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Levy’s conjecture∗
PrimeFan†
2013-03-21 23:36:17
Conjecture (Émile Lemoine). All odd integers greater than 5 can be represented as the sum of an odd prime and an even semiprime. In other words,
2n + 1 = p + 2q always has a solution in primes p and q (not necessarily distinct)
for n > 2.
For example, 47 = 13 + 2 × 17 = 37 + 2 × 5 = 41 + 2 × 3 = 43 + 2 × 2. A046927
in Sloane’s OEIS counts how many different ways 2n + 1 can be represented as
p + 2q.
The conjecture was first stated by Émile Lemoine in 1894. In 1963, Hyman
Levy published a paper mentioning this conjecture in relation to Goldbach’s
conjecture.
References
[1] L. E. Dickson, History of the Theory of Numbers Vol. I. Providence, Rhode
Island: American Mathematical Society & Chelsea Publications (1999): 424
[2] R. K. Guy, Unsolved Problems in Number Theory New York: Springer-Verlag
2004: C1
[3] L. Hodges, “A lesser-known Goldbach conjecture”, Math. Mag., 66 (1993):
45 - 47.
[4] É. Lemoine, “title” L’intermediaire des mathematiques 179 3 (1896): 151
[5] H. Levy, “On Goldbach’s Conjecture”, Math. Gaz. 47 (1963): 274
∗ hLevysConjecturei
created: h2013-03-21i by: hPrimeFani version: h39822i Privacy
setting: h1i hConjecturei h11P32i
† This text is available under the Creative Commons Attribution/Share-Alike License 3.0.
You can reuse this document or portions thereof only if you do so under terms that are
compatible with the CC-BY-SA license.
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