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.
closed as unclear what you're asking by Erick Wong, Michael Albanese, studiosus, martini, Davide Giraudo Jul 13 '14 at 10:10
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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.