A157764 Primes p such that p^16 + 2^16 is also prime.

89, 107, 127, 139, 173, 179, 229, 233, 349, 421, 461, 521, 557, 571, 727, 863, 991, 1019, 1051, 1069, 1433, 1459, 1627, 1747, 1831, 1877, 2081, 2083, 2591, 2837, 3229, 3319, 3361, 3541, 3677, 3697, 3761, 3877, 4201, 4229, 4259, 4271, 4349, 4451, 4561, 4591, 5011, 5119, 5147, 5171, 5531

Offset: 1

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 06 2009

Keywords

• nonn

Comments

Primes Q = n^16 + 2^16 only for odd n note: Q is divisible by 97 if n = 97k +- 48, n = 97k +- 50, n = 97k +- 66, n = 97k +- 70, n = 97k +- 78, n = 97k +- 84, n = 97k +- 90, n = 97k +- 92 of course there are similar rules for each prime divisor.

Examples

			For n=89: 89^16 + 2^16 = 15496731425178936435099327796097 is prime and 89 is prime too.
For n=3: 3 is (first odd) prime but 3^16 + 2^16 = 43112257 = 3041*14177 (not prime).
For n=85: 85^16 + 2^16 = 7425108623606394726715087956161 is prime too, but 85 is not.
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..2915

Crossrefs

Cf. A062324.

Programs

GAP

Filtered(Filtered([1..10^3],IsPrime),p->IsPrime(p) and IsPrime(p^16+2^16)); # Muniru A Asiru, Feb 04 2018

Maple

select(p->isprime(p) and isprime(p^16+2^16), [$1..10^4]); # Muniru A Asiru, Feb 04 2018

Mathematica

Select[Prime[Range[800]],PrimeQ[#^16+65536]&] (* Harvey P. Dale, Sep 07 2019 *)

PARI

isA157764(n) = isprime(n) && isprime(n^16+65536) \\ Michael B. Porter, Dec 17 2009

Extensions

More terms from Muniru A Asiru, Feb 05 2018