Who's Who in Landau's Problems Research
A directory of researchers working on Landau's problems on prime numbers
At the 1912 International Congress of Mathematicians, Edmund Landau listed four problems about primes that mathematics could not yet prove. Now known as Landau's problems, all four remain open: the Goldbach conjecture, the twin prime conjecture, Legendre's conjecture, and the conjecture that infinitely many primes have the form n2+1. Every one is still open.
This site is the umbrella reference directory for all four problems and the shared sieve and analytic techniques behind them. It catalogs the Top 100 researchers most active across the Landau-problems family, ranked from arXiv preprint output, OpenAlex citation data, and zbMATH classifications, with their institutions, and offers a curated reading list.
Where to start
- Home: This page.
- The Top 100: the canonical ranked list, sortable and filterable in your browser.
- Locations: where the Top 100 are based, shown by world region with maps.
- In Memoriam: researchers in this directory who are no longer with us.
- Genealogy: close relations of the Top 100 through advisor-student lineage in the Mathematics Genealogy Project.
- Network: the coauthorship graph among the Top 100: who has written papers with whom.
- Reading List: the recent topical papers ranked by the prominence of their authors in this directory, plus the most-cited papers of all time.
- Overlap: the researchers who also appear across the related conjecture sites.
- About: what this site is, who built it, and where to find the methodology, the open dataset, and how to request a correction.
How the list is built
Three independent signals are combined into one composite ranking:
- arXiv preprint output, filtered to math.NT and math.CO categories, matched against 17 search terms.
- OpenAlex topical citations.
- zbMATH Open, using the MSC subject classes (11P32, 11N05, 11N35, 11N36, 11N32).
The three pipeline ranks are combined with a weighted order statistic: for each researcher the three ranks are sorted and weighted 70% on the best, 20% on the middle, and 10% on the worst. Lower is better. See the methodology for details.
Citing this site
Hubbard, S. (2026). Who's Who in Landau's Problems Research. Zenodo. https://doi.org/10.5281/zenodo.20674899