English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We prove the infinitude of shifted primes $p-1$ without prime factors above$p^{0.2844}$. This refines $p^{0.2961}$ from Baker and Harman in 1998.Consequently, we obtain an improved lower bound on the the distribution ofCarmichael numbers. Our main technical result is a new mean value theorem forprimes in arithmetic progressions to large moduli. Namely, we estimate primesof size $x$ with quadrilinear forms of moduli up to $x^{17/32}$. This extendsmoduli beyond $x^{11/21}$, recently obtained by Maynard, improving $x^{29/56}$from well-known 1986 work of Bombieri, Friedlander, and Iwaniec.

Primes in arithmetic progressions to large moduli, and shifted primes without large prime factors