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 A191623 Primes of the form 1 + Prod{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. CROSSREFS Cf. A000040, A191554. Sequence in context: A098796 A120563 A182344 * A164063 A092828 A117844 Adjacent sequences:  A191620 A191621 A191622 * A191624 A191625 A191626 KEYWORD nonn AUTHOR Jonathan Vos Post, Jun 09 2011 STATUS approved

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Last modified July 21 17:19 EDT 2019. Contains 325198 sequences. (Running on oeis4.)