# Sexy Primes

**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.

## External links

- Sexy Primes at Mathworld