4 Jul
2006
4 Jul
'06
4:19 a.m.
with an even exponent. And Erdos proved the following refinement of Bertrand's postulate: the interval from n to 2n always contains both a 1 mod 4 and a 3 mod 4 prime.
The Prime Number Theorem implies that given e>0, there exists N such that for all x>N there is a prime between x and (1+e)x. Can this be strengthened to "there is a prime = 1 mod 4 and a prime = 3 mod 4 between x and (1+e)x" ? Gary McGuire