By analogy with the definition of the factorial function
, the primorial
of a prime
(often denoted by a hash
#) is defined as the product of all primes up to and including p
. For example,
7# = 2 x 3 x 5 x 7 = 210
Mathematicians (with perhaps more computer time than they deserve) have searched out many huge primes which are one greater or less than various primorials. This is reminiscent of the use of primorials in Euclid's proof of the infinitude of primes.
An interesting conjecture put forward by Odlyzko, Rubinstein and Wolf in Experimental Mathematics (Vol. 8, No. 2, 1999) states that the set of primorials, along with the number 4, is precisely the set of jumping champions.