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

Author

Eric Chen, Dec 24 2014

Keywords

• nonn
• hard
• more

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

Examples

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

Links

• 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).

Crossrefs

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

Programs

Mathematica

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

Formula

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

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