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A191623 Primes of the form 1 + Product_{k=1..n} prime(k)^(2^(k-1)). 1
3, 19, 11251, 2980024297506569894680811251 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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.
LINKS
EXAMPLE
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.
MATHEMATICA
Select[Array[1 + Product[Prime[k]^(2^(k - 1)), {k, #}] &, 5], PrimeQ] (* Michael De Vlieger, Feb 15 2020 *)
CROSSREFS
Sequence in context: A365579 A120563 A182344 * A164063 A092828 A117844
KEYWORD
nonn
AUTHOR
Jonathan Vos Post, Jun 09 2011
STATUS
approved

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Last modified March 29 09:32 EDT 2024. Contains 371268 sequences. (Running on oeis4.)