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A250293
Primes p such that p#+1 is a semiprime, where # is the primorial (A034386).
2
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
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
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