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


def primes:
  2, range(3; infinite; 2) | select(is_prime);
 
# generate an infinite stream of primorials
def primorials:
  foreach primes as $p (1; .*$p; .);
 
# Emit a sorted array of the first $limit distinct fortunate numbers
# generated in order of the primoridials
def fortunates($limit):
  label $out
  | foreach primorials as $p ([];
      first( range(3; infinite; 2) | select($p + . | is_prime)) as $q
      | . + [$q] | unique;
      if length >= $limit then ., break $out else empty end);
 
fortunates(10)