Just to find a large prime number....

Starting from 2, generate a set of subsequent numbers like this:

a1 = 2
a2 = a1 + 1
a3 = a1*a2 + 1
a4 = a1*a2*a3 + 1
.
.
.
an = a1*...*a(n-1) + 1

This set of numbers should all be primes, but it doesn't contain all the prime numbers in order.