# Twin primes

**Twin primes** (also known as prime twins) are pairs of prime numbers whose difference is 2.

The smallest twin primes are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43).

All twin primes except (3, 5) are of the form 6n +/- 1.^{[1]}

Twin primes become increasingly scarce among larger numbers. For example, there are twenty-four sets of twin primes between 0 and 500, but only eleven sets between 500 and 1000. Mathematicians have long been fascinated by twin primes and the relationship between them. There seems to be no distinct pattern in their occurrence. For example, there are no twin primes between 700 and 800, or between 900 and 1000, but there are five sets between 800 and 900 (809 and 811; 821 and 823; 827 and 829; 857 and 859; 881 and 883).

Computer programmes have calculated some extremely large sets of twin primes. While there are undoubtedly an unlimited number of primes, opinions differ as to whether there is also an infinite number of twin primes or whether there is an upper limit. This conundrum (the twin prime conjecture) is one of the great unsolved problems in mathematics.