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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.

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Q: What 2 prime numbers make 123?
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