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It is not clear what you mean by "3p added by 1." If you mean 3p+1, there is only one such prime and that is 7, where p is 2. The reason is that every prime greater than 2 is odd and 3 times an odd number is odd and 1 plus that is even and no prime greater than 2 is even. If you mean 3p-1, the only prime is 5 for the same reason except that every odd number minus 1 is even. So again, 2 is the only value of p that produces a prime.

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Q: Is the integer 5the only prime number of the form 3p added by 1 where p represents any prime number?
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