A191555 -id:A191555 - cp's OEIS frontend

A191623 Primes of the form 1 + Product_{k=1..n} prime(k)^(2^(k-1)).

3, 19, 11251, 2980024297506569894680811251

Offset: 1

Jonathan Vos Post, Jun 09 2011

nonn

Primes of the form 1 + A191554(k), associated with positions k = 1, 2, 3, and 5 there. The next one (if it exists) occurs at k >= 15 and has > 53500 digits. [Edited by R. J. Mathar, Jun 17 2011 and Joerg Arndt, Jun 21 2011]

This connects A191554 and A191555, which are deeply about primes and monic polynomial irreducible by Eisenstein's Criterion, to primes by another way, connecting additive and multiplicative number theory analogously to the relationship in Primorial primes: A014545, n such that n-th Euclid number (A006862(n)) = 1 + (Product of first n primes) is prime.

			a(1) = 1 + 2^1 = 1 + 2 = 3 is prime.
a(2) = 1 + (2^1 * 3^2) = 1 + 18 = 19 is prime.
a(3) = 1 + (2^1 * 3^2 * 5^4) = 1 + 11250 = 11251 is prime.

Cf. A000040, A191554.

Select[Array[1 + Product[Prime[k]^(2^(k - 1)), {k, #}] &, 5], PrimeQ] (* Michael De Vlieger, Feb 15 2020 *)

cp's OEIS Frontend

A191623 Primes of the form 1 + Product_{k=1..n} prime(k)^(2^(k-1)).

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