> Let a,b,c be consecutive natural numbers, where a >1

why?

> (a*c)-b appears to offer a greater density of primes than the norm;

Call them n-1, n, and n+1 instead of a, b and c. Then a*c-b is

n^2 - n - 1. This is never divisible by 2, so produces twice the

primes "as usual." It is never divisible by 3, so that gives a

factor of 3/2. Nor by 7, that gives 7/6. So with these alone

we expect 3.5 times the usual number.

CC