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


my @primorials = [\*] grep *.is-prime, ^∞;
 
say display :title("First 50 distinct fortunate numbers:\n"),
   (squish sort @primorials[^75].hyper.map: -> $primorial {
       (2..∞).first: (* + $primorial).is-prime
   })[^50];
 
sub display ($list, :$cols = 10, :$fmt = '%6d', :$title = "{+$list} matching:\n") {
    cache $list;
    $title ~ $list.batch($cols)».fmt($fmt).join: "\n"
}