Primorial primes are primes of the form p_n # ± 1, where p_n # is the primorial of p_n. A coordinated search for such primes is being conducted on PrimeGrid. p_n # - 1 is prime for n = 2, 3, 5, 6, 13, 24, 66, 68, 167, 287, 310, 352, 564, 590, 620, 849, 1552, 1849, 67132, 85586, ... (OEIS A057704; Guy 1994, pp. 7-8; Caldwell 1995). These correspond to p# - 1 with p = 3, 5, 11, 13, 41, 89, 317, 337, 991, 1873, 2053, 2377, 4093, 4297, 4583, 6569, 13033, 15877, 843301, 1098133, ... (OEIS A006794). The largest known primorial primes p_n # - 1 as of Nov. 2015 are summarized in the following table.

factorial | factorial prime | integer sequence primes | primorial