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Gaps between integers with the same prime factors

Authors:	Todd Cochrane Robert E. Dressler.

Affiliation:	Kansas State University, Manhattan KS 66506, U. S. A. ; Kansas State University, Manhattan KS 66506, U. S. A.

Abstract:	We give numerical and theoretical evidence in support of the conjecture of Dressler that between any two positive integers having the same prime factors there is a prime. In particular, it is shown that the abc conjecture implies that the gap between two consecutive such numbers is $gg a^{1/2 - epsilon }$ , and it is shown that this lower bound is best possible. Dressler's conjecture is verified for values of and up to $7cdot 10^{13}$ .

Keywords:	Primes abc

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