Analog of the Skewes number for twin primes
Marek Wolf

TL;DR
This paper reports extensive computational evidence on the sign changes of the difference between twin prime counts and the Hardy-Littlewood conjecture, suggesting a new analog of the Skewes number for twin primes.
Contribution
It provides the first large-scale computational investigation into the sign changes of the twin prime counting difference and proposes a conjecture for their distribution.
Findings
Over 90000 sign changes for x<2^42
Sign changes occur at unexpectedly low x values
Conjecture: number of sign changes ~ sqrt(T)/log(T)
Abstract
The results of the computer investigation of the sign changes of the difference between the number of twin primes and the Hardy--Littlewood conjecture are reported. It turns out that changes the sign at unexpectedly low values of and for there are over 90000 sign changes of this difference. It is conjectured that the number of sign changes of for is given by .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Identities · Finite Group Theory Research
