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Euclid Second Theorem

It says in the book I'm reading, 'there are infinitely many prime pairs (p, p+2)', so it says, 'p, p+2, p+4, cannot all be prime since once of them must be divisible by 3'.

Why must it be divisible by 3?
because either p is a multiple of three, or it is one more than a multiple of three, or it is one less than a multiple of three.

if it is one more than 3x (for some x), p+2 is 3x+3=3(x+1) which is also a multiple of three.

if it is 3x-1, p+4=3(x+1), and ditto.

thus, one of p, p+2 or p+4 is a multiple of three.
Original post by sollythewise
because either p is a multiple of three, or it is one more than a multiple of three, or it is one less than a multiple of three.

if it is one more than 3x (for some x), p+2 is 3x+3=3(x+1) which is also a multiple of three.

if it is 3x-1, p+4=3(x+1), and ditto.

thus, one of p, p+2 or p+4 is a multiple of three.


Oh right, I get it thanks alot, much appreciated, would you like a positive or negative rep?

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