Almost primes and primes that are sums of two squares plus 1
Volume 223 / 2026
Acta Arithmetica 223 (2026), 51-82
MSC: Primary 11N05; Secondary 11N35, 11N36
DOI: 10.4064/aa250227-19-11
Published online: 20 March 2026
Abstract
We obtain a lower bound for the number of primes $ p \leq x $ such that $ p - 1 $ is a sum of two squares and $ p + 2 $ has a bounded number of prime factors. The proof uses the vector sieve framework involving a semi-linear sieve and a linear sieve.
