Occurs when a prime number (p), and its reciprocal (1/p) in decimal form is recurring with (p-1) digits. The first prime with this property is 7 which gives:1/7 = 0.142857142857. Take the first six digits, 142857, to obtain the first cyclic number. The next five cyclic numbers can be obtained by finding the reciprocals of the primes 17, 19, 23, 29 and 47. If you take 142857 and multiply it by any figure from 2 to 6 you get the same number in various orders yet still in the same sequence

Source: Fermat's Enigma : The Epic Quest to Solve the World's Greatest Mathematical Problem by Simon Singh.

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