The compositorial of n is defined as n!/n#, where n# is the primorial of n. It was named by Iago Camboa.[1][2] 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.[1]
- 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, ...[3]
- 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, ...[4]
As 280 is in both of these sequences, 280!/280# ± 1 are twin primes (281!/281# ± 1 is the same value).
Sources[]
- ↑ 1.0 1.1 Prime glossary. Prime Glossary
- ↑ PlanetMath. Compositorial
- ↑ OEIS. A140294 Numbers k such that k!/k# + 1 is prime, where k# is the primorial function.
- ↑ OEIS. A140293 Numbers k such that k!/k#-1 is prime, where k# is the primorial function