Prime numbers with an almost prime reverse
Prime numbers with an almost prime reverse
Let $b$ be an integer greater than or equal to $2$. For any integer $n\in \left[b^{λ-1}, b^λ-1\right]$, we denote by $R_λ(n)$ the reverse of $n$ in base $b$, obtained by reversing the order of the digits of $n$. We establish a Bombieri-Vinogradov type theorem for the set of the reverses of the prime numbers. Combined with sieve methods, this permits us to prove that there exist $Ω_b\in\mathbb{N}$ and $c_b>0$ such that, for at least $c_b b^λ λ^{-2}$ primes $p\in \left[b^{λ-1}, b^λ-1\right]$, the reverse $R_λ(p)$ has at most $Ω_b$ prime factors. Some explicit admissible values of $Ω_b$ are given.
Cécile Dartyge、Joël Rivat、Cathy Swaenepoel
数学
Cécile Dartyge,Joël Rivat,Cathy Swaenepoel.Prime numbers with an almost prime reverse[EB/OL].(2025-07-10)[2025-07-16].https://arxiv.org/abs/2506.21642.点此复制
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