Difference between revisions of "Twin prime"
(→Twin Prime Conjecture) |
|||
| Line 12: | Line 12: | ||
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 17:19, 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
Documentation
Use {{hatnote|text}} </noinclude>
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.
