A124225 Numbers n such that the sum of the first n primes is prime and the sum of the squares of the first n primes is also prime.

2, 158, 192, 216, 356, 426, 548, 680, 1178, 1196, 1466, 1500, 1524, 2324, 2438, 2904, 2990, 3060, 3146, 3618, 3902, 4110, 4134, 4346, 4602, 5790, 5840, 6186, 6344, 6710, 6720, 6836, 6990, 7592, 7632, 7716, 7790, 7838, 8156, 8420, 8622, 8658, 8664, 9092

Offset: 1

Author

Tanya Khovanova, Dec 13 2006

Keywords

• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 3618
• Carlos Rivera, Puzzle 978. Improve this curio, Prime Puzzles and Problems Connection.

Crossrefs

Intersection of A098561 (Numbers n such that the sum of the squares of the first n primes is prime) and A013916 (Numbers n such that the sum of the first n primes is prime).

Programs

Magma

a013916:=func; a098561:=func; [n: n in [1..10000]|a013916(n) and a098561(n)];  // Bruno Berselli, Dec 28 2011

Mathematica

With[{nn=9100},Position[Thread[{Accumulate[Prime[Range[nn]]],Accumulate[ Prime[ Range[ nn]]^2]}],?(PrimeQ[ #[[1]]]&&PrimeQ[#[[2]]]&),1,Heads-> False]]//Flatten (* _Harvey P. Dale, Aug 18 2020 *)

PARI

s=0;t=0;n=0;forprime(p=2,1e6,s+=p;t+=p^2;n++;if(isprime(t)&&isprime(s),print1(n", "))) \\ Charles R Greathouse IV, Dec 28 2011

Extensions

More terms from Bruno Berselli, Dec 28 2011

Definition rephrased by Harvey P. Dale, Aug 18 2020