A Power Law Correction to the Simplified Hardy Littlewood Formula for Twin Primes

We show that the systematic error in the simplified Hardy–Littlewood approximation for twin primes follows a perfect power law with exponent α = 0.900, R² > 0.9999 — providing an instant, accurate prediction for twin prime counts across 8 orders of magnitude. We also falsify the oscillatory zero-pair interaction model (PRIT).

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-01
DOI
https://doi.org/10.5281/zenodo.21107958
Citations
2
Primary Topic
Analytic Number Theory Research
Type
article
Field-Weighted Citation Impact
84.41
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article

A Power Law Correction to the Simplified Hardy Littlewood Formula for Twin Primes

Subhansh Kumar
2 citations
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
84.41
article

A Power Law Correction to the Simplified Hardy Littlewood Formula for Twin Primes

Subhansh Kumar
article en
2 citations

Abstract

We show that the systematic error in the simplified Hardy–Littlewood approximation for twin primes follows a perfect power law with exponent α = 0.900, R² > 0.9999 — providing an instant, accurate prediction for twin prime counts across 8 orders of magnitude. We also falsify the oscillatory zero-pair interaction model (PRIT).

Zenodo (CERN European Organization for Nuclear Research)
Peace, Justice and strong institutions
Openalex Percentile: Top 0%
Analytic Number Theory Research
84.41
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A Power Law Correction to the Simplified Hardy Littlewood Formula for Twin Primes — Subhansh Kumar · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS