Gaps between primes

素数之间的间隙

基本信息

  • 批准号:
    2099955
  • 负责人:
  • 金额:
    --
  • 依托单位:
  • 依托单位国家:
    英国
  • 项目类别:
    Studentship
  • 财政年份:
    2018
  • 资助国家:
    英国
  • 起止时间:
    2018 至 无数据
  • 项目状态:
    已结题

项目摘要

This project falls within the EPSRC Digital Economy research area. Many critical computer programs rely on properties of prime numbers, but unfortunately these properties are poorly understood from a theoretical viewpoint. This poses a critical security risk: if primes behaved differently to how algorithms assume, then several vital parts of the digital economy would fail. For example, many cryptographic algorithms require one to find an auxiliary prime of a certain size, and they do this by testing consecutive integers for primality. Whilst we know that we can test an individual number quickly, this would take thousands of years if there were no primes close to our starting point, meaning the whole cryptographic algorithm would hang and security would be lost. We believe there should never be such a long string of consecutive integers which are not prime, but we do not know how to prove this. This is just one example; there are many similar cases where critical day-to-day algorithms rely on assumptions about primes, which in turn can be resolved if we can solve some of the most famous problems in theoretical mathematics. Unfortunately such theoretical questions are notoriously difficult and have been thought about by mathematicians for hundreds of years without resolution. Fortunately, in the past few years several new techniques for studying gaps between primes have been developed, which offer new insights into the primes and these old famous problems.This project is aimed at improving our understanding of gaps between primes, thereby moving in the direction of solving these critical issues for the Digital economy. It will investigate further the new techniques developed in recent years, building on recent breakthroughs to further our understanding of gaps between primes. This naturally requires an interdisciplinary approach to make progress - the intention is to bring together disparate ideas from combinatorics, functional analysis, analytic number theory, numerical analysis and sieve theory to improve the current techniques for studying gaps between primes. This will therefore require significant novelty by introducing new external ideas to build upon and improve the current techniques, making partial progress towards the overall aims which have significant impacts on the digital economy.There will be no direct companies or collaborators involved in this project, although it is hoped that links will be made with other world experts in this area to strengthen the outcome and impacts of the research performed.
该项目属于EPSRC数字经济研究领域。许多重要的计算机程序依赖于素数的性质,但不幸的是,从理论的角度来看,人们对这些性质的理解很少。这带来了严重的安全风险:如果质数的行为与算法的假设不同,那么数字经济的几个关键部分就会失效。例如,许多加密算法要求找到一定大小的辅助素数,它们通过测试连续整数的素数来实现这一点。虽然我们知道我们可以快速测试单个数字,但如果在我们的起点附近没有质数,这将需要数千年的时间,这意味着整个加密算法将挂起,安全性将丧失。我们相信不可能有这么长的非素数连续整数串,但我们不知道如何证明。这只是一个例子;在许多类似的情况下,关键的日常算法依赖于对质数的假设,如果我们能解决理论数学中一些最著名的问题,这些假设反过来也可以解决。不幸的是,这样的理论问题是出了名的困难,数学家们已经思考了几百年没有解决。幸运的是,在过去的几年里,一些研究质数间隙的新技术被开发出来,为质数和这些古老的著名问题提供了新的见解。该项目旨在提高我们对质数间隙的理解,从而朝着解决数字经济中这些关键问题的方向发展。它将进一步研究近年来发展起来的新技术,以最近的突破为基础,进一步了解质数之间的差距。这自然需要跨学科的方法来取得进展——其目的是将组合学、泛函分析、解析数论、数值分析和筛理论等不同的思想结合起来,以改进目前研究质数间隙的技术。因此,这将需要通过引入新的外部思想来建立和改进现有技术,从而实现对数字经济产生重大影响的总体目标,从而取得重要的新颖性。该项目将没有直接的公司或合作者参与,但希望与这一领域的其他世界专家建立联系,以加强所进行研究的成果和影响。

项目成果

期刊论文数量(1)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
A variation of the prime k-tuples conjecture with applications to quantum limits
素数 k 元组猜想的变体及其在量子极限上的应用
  • DOI:
    10.1007/s00208-021-02321-4
  • 发表时间:
    2021
  • 期刊:
  • 影响因子:
    1.4
  • 作者:
    McGrath O
  • 通讯作者:
    McGrath O
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其他文献

吉治仁志 他: "トランスジェニックマウスによるTIMP-1の線維化促進機序"最新医学. 55. 1781-1787 (2000)
Hitoshi Yoshiji 等:“转基因小鼠中 TIMP-1 的促纤维化机制”现代医学 55. 1781-1787 (2000)。
  • DOI:
  • 发表时间:
  • 期刊:
  • 影响因子:
    0
  • 作者:
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LiDAR Implementations for Autonomous Vehicle Applications
  • DOI:
  • 发表时间:
    2021
  • 期刊:
  • 影响因子:
    0
  • 作者:
  • 通讯作者:
生命分子工学・海洋生命工学研究室
生物分子工程/海洋生物技术实验室
  • DOI:
  • 发表时间:
  • 期刊:
  • 影响因子:
    0
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吉治仁志 他: "イラスト医学&サイエンスシリーズ血管の分子医学"羊土社(渋谷正史編). 125 (2000)
Hitoshi Yoshiji 等人:“血管医学与科学系列分子医学图解”Yodosha(涉谷正志编辑)125(2000)。
  • DOI:
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  • 影响因子:
    0
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Effect of manidipine hydrochloride,a calcium antagonist,on isoproterenol-induced left ventricular hypertrophy: "Yoshiyama,M.,Takeuchi,K.,Kim,S.,Hanatani,A.,Omura,T.,Toda,I.,Akioka,K.,Teragaki,M.,Iwao,H.and Yoshikawa,J." Jpn Circ J. 62(1). 47-52 (1998)
钙拮抗剂盐酸马尼地平对异丙肾上腺素引起的左心室肥厚的影响:“Yoshiyama,M.,Takeuchi,K.,Kim,S.,Hanatani,A.,Omura,T.,Toda,I.,Akioka,
  • DOI:
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    0
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的其他文献

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An implantable biosensor microsystem for real-time measurement of circulating biomarkers
用于实时测量循环生物标志物的植入式生物传感器微系统
  • 批准号:
    2901954
  • 财政年份:
    2028
  • 资助金额:
    --
  • 项目类别:
    Studentship
Exploiting the polysaccharide breakdown capacity of the human gut microbiome to develop environmentally sustainable dishwashing solutions
利用人类肠道微生物群的多糖分解能力来开发环境可持续的洗碗解决方案
  • 批准号:
    2896097
  • 财政年份:
    2027
  • 资助金额:
    --
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    Studentship
A Robot that Swims Through Granular Materials
可以在颗粒材料中游动的机器人
  • 批准号:
    2780268
  • 财政年份:
    2027
  • 资助金额:
    --
  • 项目类别:
    Studentship
Likelihood and impact of severe space weather events on the resilience of nuclear power and safeguards monitoring.
严重空间天气事件对核电和保障监督的恢复力的可能性和影响。
  • 批准号:
    2908918
  • 财政年份:
    2027
  • 资助金额:
    --
  • 项目类别:
    Studentship
Proton, alpha and gamma irradiation assisted stress corrosion cracking: understanding the fuel-stainless steel interface
质子、α 和 γ 辐照辅助应力腐蚀开裂:了解燃料-不锈钢界面
  • 批准号:
    2908693
  • 财政年份:
    2027
  • 资助金额:
    --
  • 项目类别:
    Studentship
Field Assisted Sintering of Nuclear Fuel Simulants
核燃料模拟物的现场辅助烧结
  • 批准号:
    2908917
  • 财政年份:
    2027
  • 资助金额:
    --
  • 项目类别:
    Studentship
Assessment of new fatigue capable titanium alloys for aerospace applications
评估用于航空航天应用的新型抗疲劳钛合金
  • 批准号:
    2879438
  • 财政年份:
    2027
  • 资助金额:
    --
  • 项目类别:
    Studentship
Developing a 3D printed skin model using a Dextran - Collagen hydrogel to analyse the cellular and epigenetic effects of interleukin-17 inhibitors in
使用右旋糖酐-胶原蛋白水凝胶开发 3D 打印皮肤模型,以分析白细胞介素 17 抑制剂的细胞和表观遗传效应
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    2890513
  • 财政年份:
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  • 项目类别:
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CDT year 1 so TBC in Oct 2024
CDT 第 1 年,预计 2024 年 10 月
  • 批准号:
    2879865
  • 财政年份:
    2027
  • 资助金额:
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  • 项目类别:
    Studentship
Understanding the interplay between the gut microbiome, behavior and urbanisation in wild birds
了解野生鸟类肠道微生物组、行为和城市化之间的相互作用
  • 批准号:
    2876993
  • 财政年份:
    2027
  • 资助金额:
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  • 项目类别:
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