An Introduction to The Twin Prime Conjecture
نویسنده
چکیده
Twin primes are primes of the form (p, p + 2). There are many proofs for the infinitude of prime numbers, but it is very difficult to prove whether there are an infinite number of pairs of twin primes. Most mathemati cians agree that the evidence points toward this conclusion, but numerous attempts at a proof have been falsified by subsequent review. The prob lem itself, one of the most famous open problems in mathematics, has yielded a number of related results, including Brun’s conjecture, Mertens’ theorems, and the Hardy-Littlewood Conjecture. Along with these con jectures, there are a number of results which are easier to arrive at, but nevertheless help mathematicians think about the infinitude of primes, and the special properties of twin primes. This paper will introduce the aforementioned conjectures associated with the twin prime conjecture, and work through some exercises that illuminate the difficulties and intricacies of the twin prime conjecture.
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