A twin prime is a prime number that has a prime gap of two. In other words, to qualify as a twin prime, the prime number must be either 2 less or 2 more than another prime number (which by definition would mean that it, too, is a twin prime)—for example, the twin prime pair (41, 43). Two is not considered a twin prime with the number three, since it violates the aforementioned rule. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Twin primes appear despite the general tendency of gaps between adjacent primes to become larger...