Hello Bill,

your observation is well-known. It is simply because of the fact that

by N=p1*p2*p3*... +px the p1, p2, p3
are excluded as prime divisors

and therefore N with relatively large probability is prime. If N is

nevertheless not prime and you add 30 until it is prime, that is

because of the fact that after Dirichlet each arithmetic sequence of

the form a*n+b (thus also 30*n+N) contains infintitely many prime

numbers. Btw you may as well choose - instead of +: N=p1*p2*p3*... -px

and powers of p: N=p1^k1*p2^k2*p3^k3... + or - px^kx, where px^kx may

also be 1. By + or - you get a sort of symmetry in the distribution of

(small) prime numbers.

Werner