The  closest known attempted proof of  the twin prime conjecture

Abstract: Using a primitive formulation of the circle method we present a sufficient condition for the twin prime conjecture that misses being true by just an epsilon. We also show that the well-known sufficient condition for the twin prime conjecture implies the patently false statement that for each positive integer m, there exists an infinite number of prime pairs whose difference is $m$.

Mathematics

Audience: researchers in the topic

Combinatorial and additive number theory (CANT 2025)