Chinese hypothesis

The Chinese hypothesisMathworldPlanetmath states that a number n is prime if and only if 2n-2 is a multipleMathworldPlanetmath of n. By Fermat’s little theorem we have that 2p2modp, so that means n does divide 2n-2 if n is prime. However, if n is composite Fermat’s little theorem does not rule out that n could divide 2n-2. The Chinese hypothesis checks out for the small powers of two. The first counterexample is n=341, but since 2341 has more than a hundred digits, it wasn’t easy to check it back in the 18th century when this test was first proposed. Though back then they attributed it to ancient Chinese mathematicians, hence the name.

Title Chinese hypothesis
Canonical name ChineseHypothesis
Date of creation 2013-03-22 18:11:08
Last modified on 2013-03-22 18:11:08
Owner FourDozens (21006)
Last modified by FourDozens (21006)
Numerical id 6
Author FourDozens (21006)
Entry type Definition
Classification msc 11A51