In number theory, a Fortunate number, named after Reo Fortune, is the smallest integer m > 1 such that, for a given positive integer n, pn# + m is a prime number, where the primorial pn# is the product of the first n prime numbers.
For example, to find the seventh Fortunate number, one would first calculate the product of the first seven primes (2, 3, 5, 7, 11, 13 and 17), which is 510510.
If a composite Fortunate number does exist, it must be greater than or equal to pn+12.
[1] A Fortunate prime is a Fortunate number which is also a prime number.
As of 2017[update], all known Fortunate numbers are prime, checked up to n=3000.