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Lucky numbers of Euler
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 integer values of x from 0 to 40. Obviously, when x is equal to 41, the value cannot be prime anymore 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.
See also
Heegner number
List of topics named after Leonhard Euler
Formula for primes
References
Le Lionnais, F. Les Nombres Remarquables. Paris: Hermann, pp. 88 and 144, 1983.
External links
Weisstein, Eric W., "Lucky Number of Euler", MathWorld.
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