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


import "/math" for Int
import "/big" for BigInt
import "/sort" for Sort
import "/seq" for Lst
import "/fmt" for Fmt
 
var primes = Int.primeSieve(379)
var primorial = BigInt.one
var fortunates = []
for (prime in primes) {
    primorial = primorial * prime
    var j = 3
    while (true) {
        if ((primorial + j).isProbablePrime(5)) {
            fortunates.add(j)
            break
        }
        j = j + 2
    }
}
fortunates = Lst.distinct(fortunates)
Sort.quick(fortunates)
System.print("After sorting, the first 50 distinct fortunate numbers are:")
for (chunk in Lst.chunks(fortunates[0..49], 10)) Fmt.print("$3d", chunk)