Gaps between integers

with the same prime factors

Authors:
Todd Cochrane and Robert E. Dressler

Journal:
Math. Comp. **68** (1999), 395-401

MSC (1991):
Primary 11N25, 11N05

MathSciNet review:
1613691

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 , and it is shown that this lower bound is best possible. Dressler's conjecture is verified for values of and up to .

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Additional Information

**Todd Cochrane**

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

Email:
cochrane@math.ksu.edu

**Robert E. Dressler**

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

Email:
dressler@math.ksu.edu

DOI:
https://doi.org/10.1090/S0025-5718-99-01024-8

Keywords:
Primes,
abc

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.

Article copyright:
© Copyright 1999
American Mathematical Society