I Have a mathematician friend and I am trying to convince him of the

following:

Take P(m) to be the set of primes less than the square root of an

integer n.

Take a(m) to be their product.

Consider a matrix in which members of P(m) index rows and in which

each column that is defined as 'unoccupied' is on that does not index

a multiple of a member of P(m).

Take the number of unoccupied columns in an interval of length a(m) to

be u.

By the proof of the Prime Number Theorem, as n increases

pi(n)converges on u*n/a(m).

How can I do this?

Cheers.

Tom