Dear number theorists,
Anyone who uses google to search "Levy's conjecture" will find many
entries and articles related to the so-called Levy's conjecture which
states that any odd number greater than 5 can be written as p+2q where p
and q are primes. Levy stated this conjecture in his following paper:
H. Levy, "On Goldbach's Conjecture", Math. Gaz. 47 (1963), 274.
Here are links to some entries on Levy's conjecture:
http://en.wikipedia.org/wiki/Levy's_conjecture (Wikipedia)
http://mathworld.wolfram.com/LevysConjecture.html (MathWorld
http://planetmath.org/encyclopedia/LevyConjecture.html (PlanetMath)
http://www.research.att.com/~njas/sequences/A046927 (OEIS)
However, here I want to point out that Levy's conjecture is not new.
In fact, on page 424 of L. E. Dickson's book "History of the Theory of
Numbers", Vol. I (Amer. Math. Soc., Chelsea Publ., 1999), there is the
following sentence:
"E. Lemoine [L'intermediaire des math., 1(1894), 179; 3(1896), 151]
stated empirically that every odd number >3 is a sum of a prime p and
the double of a prime q, and is also of the forms p-2q and 2q'-p'. "
[3 might be a typo for 5; and I use q to replace $\pi$ in the original
sentence.]
Thus, Levy's conjecture should be corrected as Lemoine's conjecture.
This should be made widely known to number theorists.
Zhi-Wei Sun
http://math.nju.edu.cn/~zwsun
