About

• Methodology: how the rankings are built, the sources and weights, and what is deliberately left out.
• Data and citations: the full Top 100 as an open downloadable dataset, plus the DOI and how to cite this site.
• Contact: fix a profile, suggest someone missing, request removal, or just get in touch.

Why this site exists

At the 1912 International Congress of Mathematicians in Cambridge, Edmund Landau presented four specific problems about prime numbers that he regarded as inaccessible to current methods. They have remained unsolved for more than 110 years. The four problems, Goldbach's conjecture, the twin prime conjecture, Legendre's conjecture, and the conjecture that infinitely many primes of the form n²+1 exist, share analytic methods and a common research community. Significant advances on any one of them typically use techniques (sieve theory, the circle method, exponential sums, and Fourier-analytic tools on primes) that advance the others as well.

This site is a starting point for anyone wanting to know who is working on this family of problems today, where they are, and what they have been writing recently. The ranking covers the whole Landau-problems family at once. Individual problem sites linked from this page provide narrower, problem-specific rankings.

The four problems

• Goldbach conjecture: every even integer greater than 2 is the sum of two primes. Directory: wwigb.org.
• Twin prime conjecture: there are infinitely many pairs of primes differing by 2. Directory: wwitp.org.
• Legendre's conjecture: for every positive integer n, there is a prime between n² and (n+1)². Directory: wwileg.org.
• Primes of the form n²+1: there are infinitely many primes of this polynomial form. Directory: wwin2p1.org.

Who built it

Steve Hubbard built this as part of the Who's Who in Mathematics Research network, alongside Who's Who in Goldbach Research, Who's Who in Twin Prime Research, and Who's Who in Riemann Hypothesis Research, using the same open pipeline and documented methodology. Suggestions, corrections, and additions are welcome.