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=2

^{n} 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=2

^{n} because exactly one of 2

^{n+1}-1, 2

^{n+1}, 2

^{n+1}+1 will be

divisible by 3, and x would have 3 as an antidivisor, and also the other

factor of either 2

^{n+1}-1 or 2

^{n+1}+1.