Every soul is allotted 6 numbers, chosen at random from the positive integers.

If such numbers are relatively prime, then the soul is admitted to Heaven - otherwise, not.

What is the probability of an eternal reward?

What is the probability of an eternal reward, if such numbers must be pairwise prime?

Note: the integers 30, 42, 70, and 105 are relatively prime, while the numbers 121, 122, and 123 are pairwise prime, see the definitions at https://primes.utm.edu/glossary/xpage/RelativelyPrime.html

Not from an infinite uniform distribution.  But hey, that's God choosing. As for this puzzle, I'd say it's we're talking about the limit as the size of the range goes to infinity.