Chen Jingrun

Native spelling: 陈景润

1933–1996, Fuzhou, Fujian, China, Beijing, China

Arithmetic and number theory

Chinese number theorist who proved Chen's theorem (announced 1966, full proof 1973): every sufficiently large even integer is the sum of a prime and a product of at most two primes — the closest unconditional result to binary Goldbach's conjecture.

Chen Jingrun was born in Fuzhou, Fujian, the third of twelve children of a postal clerk, and first heard of Goldbach's conjecture from his high-school teacher Shen Yuan. He graduated from Xiamen University in 1953; while working back at Xiamen as a library assistant, he studied Hua Luogeng's 'Additive Prime Number Theory' and improved several of its results on Tarry's problem. Hua invited him to the Institute of Mathematics of the Chinese Academy of Sciences in Beijing in 1957.

At the Academy, Chen improved bounds in Waring's problem (proving g(5) = 37 in 1964), lattice-point problems, and divisor problems. In May 1966, on the eve of the Cultural Revolution, he announced what is now called Chen's theorem: every sufficiently large even integer N can be written as N = p + P₂, where p is prime and P₂ is either a prime or the product of two primes ('1 + 2'). Persecuted and confined to a converted tiny room during the Cultural Revolution, he continued working by kerosene lamp and published the complete proof in 1973.

Chen's weighted sieve technique also showed that there are infinitely many primes p such that p + 2 is a P₂ (now called Chen primes), and his proof became the climax of Halberstam and Richert's 1974 treatise 'Sieve Methods'. He was elected an academician of the Chinese Academy of Sciences in 1980.

Workplaces: Xiamen University, Institute of Mathematics, Chinese Academy of Sciences

China

Contributions, linked to the library

Great problemGoldbach conjectureProved Chen's theorem (1966/1973): every sufficiently large even integer is the sum of a prime and an integer with at most two prime factors (a P₂, or P2).Great problemTwin prime conjectureProved that infinitely many primes p have p + 2 a product of at most two primes (Chen primes).Library topicSieve methodsRefined weighted linear sieve methods to prove the '1 + 2' theorem.