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The prime numbers that add up to 66 are 31 and 35. To find these numbers, we can start by listing out the prime numbers less than 66, which are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, and 61. Then, we can check which pair of these prime numbers add up to 66, which in this case are 31 and 35.
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