| 词条 | Lemoine's conjecture |
| 释义 |
In number theory, Lemoine's conjecture, named after Émile Lemoine, also known as Levy's conjecture, after Hyman Levy, states that all odd integers greater than 5 can be represented as the sum of an odd prime number and an even semiprime. HistoryThe conjecture was posed by Émile Lemoine in 1895, but was erroneously attributed by MathWorld to Hyman Levy who pondered it in the 1960s.[1] A similar conjecture by Sun in 2008 states that all odd integers greater than 3 can be represented as the sum of prime number and the product of two consecutive positive integers ( p+x(x+1) ).[2] Formal definitionTo put it algebraically, 2n + 1 = p + 2q always has a solution in primes p and q (not necessarily distinct) for n > 2. The Lemoine conjecture is similar to but stronger than Goldbach's weak conjecture. ExampleFor example, 47 = 13 + 2 × 17 = 37 + 2 × 5 = 41 + 2 × 3 = 43 + 2 × 2. {{OEIS|id=A046927}} counts how many different ways 2n + 1 can be represented as p + 2q. EvidenceAccording to MathWorld, the conjecture has been verified by Corbitt up to 109.{{citation needed|date=December 2018}} See also
Notes1. ^{{MathWorld|title=Levy's Conjecture|urlname=LevysConjecture}} 2. ^Sun, Zhi-Wei. "On sums of primes and triangular numbers." [https://arxiv.org/abs/0803.3737 arXiv preprint arXiv:0803.3737] (2008). References
External links
2 : Additive number theory|Conjectures about prime numbers |
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