Gaps between integers with the same prime factors

Cochrane, Todd; Dressler, Robert

doi:10.1090/S0025-5718-99-01024-8

Gaps between integers with the same prime factors
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by Todd Cochrane and Robert E. Dressler PDF

Math. Comp. 68 (1999), 395-401 Request permission

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 $a <c$ 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 $a$ and $c$ up to $7\cdot 10^{13}$.

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