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


require "gmp"
 
primorials = Enumerator.new do |y|
  cur = prod = 1
  loop {y << prod *= (cur = GMP::Z(cur).nextprime)}
end
 
limit = 50
fortunates = []
while fortunates.size < limit*2 do
  prim = primorials.next
  fortunates << (GMP::Z(prim+2).nextprime - prim)
  fortunates = fortunates.uniq.sort
end
 
p fortunates[0, limit]
 