This question applies only to those composite numbers that are between 2 "Twin Primes" that are >18. Here is a list of twin primes >18 and <1,000. (29, 31) | (41, 43) | (59, 61) | (71, 73) | (101, 103) | (107, 109) | (137, 139) | (149, 151) | (179, 181) | (191, 193) | (197, 199) | (227, 229) | (239, 241) | (269, 271) | (281, 283) | (311, 313) | (347, 349) | (419, 421) | (431, 433) | (461, 463) | (521, 523) | (569, 571) | (599, 601) | (617, 619) | (641, 643) | (659, 661) | (809, 811) | (821, 823) | (827, 829) | (857, 859) | (881, 883) ...
The definition of a prime number is that it has ONLY 2 prime divisors, i.e., itself and 1. Since two prime divisors will only have 2 exponents, which would only give:(1+1) x (1+1)=4 divisors. A composite number between 2 twin primes must, by definition, necessarily have at least (1+1) extra divisor for a total of: (1+1) x (1+1) x (1+1) =8 divisors as " a minimum" to distinguish it from a prime number which MUST have only 4 divisors. And that is the best that I can give you as a "proof".