RE: primes between squares calcs
- OOPs! I left out a ">" in my definition of Legendre's conjecture.
Legendre's conjecture is of course for n=2 and m >= 1.
My apologies Bill
- --- In firstname.lastname@example.org, "Bill" <bill2math@...> wrote:
>Intuitively Legendre's conjecture would appear to be true: the
> 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.
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!
- On Sun, 2010-12-12 at 10:13 +0000, Aldrich wrote:
> However the pattern of these gaps can be very uneven and I believeThe proof is trivial. For prime p, all integers n s.t.
> it HAS been proven that the gap between primes can be arbitrarily
> large. This does not disprove Legendre's conjecture - probably
p!+1 < n <= p!+p are divisible by at least one prime <= p and p can be
taken arbitrarily large.