Sexy primes are pairs of prime numbers which differ in value by six, for example, 5 and 11 are sexy primes as they are both prime numbers and the difference between then is 6. The term comes from the Latin root word sex, meaning six. Sexy primes are often written algebraically in the form (p, p+6). The largest known pair of sexy primes have 10154 digits.
Groups of consecutive sexy primes are known as sexy constellations. A sexy triplet contains prime numbers in the form (p, p+6, p+12), for example (17, 23, 29). The numbers making up the largest known sexy triplet contain 5132 digits. Sexy quadruplets are those containing four prime numbers in the form (p, p+6, p+12, p+18), for example (41, 47, 53, 59), the first number of which must end in a 1. The largest known sexy quadruplet is made of primes each having 1002 digits.
- Sexy Primes at Mathworld