# Prime Problem

Take some time to read the statements below.

$$[1]$$. It is impossible for $$p$$, $$p+2$$ and $$p+4$$ to be all prime numbers where $$p$$ is a prime number greater than $$3$$.

$$[2]$$. It is possible for both $$8p-1$$ and $$8p+1$$ to be prime when $$p$$ is a prime number.

$$[3]$$. If $$p$$ is a prime greater than $$3$$, then $$p^2-1$$ is always divisible by $$12$$

Which of these statements are true?

Note: This problem is a part of the set "I Don't Have a Good Name For This Yet". See the rest of the problems here. And when I say I don't have a good name for this yet, I mean it. If you like problems like these and have a cool name for this set, feel free to comment here.

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