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As long as 2 is not one of the primes that you are adding, then I can guarantee that you will get a composite. 2 is the only even Prime number. Any time you add two odd numbers together, you will get an even number (which is not prime). So if you add them in pairs, you will have three even numbers, which added together result in an even number, so it is composite. If you throw in 2 as one of the primes that you're adding, then your result is odd, and I don't know what else to say about your result.

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Q: Can you add 6 prime numbers and get a composite number?
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