In number theory, Levy's conjecture states that all odd integers greater than 5 can be represented as the sum of an odd prime number and an even semiprime. Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes In Mathematics, the parity of an object states whether it is even or odd In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1 In Mathematics, a semiprime (also called biprime or 2- Almost prime, or pq number) is a Natural number that is the product To put it algebraically, 2n + 1 = p + 2q always has a solution in primes p and q (not necessarily distinct) for n > 2. The Levy conjecture is similar to but stronger than Goldbach's weak conjecture. In Number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem
For example, 47 = 13 + 2 × 17 = 37 + 2 × 5 = 41 + 2 × 3 = 43 + 2 × 2. (sequence A046927 in OEIS) counts how many different ways 2n + 1 can be represented as p + 2q. The On-Line Encyclopedia of Integer Sequences ( OEIS) also cited simply as Sloane's, is an extensive searchable Database of Integer sequences
According to MathWorld, the conjecture has been checked for all odd positive integers less than 109. MathWorld is an online Mathematics reference work created and largely written by Eric W In Mathematics, a natural number (also called counting number) can mean either an element of the set (the positive Integers or an
The conjecture was posed by Émile Lemoine in 1895, but in more recent years came to be attributed to Hyman Levy who pondered it in the 1960s. Émile Michel Hyacinthe Lemoine (emil ləmwan November 22 1840 – February 21 1912) was a French Civil engineer and a Hyman Levy ( 1889 &ndash 1975) was a Scottish Mathematician and author
References
- Eric W. Weisstein, Levy's Conjecture at MathWorld. Eric W Weisstein (born March 18, 1969, in Bloomington Indiana) is an Encyclopedist who created and maintains MathWorld MathWorld is an online Mathematics reference work created and largely written by Eric W
- Richard K. Guy, Unsolved Problems in Number Theory New York: Springer-Verlag 2004: C1
- L. Richard Kenneth Guy (born 1916 Nuneaton, Warwickshire) is a British mathematician Professor Emeritus in the Department of Mathematics Hodges, "A lesser-known Goldbach conjecture", Math. Mag. , 66 (1993): 45 - 47.
- H. Levy, "On Goldbach's Conjecture", Math. Gaz. 47 (1963): 274
External links
- Levy's Conjecture by Jay Warendorff, The Wolfram Demonstrations Project.
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