A283072 Primes of the form x^2 + y^2 such that x^k + y^k is prime for each k = 4, 8, 16, and 32.

2, 2823521, 5402681, 6272737, 7641961, 11046193, 11139761, 15785213, 17669153, 20109377, 25855177, 28083953, 37168961, 37681297, 40466033, 41565049, 42025793, 42221269, 42550577, 42911753, 48066173, 52249657, 64377449, 71213257, 76895761, 77051053, 82456481, 85983349, 89197877

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..3900

Example

Prime 5 = 2^2 + 1^2 is not a term since 641 divides 2^32 + 1^32.
Prime 7641961 = 2669^2 + 720^2 is a term since 2669^4 + 720^4, 2669^8 + 720^8, 2669^16 + 720^16, and 2669^32 + 720^32 are prime numbers.

Prog

(PARI) list(lim)=my(v=List([2]), t); for(a=1, sqrt(lim), forstep(b=1+a%2, min(a, sqrt(lim-a^2)), 2, if(isprime(t=a^2+b^2) && isprime(a^4+b^4) && isprime(a^8+b^8) && isprime(a^16+b^16) && isprime(a^32+b^32), listput(v, t)))); vecsort(Vec(v)) \\ after Charles R Greathouse IV at A182313

Crossrefs

Subsequence of A182313.

Sequence in context: A303255 A322096 A037051 * A214599 A071066 A337368

Adjacent sequences: A283069 A283070 A283071 * A283073 A283074 A283075

Keyword

nonn

Author

Altug Alkan and Thomas Ordowski, Feb 28 2017

Status

approved