A091367 Primes p such that the sum of the digits raised to the 4th power is prime.

11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 113, 131, 179, 191, 197, 223, 269, 311, 313, 331, 353, 379, 397, 401, 443, 461, 601, 607, 641, 661, 719, 739, 809, 883, 911, 937, 971, 1013, 1019, 1031, 1033, 1091, 1097, 1103, 1109, 1181, 1301, 1303, 1367, 1433

Offset: 1

Author

Chuck Seggelin, Jan 03 2004

Keywords

• base
• nonn

Examples

			a(1) = 11 because 1^4 + 1^4 = 2 which is prime.
a(10) = 89 because 8^4 + 9^4 = 10657 which is prime.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046704 (primes whose digits sum to a prime), A052034 (primes whose digits squared sum to a prime), A091366 (primes whose digits cubed sum to a prime).

Programs

Mathematica

upto=500;Select[Prime[Range[upto]],PrimeQ[Total[IntegerDigits[#]^4]]&] (* Paolo Xausa, Nov 23 2021 *)

Python

from sympy import isprime, primerange
def ok(p): return isprime(sum(int(d)**4 for d in str(p)))
def aupto(limit): return [p for p in primerange(1, limit+1) if ok(p)]
print(aupto(1433)) # Michael S. Branicky, Nov 23 2021