Lucky numbers of Euler
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Euler's "lucky" numbers are positive integers n such that m2 − m + n is a prime number for m = 0, …, n − 1.
Leonhard Euler published the polynomial x2 − x + 41 which produces prime numbers for all values of x from 0 to 40. Obviously, when x is equal to 41, the value cannot be prime any more since it is divisible by 41. Only 6 numbers have this property, namely 2, 3, 5, 11, 17 and 41 (sequence A014556 in OEIS).
These numbers are not related to the so-called lucky numbers.
[edit] See also
[edit] References
- F. Le Lionnais, Les Nombres Remarquables. Paris: Hermann, pp. 88 and 144, 1983.
