[The French priest Marin] Mersenne was intrigued by numbers of the form 2^{n} – 1 […] he asserted that the only primes between 2 and 257 for which 2^{p} – 1 is prime are p = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257. Unfortunately, Father Mersenne’s assertion contained sins of both commission and omission. For instance, he missed the fact that the number 2^{61} – 1 is prime. On the other hand, 2^{67} – 1 turned out not to be prime at all. This latter fact was established in 1876 by Edouard Lucas (1842-1891), who demonstrated that the number was composite using an argument so indirect that it did not explicitly exhibit any of the factors.

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