: Mathématiques: lucky number of Euler

mathematical analysis > calculus > sequence > integer sequence > lucky number of Euler

number > natural numbers > lucky number of Euler

lucky number of Euler

Euler's "lucky" numbers are positive integers n such that for all integers k with 1 ≤ k < n, the polynomial k² − k + n produces a prime number. When k is equal to n, the value cannot be prime since n² − n + n = n² is divisible by n. Since the polynomial can be written as k(k−1) + n, using the integers k with −(n−1) < k ≤ 0 produces the same set of numbers as 1 ≤ k < n. These polynomials are all members of the larger set of prime generating polynomials.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Lucky_numbers_of_Euler)

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