# On the Probability That Two Random Integers Are Coprime

@article{Lei2018OnTP,
title={On the Probability That Two Random Integers Are Coprime},
author={Jing Lei and Joseph B. Kadane},
journal={arXiv: Probability},
year={2018}
}
• Published 31 May 2018
• Mathematics
• arXiv: Probability
We show that there is a non-empty class of finitely additive probabilities on $\mathbb N^2$ such that for each member of the class, each set with limiting relative frequency $p$ has probability $p$. Hence, in that context the probability that two random integers are coprime is $6/\pi^2$. We also show that two other interpretations of "random integer," namely residue classes and shift invariance, support any number in $[0, 6/\pi^2]$ for that probability. Finally, we specify a countably additive… Expand
1 Citations
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• Mathematics
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This paper is devoted to survey the rich theory, some of it quite recent, concerning the divisibility properties, of various kinds, of random r-tuples of positive integers.

#### References

SHOWING 1-10 OF 11 REFERENCES
Uniform Distributions on the Natural Numbers
• Mathematics
• 2007
Abstract We compare the following three notions of uniformity for a finitely additive probability measure on the set of natural numbers: that it extend limiting relative frequency, that it beExpand
Using Finitely Additive Probability: Uniform Distributions on the Natural Numbers
• Mathematics
• 1995
Abstract In the usual, countably additive definition of probability, it is not possible to have a distribution giving equal probabilities to every one of the natural numbers. Yet such a distributionExpand
Relative frequencies
The probability of an event is the limit of its relative frequency in the long run. This was the concept or interpretation developed and advocated in Reichenbach's The Theory of Probability. ItExpand
An Introduction to the Theory of Numbers
• Mathematics, Philosophy
• 1938
This is the fifth edition of a work (first published in 1938) which has become the standard introduction to the subject. The book has grown out of lectures delivered by the authors at Oxford,Expand
Theory of Probability: A Critical Introductory Treatment
• Mathematics
• 2017
Part 7 A preliminary survey: heads and tails - preliminary considerations heads and tails - the random process laws of "large numbers" the "central limit theorem". Part 8 Random processes withExpand
Foundations of the theory of probability
Theories of ProbabilityFoundations of Probabilistic Logic ProgrammingGood ThinkingStatistical Foundations of Data ScienceFoundations of Risk AnalysisFoundations of Estimation TheoryThe Foundations ofExpand
Theory of Charges
• 1983
Set Theoretic Structures in Science.
• 1967