In 1895, French mathematician รmile Lemoine proposed that :
2n + 1 = p + 2q always has a solution in primes p and q (not necessarily distinct) for n > 2.
In plain language :
All odd integers greater than 5 can be represented as the sum of an odd prime number and an even semiprime.
Although the conjecture has been computationally checked up to at least 1010, there is currently no proof (or disproof).
More info at Wikipedia
Note: The conjecture is also called Levy's Conjecture which was (re)proposed in 1963.
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