# Jared Lichtman (Oxford) - Twin primes & a modified linear sieve

Dates: | 3 May 2022 |
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Times: | 15:00 - 16:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Adults, Alumni, Current University students |

Speaker: | Jared Lichtman |

Abstract : The linear sieve is a powerful tool to tackle problems related to the primes, when combined with equidistribution estimates for the remainder. In 1977 Iwaniec introduced a well-factorable modification of the linear sieve to prove there are infinitely many integers n such that n^2+1 has at most two prime factors. Furthermore, the (well-factorable) linear sieve leads to the best known upper bounds for twin primes. These bounds use work of Bombieri, Friedlander, and Iwaniec from 1986, showing these sieve weights equidistribute primes of size x in arithmetic progressions to moduli up to x^{4/7}. This level was recently increased to x^{7/12} by Maynard. We introduce a new modification of the linear sieve whose weights equidistribute primes of size x to level x^{10/17}. As an application we refine a 2004 upper bound for twin primes of Wu, which gives the largest percent improvement since the work of Bombieri, Friedlander, and Iwaniec.

### Speaker

Jared Lichtman

Organisation: Oxford