The Top 100

Researchers active on Goldbach, twin primes, Legendre's conjecture, n2+1 primes, sieve methods, and the analytic techniques shared across Landau's four problems

The list is sortable on any column. Type in the search box to filter by name, institution, or country. Click any name for that researcher's profile page.

This page shows the 100 highest-ranked living researchers, renumbered 1 to 100. Researchers in the ranked pool who have passed away are remembered on the In Memoriam page.

Reading the columns. arXiv rank, OA rank, and zbMATH rank are the researcher's position in the composite score for each of three pipelines. For arXiv and OpenAlex a keyword match in a paper title counts at full weight and an abstract-only mention at half (A=0.5), so papers that only cite Landau's problems on prime numbers in passing are discounted; each composite is then 60% weighted paper count + 40% network or citation signal. zbMATH uses the MSC classes 11P32, 11N05, 11N35, 11N36, 11N32. The overall rank combines the three with a weighted order statistic, 70/20/10 on each researcher's best, middle and worst of the three ranks. A value in [square brackets] is an interpolated estimate (see below); a plain number is measured. See the methodology for details.

Ranks shown in [square brackets] are interpolated estimates, not measured values. How interpolation works.

Source column legend

The Source column records which of the pipelines ranked each researcher directly.

• all_three: ranked directly by arXiv, OpenAlex, and zbMATH. The unanimous core.
• arx+oa: ranked by arXiv and OpenAlex, but not zbMATH.
• arx+zb: ranked by arXiv and zbMATH, but not OpenAlex.
• oa+zb: ranked by OpenAlex and zbMATH, but not arXiv.
• arxiv_only: ranked only by the arXiv pipeline.
• oa_only: ranked only by OpenAlex. Often senior figures who publish in journals and do not post preprints.
• zb_only: ranked only by zbMATH. Often pre-1995 Russian and Chinese number theorists.

Limitations

This list reflects publication output and citation network density, not subjective importance. A starting point, not a verdict.