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

1,1

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.

Links

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

Example

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.

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 *)

Prog

(PARI) isA157764(n) = isprime(n) && isprime(n^16+65536) \\ Michael B. Porter, Dec 17 2009
(GAP) Filtered(Filtered([1..10^3], IsPrime), p->IsPrime(p) and IsPrime(p^16+2^16)); # Muniru A Asiru, Feb 04 2018

Crossrefs

Cf. A062324.

Sequence in context: A226241 A033254 A215165 * A032691 A146332 A146352

Adjacent sequences: A157761 A157762 A157763 * A157765 A157766 A157767

Keyword

nonn

Author

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

Extensions

More terms from Muniru A Asiru, Feb 05 2018

Status

approved