====== Lemoine's conjecture ======

In 1895, French mathematician Émile Lemoine proposed that :

>2//n// + 1 = //p// + 2//q// always has a solution in primes //p// and //q// (not necessarily distinct) for //n// > 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.* <sup>see notes</sup>
>\\ [source below]

e.g.

13=3+(2×5)\\ 19=5+(2×7)

Although the conjecture has been computationally checked up to at least 10<sup>10</sup>, there is currently no proof (or disproof).

More info at [[https://en.wikipedia.org/wiki/Lemoine%27s_conjecture|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.