On improving a Schur-type theorem in shifted primes

Abstract

We show that if $N\ge \exp (\exp (\exp (k^{O(1)})))$, then any $k$-colouring of the primes that are less than $N$ contains a monochromatic solution to $p_1-p_2=p_3-1$.

References in corpus (2)

• Difference sets and the primes
• On a theorem of Sárközy for difference sets and shifted primes