Primes p such that p-b Has a Large Power Factor and Few Other Prime Divisors

2024/10/18 by Xie, Likun
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2410.14133

Abstract

We prove lower bounds for the number of primes p ≤ N + b such that p-b is divisible by 2^k(N) and has at most k odd prime factors (k ≥ 2), assuming 2^k(N) ≤ N^θ for some θ> 0 depending on k. The proof uses a variant of Chen's method, weighted sieves, and Elliott's results on primes in arithmetic progressions with large power-factor moduli.

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