11 and 13
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The prime numbers below 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
11+13+19=43 all are prime numbers and these are the only three that are above 7 and work.
The prime numbers less than 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 So their sum is 328
All prime numbers are rational.
There is no need to do prime factorization as prime numbers are already prime.