The great trinomial hunt
Richard P. Brent, Paul Zimmermann
TL;DR
This paper details a comprehensive search for primitive trinomials of high degree, focusing on those related to known Mersenne primes, and explores their connection with the GIMPS project.
Contribution
It provides the first complete search for primitive trinomials at degrees corresponding to all known Mersenne primes, linking polynomial search with prime discovery efforts.
Findings
Complete list of primitive trinomials for 47 known Mersenne prime exponents
Insights into the interaction between polynomial search and GIMPS
Foundation for future searches at higher degrees
Abstract
We describe a search for primitive trinomials of high degree and its interaction with the Great Internet Mersenne prime search (GIMPS). The search is complete for trinomials whose degree is the exponent of a Mersenne prime, for all 47 currently known Mersenne primes.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCoding theory and cryptography · Algebraic Geometry and Number Theory · Cryptography and Residue Arithmetic