A098563 Numbers n such that the sum of the cubes of the first n primes is prime.

4, 8, 38, 48, 98, 102, 118, 128, 130, 132, 156, 168, 172, 178, 180, 190, 202, 208, 308, 346, 358, 364, 424, 482, 540, 600, 602, 614, 646, 676, 722, 748, 768, 776, 782, 792, 838, 902, 1016, 1028, 1036, 1058, 1062, 1082, 1086, 1100, 1102, 1132, 1144, 1176

Offset: 1

Author

Rick L. Shepherd, Sep 14 2004

Keywords

• nonn

Comments

n must clearly be even.

Examples

			4 is a term as the sum of the cubes of the first four primes is 2^3 + 3^3 + 5^3 + 7^3 = 503, which is prime.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A066525 (corresponding primes), A098561 (sums of squares of primes), A013916 (sums of primes), A098999 (sums of cubes of primes).

Programs

Maple

with(numtheory): P:=proc(n) add(ithprime(k)^3, k=1..n): end:
A098563 := proc(n)local m: option remember: if(n=0)then return 0: fi: m:=procname(n-1)+2: while true do if(isprime(P(m)))then return m:fi: m:=m+2:od: end:
seq(A098563(n), n=1..50); # Nathaniel Johnston, Apr 21 2011

Mathematica

Select[Range[1000], PrimeQ[Sum[Prime[i]^3, {i, #}]] &] (* Carl Najafi, Aug 22 2011 *)

PARI

lista(nn) = {s = 0; ip = 0; forprime (p=1, nn, ip++; if (isprime(s+=p^3), print1(ip, ", ")););} \\ Michel Marcus, Aug 22 2015