Composite number

It is evident, moreover, that if a composite number terminates in any one of the digits 1, 3, 7, 9, no one of its factors can be the number 5, or any number ending in 5.

The above remark applies also to many composite numbers which are not Carmichael numbers, but which are still not shown to be composite by Fermat's theorem for a specific base a.[…]Therefore, using Euler's criterion or a strong primality test with enough bases will finally reveal any composite number or, alternatively, prove the primality of any prime N.

It is interesting that in each interval composite numbers are one-to-one assigned to the comparable composite knots while prime numbers are one-to-one assigned to prime knots.