- Experiment. Math.
- Volume 20, Issue 4 (2011), 400-411.
Frequencies of Successive Pairs of Prime Residues
We consider statistical properties of the sequence of ordered pairs obtained by taking the sequence of prime numbers and reducing modulo $m$. Using an inclusion/exclusion argument and a cutoff of an infinite product suggested by Pólya, we obtain a heuristic formula for the "probability" that a pair of consecutive prime numbers of size approximately $x$ will be congruent to $(a, a + d)$ modulo $m$. We demonstrate some symmetries of our formula. We test our formula and some of its consequences against data for $x$ in various ranges.
Experiment. Math., Volume 20, Issue 4 (2011), 400-411.
First available in Project Euclid: 8 December 2011
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Ash, Avner; Beltis, Laura; Gross, Robert; Sinnott, Warren. Frequencies of Successive Pairs of Prime Residues. Experiment. Math. 20 (2011), no. 4, 400--411. https://projecteuclid.org/euclid.em/1323367154