Professor Stewart's Cabinet of Mathematical Curiosities by Ian Stewart

Author:Ian Stewart [Stewart, Ian]
Language: eng
Format: epub
Tags: General, Mathematics
ISBN: 9781847651280
Google: Y0Jggtb7DB0C
Amazon: 0465013023
Publisher: Profile Books
Published: 2009-01-05T16:00:00+00:00

4, 14, 194, 37634, . . .

in which each number is the square of the previous one, decreased by 2. It can be proved that the nth Mersenne number is prime if and only if it divides the (n - 1)th term of this sequence. This test can prove that a Mersenne number is composite without finding any of its prime factors, and it can prove the number is prime without testing for any prime factors. There’s a trick to keep all numbers involved in the test smaller than the Mersenne number concerned.

Looking for new, larger Mersenne primes is an amusing way to try out new, fast computers, and over the years prime-hunters have extended the list. It now includes 44 primes:

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