About
Why this site exists
The n2+1 conjecture is one of four classical problems posed by Edmund Landau at the 1912 ICM. It asks whether infinitely many integers of the form n2+1 are prime. Nearly a century after Landau posed it and nearly five decades after Iwaniec result on almost-primes, the conjecture remains open. The community working on it sits at the intersection of sieve theory, the theory of polynomial prime values, and analytic number theory. This site is a starting point for anyone wanting to know who is working on this problem, where they are based, and what they have been writing.
Who built it
Steve Hubbard built this site as part of the Who's Who in Landau's Problems family, alongside sister sites for Goldbach conjecture (wwigr.org), the twin prime conjecture (wwitp.org), and Legendre conjecture (wwileg.org). The same open pipeline and documented methodology drives all four sites.
Contact
Questions, corrections, or additions: admin@wwin2p1.org.
Sources of error
- Surname matching is fragile. Mathematicians with common surnames may be conflated with others. The pipeline handles the worst cases but misses are possible.
- The field is partly pre-arXiv. The key results by Iwaniec (1978) and Friedlander-Iwaniec (1997) predate arXiv. Researchers whose most important contributions are from that era are undercounted in the arXiv layer and appear primarily through zbMATH.
- Adjacent topics widen the pool. Terms like "Bateman-Horn conjecture" and "Friedlander-Iwaniec" pull in researchers working on adjacent problems (primes in arithmetic progressions, general sieve theory, other sparse polynomials) rather than n2+1 specifically. Title-weighting reduces but does not eliminate this.
- Single breakthrough papers do not score well. The ranking measures sustained output. A researcher whose contribution to the field is one landmark paper will rank lower than a productive researcher with many related papers.
- The ranked list is not a verdict. It is a starting point. Use it alongside MathSciNet, your advisor, and your own reading.
Acknowledgments
Data sources: arXiv, OpenAlex, zbMATH Open.
License and reuse
The data on this site is built from public sources (arXiv, OpenAlex, zbMATH) under their respective license terms. The compiled list and methodology are released under CC-BY 4.0: feel free to reuse with attribution.
Methodology and data
How the rankings are built, what is in the data, and what is deliberately left out is documented on the Methodology page. The full Top 100 is published as an open, downloadable dataset on the Data and citation page.
Contact and corrections
This is an independent, non-commercial directory built from public data, so some entries carry errors. To fix a profile, suggest someone missing, or ask not to be listed, see the Corrections and removal page, or email admin@wwin2p1.org. Every message is read and acted on by a person.