The composite number problem asks if for a given positive integer 
there exist positive integers 
and 
such that 
.
The complexity of the composite number problem was unknown for many years, although the problem was known to belong to 
(Pratt 1975, Garey and Johnson 1983).
Agrawal et al. (2004) subsequently and unexpectedly discovered a polynomial-time
algorithm now known as the AKS primality test.
