A340468 a(n) is the least prime of the form 2 + Product_{i=n..m} prime(i).

5, 7, 79, 13, 223, 19, 439, 130753887906569681111538991218568790437537693430279000532630035672131604633987039552816424896353327834998483765849409837393409377729040653460715050958787058270805333463, 31, 34826927179023475480751694965449235272424989980919

Offset: 2

Author

Robert Israel, Jan 08 2021

Keywords

• nonn

Comments

If n is in A029707, a(n) = 2+prime(n).

If n is not in A029707 but prime(n) is in A051507, a(n) = 2+prime(n)*prime(n+1).

a(15) > 10^1000 if it exists.

Examples

			a(2) = 2+3 = 5.
a(3) = 2+5 = 7.
a(4) = 2+7*11 = 79.
a(5) = 2+11 = 13.
a(6) = 2+13*17 = 223.
a(7) = 2+17 = 19.
a(8) = 2+19*23 = 439.
a(9) = 2+23*29*...*431.
		

Links

• Robert Israel, Table of n, a(n) for n = 2..14

Crossrefs

Cf. A029707, A051507.

Programs

Maple

f:= proc(n) local i,t;
  t:= 1;
  for i from n do
    t:= t*ithprime(i);
    if isprime(t+2) then return t+2 fi;
  od
end proc:
seq(f(n),n=2..14);

Python

from sympy import isprime, nextprime, prime
def a(n):
  prodpnpm = pm = prime(n)
  while not isprime(2+prodpnpm): pm = nextprime(pm); prodpnpm *= pm
  return 2+prodpnpm
print([a(n) for n in range(2, 12)]) # Michael S. Branicky, Jan 08 2021