论文标题
算术进展中的素数到大型模量，并改变了素数，而没有很大的主要因素
Primes in arithmetic progressions to large moduli, and shifted primes without large prime factors
论文作者
论文摘要
我们证明了流动的素数$ p-1 $的无限，而没有主要因素以上$ p^{0.2844} $。这是从贝克和哈曼（Harman）于1998年完善的$ p^{0.2961} $。因此，我们在Carmichael数字的分布上获得了改进的下限。我们的主要技术结果是在算术进行大型模量中的素数定理的新平均值定理。也就是说，我们估计具有$ x $的质量，具有四边形形式的Moduli，最高为$ x^{17/32} $。这将Moduli扩展到$ X^{11/21} $之外，最近由Maynard获得，从著名的1986年Bombieri，Friedlander和Iwaniec的作品提高了$ X^{29/56} $。
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 of Carmichael numbers. Our main technical result is a new mean value theorem for primes in arithmetic progressions to large moduli. Namely, we estimate primes of size $x$ with quadrilinear forms of moduli up to $x^{17/32}$. This extends moduli beyond $x^{11/21}$, recently obtained by Maynard, improving $x^{29/56}$ from well-known 1986 work of Bombieri, Friedlander, and Iwaniec.
