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%I #13 Jan 11 2021 10:51:03
%S 5,7,79,13,223,19,439,
%T 130753887906569681111538991218568790437537693430279000532630035672131604633987039552816424896353327834998483765849409837393409377729040653460715050958787058270805333463,
%U 31,34826927179023475480751694965449235272424989980919
%N a(n) is the least prime of the form 2 + Product_{i=n..m} prime(i).
%C If n is in A029707, a(n) = 2+prime(n).
%C If n is not in A029707 but prime(n) is in A051507, a(n) = 2+prime(n)*prime(n+1).
%C a(15) > 10^1000 if it exists.
%H Robert Israel, <a href="/A340468/b340468.txt">Table of n, a(n) for n = 2..14</a>
%e a(2) = 2+3 = 5.
%e a(3) = 2+5 = 7.
%e a(4) = 2+7*11 = 79.
%e a(5) = 2+11 = 13.
%e a(6) = 2+13*17 = 223.
%e a(7) = 2+17 = 19.
%e a(8) = 2+19*23 = 439.
%e a(9) = 2+23*29*...*431.
%p f:= proc(n) local i,t;
%p t:= 1;
%p for i from n do
%p t:= t*ithprime(i);
%p if isprime(t+2) then return t+2 fi;
%p od
%p end proc:
%p seq(f(n),n=2..14);
%o (Python)
%o from sympy import isprime, nextprime, prime
%o def a(n):
%o prodpnpm = pm = prime(n)
%o while not isprime(2+prodpnpm): pm = nextprime(pm); prodpnpm *= pm
%o return 2+prodpnpm
%o print([a(n) for n in range(2, 12)]) # _Michael S. Branicky_, Jan 08 2021
%Y Cf. A029707, A051507.
%K nonn
%O 2,1
%A _Robert Israel_, Jan 08 2021
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