> Let 10^n+x be the smallest PRP(prime) past 10^n

This looks like a small numbers example of the error term

> let 10^n-y be the largest PRP (prime) before 10^n

> Then f(n) = x-y and F(n) = sum f(m) for m = 1 to n

> F(n) remains negative for after n = 2652

> The conjecture is that it is always negative thereafter.

in the distribution of x and y.

I guess, it is more reasonable to assume that F(n) changes

its sign infinitely often - similar to the behaviour of

pi(x) - Li(x).

Regards,

Ronny