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Show that if three prime numbers, all greater than 3, form an arithmetic progression then the common difference of the progression is divisible by 6.

Find some examples of three primes which include the number 3 and form an AP, and show that in every such case the common difference is not divisible by 6.

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Explorations of arithmetic progressions of prime numbers are an ongoing subject of mathematics research.

Explorations of arithmetic progressions of prime numbers are an ongoing subject of mathematics research.