Difference between revisions of "Twin prime"
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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. | 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 | + | 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. |
Revision as of 16:19, 20 July 2009
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
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.
This article is a stub. Help us out by expanding it.
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.
