RED2 is an experimental prime sieving algorithm optimized for computing primes up to 10 trillion, achieving significant memory reductions through cofactor compression and tighter calendar bounds compared to the frozen v0.34 version. The package includes benchmarking tools to compare performance against primesieve across various thread counts and limits, with results dependent on compiler, cache, and memory bandwidth rather than CPU-specific optimizations.
OpenAI announced progress on the Millennium Prize problems in mathematics, including an apparent solution to Navier-Stokes in September. The article explains five remaining open questions, focusing on the Riemann hypothesis, which concerns the distribution of prime numbers formulated by Bernhard Riemann in 1859.
This paper proves that prime ideals of certain rings associated with Honda formal groups that are stable under the Morava stabilizer group are exactly the height ideals, and establishes a classification of thick tensor ideals in K(n)-local spectra. The proof uses geometric methods involving Cartier structures, formal quotients, and period maps.