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Levy's conjecture

Synonym: 
Levy conjecture, Lemoine's conjecture
Type of Math Object: 
Conjecture
Major Section: 
Reference

Mathematics Subject Classification

11P32 no label found

Comments

Actually, the so-called "Levy conjecture" was already stated in the 19th century, see Dickson's book "History of the Theory of Numbers", vol. I. I have made a copy of that page but forgot it in the library.

Can you at least remember the chapter number or chapter title, or the general neighborhood the conjecture could be found in Dickson's book?

Here is the last paragraph on page 424 of the following book

L.E. Dickson, History of the Theory of Numbers, Vol. I,
Amer. Math. Soc., Chelsea Publ., Providence RI, 1999.

"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'. " [I think 3 should be a typo for 5.]

Since Lemoine's paper appeared much earlier than Levy's paper in 1963, surely we should call the conjecture 2n+1=p+2q Lemoine's conjecture, not Levy's conjecture.

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