A250293 Primes p such that p#+1 is a semiprime, where # is the primorial (A034386).

13, 19, 23, 43, 61, 67, 73, 83, 101, 139, 151, 173, 223, 251, 383, 457, 571, 673, 761

Offset

1,1

Comments

The next candidate after 571 is 859. 859# + 1 is a 359-digit composite with no known factors. - Hugo Pfoertner, Feb 05 2021

Links

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

factordb.com, Status of 859#+1.

Hisanori Mishima, Factorizations of many number sequences, PI Pn + 1 (n = 1 to 110) (2012).

Formula

a(n) = prime(A085725(n)). - Hugo Pfoertner, Feb 05 2021

Example

a(1) = 13 so 13# + 1 = 30031 = 59 * 509 is a semiprime.

Mathematica

Prime[#]&/@(Module[{pmrl=FoldList[Times, Prime[Range[50]]]}, Position[ pmrl, _?(PrimeOmega[ #+1]==2&)]]//Flatten) (* Harvey P. Dale, Apr 29 2017 *)

Crossrefs

Cf. A005234, A006862, A034386, A078778, A085725, A250294.

Sequence in context: A121877 A109902 A214031 * A058898 A227092 A123840

Adjacent sequences: A250290 A250291 A250292 * A250294 A250295 A250296

Keyword

nonn,hard,more

Author

Eric Chen, Dec 24 2014

Extensions

a(16)-a(18) using factordb.com from Hugo Pfoertner, Feb 05 2021

Missing 571 inserted by Sean A. Irvine, Mar 03 2023

Status

approved