Maths Olympiad Prep

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Number theory Difficulty 3.0 AMC 10/12 Prove it United Kingdom

Show that there are at least three prime numbers pp less than 200200 for which p+2p + 2, p+6p + 6, p+8p + 8 and p+12p + 12 are all prime. Show also that there is only one prime number qq for which q+2q + 2, q+6q + 6, q+8q + 8, q+12q + 12 and q+14q + 14 are all prime.

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