陈景润定理对筛法理论的重要贡献

    经过查证，在国际最新筛法专著的前言中，作者专门提及陈景润定理的现代意义，而我们国人却陈景润不理解。呜呼！

   注：现在是除夕夜，发表此文，以便告慰陈景润的在天之灵。

     陈景润主要论文：[Che73] Chen J., On the representation of a large even integer as the sum of a prime and the product of at most two primes, Sci. Sinica, (16), 157-176, (1973).

说明：陈景润自己写的论文提要：Abstract:

In this paper we shall prove that every sufficiently large even integer is a sum of a prime and a product of at most 2 primes. The method used is simple without any complicated numerical calculations.

请看本文附件。

袁萌  陈启清  2月4日

附件：在最新筛法专著的前言中，专门提及陈景润定理的现代意义。

Sieve Methods

DENIS XAVIER CHARLES

Preface（前言）

Sieve methods have had a long and fruitful history. The sieve of Eratosthenes (around 3rd century B.C.) was a device to generate prime numbers. Later Legendre used it in his studies of the prime number counting function π(x). Sieve methods bloomed and became a topic of intense investigation after the pioneering work of Viggo Brun (see [Bru16],[Bru19], [Bru22]). Using his formulation of the sieve Brun proved, that the sum

∑ p, p+2 both prime

1 p

converges. This was the rst result of its kind, regarding the Twin-prime problem. A slew of sieve methods were developed over the years — Selberg’s upper bound sieve, Rosser’s Sieve, the Large Sieve, the Asymptotic sieve, to name a few. Many beautiful results have been proved using these sieves. The Brun-Titchmarsh theorem and the extremely powerful result of Bombieri are two important examples. Chen’s theorem [Che73], namely that there are innitely many primes p such that p+2 is a product of at most two primes, is another indication of the power of sieve methods.

Sieve methods are of importance even in applied elds of number theory such as Algorithmic Number Theory, and Cryptography. There are many direct applications, for example nding all the prime numbers below a certain bound, or constructing numbers free of large prime factors. There are indirect applications too, for example the running time of several factoring algorithms depends directly on the distribution of smooth numbers in short intervals. The so called undeniable signature schemes require prime numbers of the form 2p+1 such that p is also prime. Sieve methods can yield valuable clues about these distributions and hence allow us to bound the running times of these algorithms.