Number Theory

    

Reverse Chebyshev Bias in the Distribution of Superprimes

Authors: Waldemar Puszkarz

We study the distribution of superprimes, a subsequence of prime numbers with prime indices, mod 4. Rather unexpectedly, this subsequenceexhibits a reverse Chebyshev bias: terms of the form 4k + 1 are more common than those of the form 4k + 3, whereas the opposite is the case in the sequence of all primes. The effect, while initially weak and easy to overlook, tends tobe several times larger than the Chebyshev bias for all primes for samples of comparable size, at least, by one simple measure. By two other measures, it can be seen as fairly strong; by the same measures the ordinary Chebyshev effectis very strong. Both of these measures also imply that the reverse Chebyshev bias for superprimes is more volatile than the ordinary Chebyshev bias.

Comments: 12 pages. Originally posted on ResearchGate in September 2023.

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Submission history

[v1] 2023-11-03 09:25:52

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