A071150 Primes p such that the sum of all odd primes <= p is also a prime.

3, 29, 53, 61, 251, 263, 293, 317, 359, 383, 503, 641, 647, 787, 821, 827, 911, 1097, 1163, 1249, 1583, 1759, 1783, 1861, 1907, 2017, 2287, 2297, 2593, 2819, 2837, 2861, 3041, 3079, 3181, 3461, 3541, 3557, 3643, 3779, 4259, 4409, 4457, 4597, 4691, 4729, 4789

Offset: 1

Author

Labos Elemer, May 13 2002

Keywords

• easy
• nonn

Examples

			29 is a prime and 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 = 127 (also a prime), so 29 is a term. - _Jon E. Schoenfield_, Mar 29 2021
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..5908

Crossrefs

Analogous to A013917.

Cf. A065091, A071148, A071149, A013916, A013917, A013918, A007504.

Programs

Maple

SoddP := proc(n)
    option remember;
    if n <= 2 then
        0;
    elif isprime(n) then
        procname(n-1)+n;
    else
        procname(n-1);
    fi ;
end proc:
isA071150 := proc(n)
    if isprime(n) and isprime(SoddP(n)) then
        true;
    else
        false;
    end if;
end proc:
n := 1 ;
for i from 3 by 2 do
    if isA071150(i) then
        printf("%d %d\n",n,i) ;
        n := n+1 ;
    end if;
end do: # R. J. Mathar, Feb 13 2015

Mathematica

Function[s, Select[Array[Take[s, #] &, Length@ s], PrimeQ@ Total@ # &][[All, -1]]]@ Prime@ Range[2, 640] (* Michael De Vlieger, Jul 18 2017 *)
Module[{nn=650,pr},pr=Prime[Range[2,nn]];Table[If[PrimeQ[Total[Take[ pr, n]]], pr[[n]],Nothing],{n,nn-1}]] (* Harvey P. Dale, May 12 2018 *)

Python

from sympy import isprime, nextprime
def aupto(limit):
  p, s, alst = 3, 3, []
  while p <= limit:
    if isprime(s): alst.append(p)
    p = nextprime(p)
    s += p
  return alst
print(aupto(4789)) # Michael S. Branicky, Mar 29 2021