Sun · Simultaneous primes n+k and n+k²

For every integer n>1, there is an integer k with 0≤k<n such that both n+k and n+k² are prime.

prime numberspolynomialsBertrand-type results

The problem

For every integer n>1, there is an integer k with 0≤k<n such that both n+k and n+k² are prime.

Open since2012preprint formulation

Last checked2026.07.27Catalog verification

Offer 01$100Zhi-Wei Sun

Personal offer

The author’s 2017 paper version announced US$100 for the first solution.