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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.

%I A329540 #12 Nov 17 2019 02:27:55
%S A329540 3618,743322,1557552,1808652,2128724,2242290,2486874,3534560,4220258,
%T A329540 4617614,4763114,5701340,5894718,5921088,6378312,8376932,8883662,
%U A329540 9021482,10113080,10766654,11172798,12168908,14188014,14806460,16369448,19775468,19954778,21259494,21855360,22533638
%N 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.
%H A329540 Daniel Suteu, <a href="/A329540/b329540.txt">Table of n, a(n) for n = 1..1000</a>
%H A329540 G. L. Honaker, Jr. and Chris Caldwell, <a href="https://primes.utm.edu/curios/page.php?short=3618">Prime Curios! 3618</a>
%H A329540 Carlos Rivera, <a href="https://www.primepuzzles.net/puzzles/puzz_978.htm">Puzzle 978. Improve this curio</a>, Prime Puzzles and Problems Connection.
%o A329540 (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, ", ")))
%Y A329540 Cf. A124225, A329539.
%K A329540 nonn
%O A329540 1,1
%A A329540 _Michel Marcus_, Nov 16 2019
%E A329540 a(13)-a(30) from _Daniel Suteu_, Nov 16 2019