Every "large" even number may be written as where is a prime and is the set of primes and semiprimes .

# Chen's Theorem

## See also

Almost Prime, Chen Prime, Goldbach Conjecture, Prime Number, Schnirelmann's Theorem, Semiprime## Explore with Wolfram|Alpha

## References

Chen, J. R. "On the Representation of a Large Even Integer as the Sum of a Prime and the Product of at Most Two Primes."*Kexue Tongbao*

**17**, 385-386, 1966.Chen, J. R. "On the Representation of a Large Even Integer as the Sum of a Prime and the Product of at Most Two Primes. I."

*Sci. Sinica*

**16**, 157-176, 1973.Chen, J. R. "On the Representation of a Large Even Integer as the Sum of a Prime and the Product of at Most Two Primes. II."

*Sci. Sinica*

**16**, 421-430, 1978.Hardy, G. H. and Wright, W. M. "Unsolved Problems Concerning Primes." Appendix §3 in

*An Introduction to the Theory of Numbers, 5th ed.*Oxford, England: Oxford University Press, pp. 415-416, 1979.Ribenboim, P.

*The New Book of Prime Number Records.*New York: Springer-Verlag, p. 297, 1996.Rivera, C. "Problems & Puzzles: Conjecture 002.-Chen's Conjecture." http://www.primepuzzles.net/conjectures/conj_002.htm.Ross, P. M. "On Chen's Theorem that Each Large Even Number has the Form or ."

*J. London Math. Soc.*

**10**, 500-506, 1975.

## Referenced on Wolfram|Alpha

Chen's Theorem## Cite this as:

Weisstein, Eric W. "Chen's Theorem." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/ChensTheorem.html