Let P(n)= The product of the first n primes.

P(n)+1 is like Euclid's method to show there are infinitely many primes, and may or not be prime itself. Now look at the difference between P(n) and the *next* prime after P(n)+1.

n=1, 5-(2)=3

n=2, 11-(2x3)=5

n=3, 37-(2x3x5)=7

n=4, 223-(2x3x5x7)=13

n=5, 2333-(2x3x5x7x11)=23

n=6, 30047-(2x3x5x7x11x13)=17

n=7, 510529-(2x3x5x7x11x13x17)=19

n=8, 9699713-(2x3x5x7x11x13x17x19)=23

Are these differences always prime?