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

Lemoine's conjecture

In 1895, French mathematician Émile Lemoine proposed that :

2n + 1 = p + 2q 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.* see notes

[source below]

e.g.

13=3+(2×5)
19=5+(2×7)

Although the conjecture has been computationally checked up to at least 1010, 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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