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I am learning about arithmetic progressions and I came across the question: "Prove that there is no infinite arithmetic sequence whose terms are all prime numbers."

I can see that there is no constant difference between all the prime numbers and hence an arithmetic sequence consisting only of prime numbers can't exist. However, I am unsure about how to prove this mathematically.

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    Terms in an arithmetic progression have the form $na+b$ for constants $a$ and $b$. $a$ and $b$ have a common factor, or they are coprime. Consider these two cases separately. – 2017-01-30
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    http://math.stackexchange.com/questions/251258/prime-arithmetic-progression-with-one-fixed-element – 2017-01-30

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