Формула Мерсенна для поиска простых чисел #vertdider #veritasium

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·Nov 3, 2024

До тех пор все совершенные числа соответствовали формуле Евклида. Искать новые Удобнее всего было, находя новые p, при котором d в степени P - 1 - это простое число. Французский математик Марин Мерсен посвятил много времени изучению этого уравнения. В 1944 году он опубликовал книгу, которой привёл список 11 значений p, при которых получались простые числа. Те, для которых это оказалось верно, известны под названием "простые числа".

Семь из предложенных им значений p действительно дают совершенные числа, как раз первые семь из них. Но всё остальное, например, даже 2 в степени p - 1, по собственному признанию РСН, проверять не стал. Если проверять, простое ли число, состоящий из 15-2 цифр, никакого времени не хватит.

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Формула Мерсенна для поиска простых чисел #vertdider #veritasium

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