content:mathematics:lemoines_conjecture

# Wikenigma - an Encyclopedia of Unknowns Wikenigma - an Encyclopedia of the Unknown

# Lemoine's conjecture

In 1895, French mathematician Ã‰mile Lemoine proposed that :

2n+ 1 =p+ 2qalways has a solution in primespandq(not necessarily distinct) forn> 2.

[source below]

In plain language :

All odd integers greater than 5 can be represented as the sum of an odd prime number and an even semiprime.*^{see notes}

[source below]

e.g.

13=3+(2Ã—5)

19=5+(2Ã—7)

Although the conjecture has been computationally checked up to at least 10^{10}, there is currently no proof (or disproof).

More info at Wikipedia

*Notes:*

[1] The conjecture is also called *Levy's Conjecture* which was (re)proposed in 1963.

[2] An 'even semiprime' is any even number which is the product of two prime numbers multiplied together.

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