Methodology

Overview

The composite ranking for wwileg.org draws on three bibliometric data sources: arXiv preprints, OpenAlex works and citations, and zbMATH editor-classified documents. Each source is scored independently, then merged using a weighted order-statistic formula.

arXiv (math.NT)

Preprints are fetched from the arXiv API in the math.NT (Number Theory) category using the search terms listed below. Author names are extracted from each matching paper. Two scores are computed: a raw paper count, and an eigenvector-centrality score from the co-authorship network. The two scores are combined and normalized to [0, 1].

Search terms used:

• Legendre's conjecture
• primes in short intervals
• prime gaps
• short interval
• large gaps between primes
• bounded gaps between primes
• difference between consecutive primes
• distribution of prime numbers
• Andrica conjecture
• Oppermann conjecture
• Baker Harman Pintz
• Hoheisel
• Goldston Pintz Yildirim

OpenAlex

Works are fetched from OpenAlex filtered to the Mathematics field, using the same search terms as arXiv. For each qualifying work, all authors are recorded along with the work's cited-by count. Each author's score combines their total qualifying works and total accumulated citations, normalized to [0, 1].

zbMATH

Documents are fetched from the zbMATH API restricted to two Mathematics Subject Classification codes: 11N05 (Distribution and density of primes) and 11N36 (Applications of sieves to the theory of numbers). Author document counts are accumulated across both classes and normalized to [0, 1].

Score merging

For each researcher, the three normalized scores (arXiv, OpenAlex, zbMATH) are sorted best to worst. The composite score is a weighted average: 0.70 × best rank + 0.20 × middle rank + 0.10 × worst rank. Researchers who appear in only one or two sources have their missing ranks estimated by linear interpolation from the neighboring scores; those estimated values appear in square brackets in the directory.

Known limitations

Author-name disambiguation is not performed beyond the automatic reconciliation provided by each source. Researchers who publish under variant name spellings may be split across multiple entries. zbMATH classes 11N05 and 11N36 are broader than Legendre's conjecture alone; highly-cited analysts who work on sieve methods generally may score higher than their Legendre-specific output would warrant. The arXiv search terms include several broad phrases (for example, "short interval") that retrieve papers not directly about Legendre's conjecture; such papers increase the score of researchers who work on the general prime-gap and short-interval problems that are the closest known approaches to proving the conjecture.