Chris K. Caldwell, The Prime Database: 815730721*2^1882432+1

Programs

Magma

[n: n in [1..700] | IsPrime((13*2^n)^8+1)]; // Vincenzo Librandi, Sep 21 2018

Mathematica

Select[Range[700], PrimeQ[(13 2^#)^8 + 1] &] (* Vincenzo Librandi, Sep 21 2018 *)

PARI

isok(k) = ispseudoprime((13*2^k)^8+1); \\ Altug Alkan, Sep 21 2018