Prime Residue Class of Uniform Charges on the Integers

There is a probability charge on the power set of the integers that gives probability 1 /  p to every residue class modulo a prime p . There exists such a charge that gives probability w to the set of prime numbers iff w ∈ [ 0 , 1 / 2 ] . Similarly, there is such a charge that gives probability x to...

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Bibliographic Details
Published in:Journal of theoretical probability 2020-03, Vol.33 (1), p.340-360
Main Authors: Spece, Michael, Kadane, Joseph B.
Format: Article
Language:English
Subjects:
Integers
Mathematics
Mathematics and Statistics
Prime numbers
Probability Theory and Stochastic Processes
Statistics
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Summary:There is a probability charge on the power set of the integers that gives probability 1 /  p to every residue class modulo a prime p . There exists such a charge that gives probability w to the set of prime numbers iff w ∈ [ 0 , 1 / 2 ] . Similarly, there is such a charge that gives probability x to a residue class modulo c , where c is composite, iff x ∈ [ 0 , 1 / y ] , where y is the largest prime factor of c .
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-018-0860-y