Prime Problem

Take some time to read the statements below.

[1][1]. It is impossible for pp, p+2p+2 and p+4p+4 to be all prime numbers where pp is a prime number greater than 33.

[2][2]. It is possible for both 8p18p-1 and 8p+18p+1 to be prime when pp is a prime number.

[3][3]. If pp is a prime greater than 33, then p21p^2-1 is always divisible by 1212

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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