HackerPapers

arXiv:1603.03720math.NT

Unexpected biases in the distribution of consecutive primes

Robert J. Lemke Oliver, Kannan Soundararajan

Abstract

While the sequence of primes is very well distributed in the reduced residue classes (mod $q$), the distribution of pairs of consecutive primes among the permissible $φ(q)^2$ pairs of reduced residue classes (mod $q$) is surprisingly erratic. This paper proposes a conjectural explanation for this phenomenon, based on the Hardy-Littlewood conjectures. The conjectures are then compared to numerical data, and the observed fit is very good.

arXiv comments
v4: Added dedication v3: Minor revisions to exposition, fixed one typo in Section 5 v2: Added references
Journal reference
DOI
doi:10.1073/pnas.1605366113
Subjects
math.NTNumber Theory

On Hacker News

Linked by 5 identifiable commenters in 5 comments across 3 threads, from Mar 2016 to Feb 2020. Found in 1 HN submission from Mar 2016 to Mar 2016. Open submission discussions.

Comments linking this paper, per year.

Discussed in comments3 threads

  1. Mathematicians Discover Prime Conspiracy (2016) 2 comments

    • paper: "Unexpected biases in the distribution of consecutive primes" http://arxiv.org/abs/1603.03720 explanation for non-experts: "The Last Digit of Prime Numbers - Numberphile" https://www.youtube.com/watch?v=YVvfY_lFUZ8

      bmn__View on HNParent context

    • Abstract: While the sequence of primes is very well distributed in the reduced residue classes (mod q), the distribution of pairs of consecutive primes among the permissible ϕ(q)2 pairs of reduced residue classes (mod q) is surprisingly erratic. This paper proposes a conjectural…

      ganzuulView on HNParent context

  2. Prime After Prime 1 comment

    • The article starts out a bit slow in a convoluted way which may be off-putting. There has been recently a major surprising discovery related to consecutive primes (prepub 11 Mar 2016 http://arxiv.org/abs/1603.03720). The value of the article here imho. compared with the…

      heisenbitView on HNParent context

  3. A previously unnoticed property of prime numbers 2 comments

    • I don't know why you're nitpicking. The article's written for a more general audience that may be interested in the property, but not necessarily the nitty-gritty math behind it. The first paragraph of the article links to the paper, so people who want more detail can get it.…

      jlaroccoView on HNParent context

    • Well, whether it's obvious or not, I think it's in the paper. Immediately under equation (1.1) of http://arxiv.org/abs/1603.03720, the authors are discussing the second correction term to the distribution of primes mod q, and they state: "We can also show that c2(q; (a, b)) =…

      SteuardView on HNParent context

Submitted to Hacker News

Connected through shared HN threads, not inferred similarity or a recommendation.