A Schur-type addition theorem for primes
Hongze Li, Hao Pan
TL;DR
This paper proves a Schur-type addition theorem for primes, showing that in any k-coloring of primes, there are monochromatic primes satisfying p1 + p2 = p3 + 1.
Contribution
It establishes a new additive property for primes analogous to Schur's theorem, extending combinatorial number theory to prime numbers.
Findings
Existence of monochromatic prime solutions to p1 + p2 = p3 + 1 in any coloring
Generalization of Schur's theorem to prime numbers
New additive structure identified among primes
Abstract
Suppose that all primes are colored with k colors. Then there exist monochromatic primes p1, p2, p3 such that p1+p2=p3+1.
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
TopicsAnalytic Number Theory Research · Limits and Structures in Graph Theory · Finite Group Theory Research