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 $7\cdot 10^{13}$.References
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Additional Information
- Todd Cochrane
- Affiliation: Kansas State University, Manhattan KS 66506, U. S. A.
- MR Author ID: 227122
- Email: cochrane@math.ksu.edu
- Robert E. Dressler
- Affiliation: Kansas State University, Manhattan KS 66506, U. S. A.
- Email: dressler@math.ksu.edu
- Received by editor(s): February 24, 1996
- Received by editor(s) in revised form: October 7, 1996
- Additional Notes: The authors wish to thank the referee for his/her helpful comments, which inspired the addition of Theorem 2 and the Example to the paper.
- © Copyright 1999 American Mathematical Society
- Journal: Math. Comp. 68 (1999), 395-401
- MSC (1991): Primary 11N25, 11N05
- DOI: https://doi.org/10.1090/S0025-5718-99-01024-8
- MathSciNet review: 1613691