2305843009213693951

Historically very important, but become too small for current cryptography, 2.305.843 009.213.693 951 is the 9th Nombre of Mersenne. It is a Prime number. It corresponds to 2⁶¹ − 1 and it counts 19 Chiffre S.

This number was discovered in 1883 by Ivan Mikheevich Pervushin.

History

Pervushin had initially discovered that 12th and 23e numbers of Fermat was made up: first is divisible by 7 × 2¹⁴ + 1 = 114 689 and the second by 5 × 2²⁵ + 1 = 167 772 161.

It is only in 1883 that Pervushin shows that the number which will be indicated a long time as the “number of Pervushin” was well a Nombre of Mersenne.

Anecdote

On the other hand, undoubtedly taken by its professional occupations, it will have calculated without computer only the second greater number of this type. Admittedly, this Russian mathematician was very known at his time so much so that its number its name carried and not that of Mersenne. Thus this “number of Pervushin” was then the larger second Prime number known (just behind the number of Lucas shown seven years earlier) until in 1911 and the advent of the Nombre of Powers.

Quotations

“2 30 (2 31 − 1) is the most perfect number which will be never discovered because, this kind of number being simply curious without being useful, it is not very probable that somebody tries to find another of them. ” (Peter Barlow which belonged to the generation preceding that by Purnishev).
In one of its books Believe it or not , Ripley indicates that 2 61 − 1 was the number of manners of making the currency on a ticket of five Dollar S.

External bonds

Only site giving another discoverer of this ninth number of Mersenne.
Another English site also and from where the essence of the article from the English wiki seems drawn and where one with the surprise to discover that the initial goal was not in fact not to prove that this number was first but that it was not it.

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