Q: What two prime numbers add up to 123?

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29

For two primes to add up to an odd number, one of them has to be two. 33 isn't prime, so there is no solution.

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There is no pair of prime numbers that sum to 123.Proof :Any two odd primes will sum to an even number, thus excluding 123 which is odd.Since 2 is the only even prime, the only possible solution is 2 + 121 = 123.But, 121 is not prime because it is 11 x 11.A similar proof shows that there is no pair of primes whose difference is 123.There are two primes that multiply to 123 : - 3 and 41.