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Twin primes
This conjecture is one of the oldest unsettled statements in mathematics. For centuries mathematicians have attempted to prove this statement, without success. The conjecture is known to hold for numbers less than 3 <math>\cdot</math>10<sup>17</sup>.
This conjecture is one of the oldest unsettled statements in mathematics. For centuries mathematicians have attempted to prove this statement, without success. The conjecture is known to hold for numbers less than 3 <math>\cdot</math>10<sup>17</sup>.
==Twin primes==
'''Twin primes''' or '''prime twins''' are pairs of prime number which differ from each other by only 2. Since all primes other than 2 are odd numbers, this is the closest two primes can be to each other, with the exception of 2 and 3. The first few twin primes are 3 and 5, 5 and 7, 11 and 13, 17 and 19, and 29 and 31.
Twin primes become increasingly scarse 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. Computer programmes have calculated some extremely large sets of prime twins. While there are undoubtedly an unlimited number of primes, opinions differ among mathematicians whether there is also an infinite number of prime twins or whether there is an upper limit.
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).
==Cryptography==
==Cryptography==