;Definition

A [https://en.wikipedia.org/wiki/Fortunate_number 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
<br><br>

