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Not true.
2 + 3 = 5, where all three are primes.
One of the primes in the sum must be 2, otherwise both primes would be odd and their sum would be even (and >2) and therefore not prime. Such primes: p and p+2 [3 and 5 in the above example] are known as twin primes and there are infiitely many twin primes.
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