Wednesday, 6 July 2016

49 prime numbers

Not all prime numbers are created equal.  Some are more "perfect" than the others.  What do the following 49 prime numbers have in common?

2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609, 57885161, 74207281

Each gives rise to one of the 49 known Mersenne primes Mp when substituted for p in the calculation

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Mersenne primes are closely related to perfect numbers.

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