A329540 Numbers m such that the sum of the first m primes as well as the sum of the squares, the sum of the cubes and the sum of 4th powers of the first m primes are prime.

3618, 743322, 1557552, 1808652, 2128724, 2242290, 2486874, 3534560, 4220258, 4617614, 4763114, 5701340, 5894718, 5921088, 6378312, 8376932, 8883662, 9021482, 10113080, 10766654, 11172798, 12168908, 14188014, 14806460, 16369448, 19775468, 19954778, 21259494, 21855360, 22533638

Offset: 1

Author

Michel Marcus, Nov 16 2019

Keywords

• nonn

Links

• Daniel Suteu, Table of n, a(n) for n = 1..1000
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 3618
• Carlos Rivera, Puzzle 978. Improve this curio, Prime Puzzles and Problems Connection.

Crossrefs

Cf. A124225, A329539.

Programs

PARI

s=0; t=0; u=0; v=0; n=0; forprime(p=2, 1e8, s+=p; t+=p^2; u+=p^3; v+=p^4; n++; if (isprime(v) && isprime(u) && isprime(t) && isprime(s), print1(n, ", ")))

Extensions

a(13)-a(30) from Daniel Suteu, Nov 16 2019