A number n is said to be anti-prime iff it has exactly one anti-divisor. The first few anti-primes are 3, 4, 6 and 96.

The anti-primes appear to be related to the twin primes, with the exception of 4, since any odd anti-divisor k of a number x is paired with another anti-divisor m so that k*m=2x+1, and only numbers x=2n for some positive integer n will lack even anti-divisors. x=4 is an anti-prime because 2*4+1 is 9=3*3, so 4 only has the anti-divisor 3. 4 is the only anti-prime of the form x=2n because exactly one of 2n+1-1, 2n+1, 2n+1+1 will be divisible by 3, and x would have 3 as an antidivisor, and also the other factor of either 2n+1-1 or 2n+1+1.