--- In

primenumbers@yahoogroups.com, "Bill" <bill2math@...> wrote:

>

> Legendre's conjecture claims there is at least one prime between the squares of consecutive integers, and is Capelle's case with n=2 and m = 1.

>

Intuitively Legendre's conjecture would appear to be true: the

rate of growth of the gap between squares looks like it would

far exceed the rate of growth in the average gap between primes.

However the pattern of these gaps can be very uneven and I believe that

it HAS been proven that the gap between primes can be arbitrarily

large. This does not disprove Legendre's conjecture - probably

the only way to do that would be to find a counterexample. Good

with that project!

a.