Помнится, в "Кванте" на заре его существования была статейка на похожую тему:
Формулы для простых чисел. №5, 1975 за авторством (недавно поминаемого в ВТФ-ветке) Ю. Матиясевича. Правда, если не ошибаюсь, там упор делался на "хитрые" формулы вида
. Здесь функция
выдает либо отрицательные числа, либо простые (при любых наборах аргументов). Причем,
явно строилась, а число аргументов у нее не превышало десятка.
У меня есть вариант с 26-ю аргументами. Брал из известной книжки "Живые числа" Боро, Цагира, Рольфса и др. Несмотря на несолидное название и популярность изложения изложенные в ней факты заслуживают доверия (поскольку доверия заслуживают авторы). К сожалению, я так и не нашел ни одного набора аргументов, при котором полином возвращал бы положительное значение
Наиболее смелые и морально устойчивые форумчане могут полюбоваться этим полиномом, заглянув внутрь тега. Нервным, женщинам и детям смотреть не рекомендуется
(Оффтоп)
Код:
P1 := 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![$$p_{n+1}=\left[1-log_2\left(\frac12+\sum_{r=1}^n \ \sum_{1\le i_1 < \dots < i_r \le n}\frac{(-1)^r}{2^{p_{i_1}\cdots p_{i_r}}-1}\right)\right]$$](https://dxdy-04.korotkov.co.uk/f/3/0/a/30a16ec54c3bf8f5b48d3eaa46926a7d82.png "$$p_{n+1}=\left[1-log_2\left(\frac12+\sum_{r=1}^n \ \sum_{1\le i_1 < \dots < i_r \le n}\frac{(-1)^r}{2^{p_{i_1}\cdots p_{i_r}}-1}\right)\right]$$")
![$p_{n+1}=\left[1-log_2\left(\frac12+\sum_{r=1}^n \ \sum_{1\le i_1 \le \dots \le i_r \le n}\frac{(-1)^r}{p_{i_1}\cdots p_{i_r}-1}\right)\right]$](https://dxdy-03.korotkov.co.uk/f/2/3/7/237bba6098b3e930e3edde1d2e156a8c82.png "$p_{n+1}=\left[1-log_2\left(\frac12+\sum_{r=1}^n \ \sum_{1\le i_1 \le \dots \le i_r \le n}\frac{(-1)^r}{p_{i_1}\cdots p_{i_r}-1}\right)\right]$")
