Gaps between integers with the same prime factors
Authors:
Todd Cochrane and Robert E. Dressler
Journal:
Math. Comp. 68 (1999), 395401
MSC (1991):
Primary 11N25, 11N05
MathSciNet review:
1613691
Fulltext PDF Free Access
Abstract 
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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:
http://dx.doi.org/10.1090/S0025571899010248
PII:
S 00255718(99)010248
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
