Difference between revisions of "Dirichlet's theorem"
Jump to navigation
Jump to search
m |
(example) |
||
| Line 4: | Line 4: | ||
</blockquote> | </blockquote> | ||
[[category:mathematics]] | [[category:mathematics]] | ||
| + | |||
| + | For example, the sequence of numbers which are one more than a multiple of 11 (1,12,23,34,45,...) is an arithmetic progression. Dirichlet's theorem states that this sequence contains infinitely many prime numbers. Equivalently, there are infinitely many values of k for which 11*k+1 is a prime number. | ||
Revision as of 20:20, September 30, 2009
Dirichlet's theorem states:
There are infinitely many prime numbers in any arithmetic progression.
For example, the sequence of numbers which are one more than a multiple of 11 (1,12,23,34,45,...) is an arithmetic progression. Dirichlet's theorem states that this sequence contains infinitely many prime numbers. Equivalently, there are infinitely many values of k for which 11*k+1 is a prime number.