Lucky numbers of Euler
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Euler's "lucky" numbers are positive integers n such that x2 + x + n is a prime number for x = 0, ..., n − 2.
Leonhard Euler published the polynomial x2 + x + 41 which produces prime numbers for all integer values of x from 0 to 39. Obviously, when x is equal to 40, 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 lucky numbers generated by a sieve algorithm.
See also
References
- Le Lionnais, F. Les Nombres Remarquables. Paris: Hermann, pp. 88 and 144, 1983.
External links
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