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I've been wondering....the conjecture which states that the number of twin primes is infinite has neither been proved nor disproved so far. We know that the number of primes is infinite and I have come across two methods of proving this.

My question is: why can't we actually prove that the number of twin primes, i.e. the number of distinct pairs of the form

(p, p+2)

or

(p-2, p)

where both members of the ordered pair are prime, is infinite? If we assume that the number is finite, would we reach an absurdity? If yes, then reductio-ad-absurdum should be the method of proof. Why then is it that no convincing methods have been proposed to prove this conjecture (or disprove it) for so many years?

Brun's Theorem (http://mathworld.wolfram.com/BrunsConstant.html) describes (perhaps not as rigorously as we would like) the scarcity of twin primes. There are conjectures of all kinds related to twin primes and they are indeed, quite interesting...

Cheers

Vivek

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# Is the number of twin primes really infinite?

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