In Mathématiques, the theorem of Chen states that: “Entire sufficiently large is the sum of a prime number and an entirety which is the product of with more the two prime numbers.”

This theorem enters within the general framework of the major results moved by famous the Conjecture of Goldbach (any even integer $\backslash \; geq\; 4$ is nap of two prime numbers). The current demonstrations rest primarily on methods of screen. The result above goes back to 1966. Thereafter, various improvements of this theorem were obtained. For example, in 1978, Chen showed the following inequality. If $P\; (NR)$ indicates the number of prime numbers $p$ such as $N-p$ is also first, one a:

$P\; (NR)\; \backslash \; Leq\; 7,8342\; \backslash \; prod\_\; \{p\; >\; 2\}\; \backslash \; left\; (1\; -\; \backslash \; frac\; \{1\}\; \{(p-1)\; ^2\}\; \backslash \; right)\; \backslash \; left\; (\backslash \; prod\_\; \{p>2,\; \backslash ,\; p\; \backslash \; mid\; NR\}\; \backslash \; frac\; \{p-1\}\; \{p-2\}\; \backslash \; right)\; \backslash \; times\; \backslash \; frac\; \{NR\}\; \{(\backslash \; ln\; NR)\; ^2\}.$

The constant $7,8342$ slightly was h. improved a few years later by D. Wu, which showed that it could be replaced by $7,81565$.