One of the numbers has to be two, and the other two odd primes, so:
{2, 3, 127}, {2, 17, 113}, {2, 23, 107}, {2, 29, 101}, {2, 41, 89}, {2, 47, 83}, and {2, 59, 71} are the possible solutions
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127, 3, 2
if you mean what three prime numbers add up to a prime number then the answer is : 5 + 7 + 11 = 23
3, 5 and 7 are consecutive odd prime numbers.
No, as all prime numbers are odd, excluding 2, and when you add two odd numbers you get an even number. This even number can't be a prime number as it will be divisible by 2. 101 and 31 are both prime, but 101+31 is 132.
Multitudes of combinations...in what context? Prime numbers or what?