Compositorial

The compositorial of n is defined as n!/n#, where n# is the primorial of n. It was named by Iago Camboa.Prime glossary. Prime GlossaryPlanetMath. Compositorial It is the product of all the composite numbers less than or equal to n.
The numbers n!/n# ± 1 (when prime) is given the name compositorial prime.
* Numbers k such that k!/k# + 1 is prime are 0, 1, 2, 3, 4, 5, 8, 14, 20, 26, 34, 56, 104, 153, 182, 194, 217, 230, 280, 281, 462, 463, 529, 1445, 2515, 3692, 6187, 6851, 13917, 17258, 48934, ...OEIS. A140294 Numbers k such that k!/k# + 1 is prime, where k# is the primorial function.
* Numbers k such that k!/k#-1 is prime are 4, 5, 6, 7, 8, 16, 17, 21, 34, 39, 45, 50, 72, 73, 76, 133, 164, 202, 216, 221, 280, 281, 496, 605, 2532, 2967, 3337, 8711, 10977, 13724, 15250, 18160, 20943, 33684, 41400, ...OEIS. A140293 Numbers k such that k!/k#-1 is prime, where k# is the primorial function
As 280 is in both of these sequences, 280!/280# ± 1 are twin primes (281!/281# ± 1 is the same value).
== Sources ==
Category:Factorials