Prime Number FormulaDate: 11/11/2001 at 18:10:27 From: Ri Subject: Prime number formula I have to find out the formula Leonhard Euler used to find prime numbers. I just need the formula so I can put it into a spreadsheet. Thank you. Date: 11/11/2001 at 19:21:56 From: Doctor Paul Subject: Re: Prime number formula Following is a somewhat celebrated result of Euler: The function f(x) = x^2 + x + 41 is prime for x = 0, 1 ,..., 39 f(41) is obviously not prime because f(41) = 41^2 + 41 + 41 = 41 * (41 + 1 + 1) f(40) = 40^2 + 40 + 41 But notice that another way to write 40^2 is: 40^2 = 40^2 + 2*40 + 1 - 2*40 - 1 = (40 + 1)^2 - 2*40 - 1 Then f(40) = 40^2 + 40 + 41 = (40 + 1)^2 - 2*40 - 1 + 40 + 41 = 41^2 hence f(40) isn't prime either. This quadratic was the record holder for centuries as a consecutive, distinct quadratic prime-producer for an initial range of input values. It is not, however, the current record holder. That distinction goes to the function: f(x) = 36x^2 - 810x + 2753 which is prime for x = 0, 1, ... , 44 I do not know who this result is attributed to. For more, see the June/July issue of "The American Mathematical Monthly" (any university library will have it) for an article entitled "Prime-Producing Quadratics," by Richard Mollin. - Doctor Paul, The Math Forum http://mathforum.org/dr.math/ |
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