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单词 EulersLuckyNumber
释义

Euler’s lucky number


A prime numberMathworldPlanetmath p is one of Euler’s lucky numbers if n2-n+p for each 0<n<p is also a prime. Put another way, a lucky number of EulerMathworldPlanetmath’s plus the nth oblong number produces a list of primes p-long. There are only six of them: 2, 3, 5, 11, 17 and 41, these are listed in A014556 of Sloane’s OEIS.

41 is perhaps the most famous of these. We can verify that 2 + 41 is 43, a prime, that 47 is also prime, so are 53, 61, 71, 83, 97, and so on to 1601, giving a list of 41 primes. Predictably, 1681 is divisible by 41, being its square. For n>p the formula does not consistently give only composites or only primes.

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更新时间:2025/5/3 20:24:45