Definition
A Fortunate number is the smallest integer m > 1 such that for a given positive integer n, primorial(n) + m is a prime number, where primorial(n) is the product of the first n prime numbers.

For example the first fortunate number is 3 because primorial(1) is 2 and 2 + 3 = 5 which is prime whereas 2 + 2 = 4 is composite.



Task
After sorting and removal of any duplicates, compute and show on this page the first 8 Fortunate numbers or, if your language supports big integers, the first 50 Fortunate numbers.



Related task
 Primorial numbers


See also
 oeis:A005235 Fortunate numbers 
 oeis:A046066 Fortunate numbers, sorted with duplicates removed


firstPrimes: select 1..100 => prime?
primorial: function [n][
    product first.n: n firstPrimes
]
 
fortunates: []
i: 1
 
while [8 > size fortunates][
    m: 3
    pmi: primorial i
    while -> not? prime? m + pmi
          -> m: m+2
    fortunates: unique fortunates ++ m
    i: i + 1
]
 
print sort fortunates