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


func fortunate(n) {
    var P = n.pn_primorial
    2..Inf -> first {|m| P+m -> is_prob_prime }
}
 
var limit = 50
var uniq = Set()
var all = []
 
for (var n = 1; uniq.len < 2*limit; ++n) {
    var m = fortunate(n)
    all << m
    uniq << m
}
 
say "Fortunate numbers for n = 1..#{limit}:"
say all.first(limit)
 
say "\n#{limit} Fortunate numbers, sorted with duplicates removed:"
say uniq.sort.first(limit)