A329539 Numbers m such that the sum of the first m primes as well as the sum of the squares and the sum of the cubes of the first m primes are all prime.
3618, 5840, 7716, 17502, 19460, 22398, 23520, 26852, 33824, 41202, 45848, 47328, 62138, 72950, 82722, 101084, 118062, 127160, 128784, 134012, 136380, 148940, 165240, 173658, 175220, 175310, 177516, 187556, 193692, 203310, 230802, 234032, 279102, 281754, 285518, 289970, 295196, 298652
Offset: 1
Keywords
Links
- G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 3618
- Carlos Rivera, Puzzle 978. Improve this curio, Prime Puzzles and Problems Connection.
Programs
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Mathematica
Module[{nn=300000,prs,m1,m2,m3},prs=Prime[Range[nn]];m1=Accumulate[ prs];m2 = Accumulate[prs^2];m3=Accumulate[prs^3];Position[Thread[ {m1,m2,m3}],? (Total[ Boole[ PrimeQ[#]]]==3&)]]//Flatten (* _Harvey P. Dale, Jul 28 2021 *) -
PARI
s=0; t=0; u=0; n=0; forprime(p=2, 1e6, s+=p; t+=p^2; u+=p^3; n++; if(isprime(u) && isprime(t) && isprime(s), print1(n, ", ")))
Extensions
Name (description) modified by Harvey P. Dale, Jul 28 2021