Concept information
Preferred term
lucky number of Euler
Definition
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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)
Broader concept
Synonym(s)
- Euler's lucky number
In other languages
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French
URI
http://data.loterre.fr/ark:/67375/PSR-KTP6JTRK-P
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