A182198 Primes of form a^2 + b^2 such that a^4 + b^4 is prime.

2, 5, 13, 17, 29, 37, 41, 53, 73, 89, 137, 149, 157, 181, 257, 269, 281, 293, 313, 349, 373, 397, 401, 409, 421, 461, 541, 557, 577, 593, 661, 709, 733, 757, 769, 773, 797, 853, 937, 953, 1021, 1049, 1069, 1181, 1237, 1277, 1301, 1373, 1429, 1433, 1453, 1489

Offset: 1

Author

Thomas Ordowski, Apr 20 2012

Keywords

• nonn

Examples

			13 = 2^2 + 3^2, 2^4 + 3^4 = 97 is prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A002313.

Cf. A003336 (numbers that are the sum of 2 nonzero 4th powers).

Cf. A002645 (quartan primes: primes of the form x^4 + y^4).

Programs

Mathematica

nn = 40; t = {}; Do[c = a^2 + b^2; If[c < nn^2 && PrimeQ[c] && PrimeQ[a^4 + b^4], AppendTo[t, c]], {a, nn}, {b, a}]; Sort[t] (* T. D. Noe, Apr 22 2012 *)
Take[#[[1]]^2+#[[2]]^2&/@Select[Tuples[Range[40],2],AllTrue[{#[[1]]^2+ #[[2]]^2, #[[1]]^4+#[[2]]^4},PrimeQ]&]//Union,60] (* Harvey P. Dale, Jun 25 2018 *)

PARI

list(lim)=my(v=List(),t);lim\=1;for(x=1,sqrtint(lim),for(y=1, min(sqrtint(lim-x^2),x), if(isprime(t=x^2+y^2)&&isprime(x^4+y^4), listput(v,t)))); vecsort(Vec(v),,8) \\ Charles R Greathouse IV, Apr 22 2012