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Does anyone know how to always get a prime from the sum of three primes?

For example: $5+7+11=23$, $17+29+43=89$, etc.

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closed as unclear what you're asking by Erick Wong, Michael Albanese, studiosus, martini, Davide Giraudo Jul 13 '14 at 10:10

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It has long been conjectured that every odd number greater than $7$ is the sum of $3$ primes. It is known that every large enough odd number is the sum of three primes. I do not know of any extra information known if the target odd number is itself prime.

If your question has to do with an efficient algorithm for finding the $3$ primes, I know very little. But it turns out that for large odd $n$, there seems to be a large number of representations of $n$ as a sum of three primes, so an efficiently conducted search works reasonably well.

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Nicolas: Thanks for the information. I have done extensive work on the Goldbach conjecture and I have developed a new method for the presentations of primes. The material can be found on MO. Most likely I will present the material again in the near future. Sometimes we obtain millions of representations of an odd number as a sum of three primes. – Vassilis Parassidis Sep 1 '12 at 3:10
@VassilisParassidis: Then nothing I wrote is new to you! Sorry, I did not know. – André Nicolas Sep 1 '12 at 3:12
It has been proven in 2013 (which I see is after you wrote this answer). – Akiva Weinberger Jul 3 '15 at 18:15

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