A250294 Primes p such that p#-1 is a semiprime, where # is the primorial (A034386).

7, 17, 29, 31, 43, 59, 71, 73, 97, 101, 223, 233, 257, 439, 503, 709, 859, 863, 1013

Offset

1,1

Comments

1153 and 1381 are also terms. - Amiram Eldar, Feb 16 2020

a(20) >= 1091. 1091# - 1 is a 458-digit composite with no known factors. - Hugo Pfoertner, Feb 05 2021

Links

Table of n, a(n) for n=1..19.

FactorDB Factorization of 1013#-1.

FactorDB Status of 1091#-1.

Hisanori Mishima, Factorizations of many number sequences, PI Pn - 1 (n = 1 to 110) (2013).

Formula

A001221(A034386(a(n)) - 1) = 2. - Amiram Eldar, Feb 16 2020

Example

a(2) = 17 so 17# - 1 = 510509 = 61 * 8369 is a semiprime.

Mathematica

p = Select[Range[101], PrimeQ]; p[[ Position[FoldList[Times, p] - 1, _?(PrimeOmega[#] == 2 &)] //Flatten ]] (* Amiram Eldar, Feb 16 2020 *)

Crossrefs

Cf. A001221, A001358, A002110, A006794, A034386, A057588, A078781, A250293.

Sequence in context: A045575 A029532 A217926 * A157417 A356293 A294133

Adjacent sequences: A250291 A250292 A250293 * A250295 A250296 A250297

Keyword

nonn,hard,more

Author

Eric Chen, Dec 24 2014

Extensions

a(15)-a(18) using factordb.com from Amiram Eldar, Feb 16 2020

a(19) using factordb.com from Hugo Pfoertner, Feb 05 2021

Edited by Max Alekseyev, Aug 26 2021

Status

approved