Twin prime

Twin primes are pairs of prime numbers of the form and . The first few pairs of twin primes are , and so on. Just as with the primes themselves, twin primes become more and more sparse as one looks at larger and larger numbers.

Twin Prime Conjecture

Main article: Twin Prime Conjecture

Documentation

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The statement that there are infinitely many pairs of twin primes is known as the Twin Prime Conjecture. It is not known whether this statement is true.

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There are infinitely many prime numbers. This can be proved by considering the following: Say the largest known prime is n. Multiply together all integers from 1 to n then add 1- 1x2x3x4x......x(n-1)xn+1. Let us call this product N. The fundamental rule of arithmetic is that all numbers are either prime or the product of primes. Therefore, n is either prime or the product of primes between n and N since n is not a multiple of 2,3,4,......,n-1, or n.

However, it is still unknown whether or not there are infinitely many prime pairs- although it is conjectured that there are (this is what the "Twin Prime Conjecture" says.