Difference between revisions of "Prime number"
(merged Prime and Prime number articles and set the redirect) |
(started famous primes section) |
||
Line 1: | Line 1: | ||
A '''prime number''' (or simply '''prime''') is a positive [[integer]] <math>p>1</math> whose only positive [[divisor | divisors]] are 1 and itself. | A '''prime number''' (or simply '''prime''') is a positive [[integer]] <math>p>1</math> whose only positive [[divisor | divisors]] are 1 and itself. | ||
Note that <math>1</math> is usually defined as being neither prime nor composite because it is its only factor among the [[natural number|natural numbers]]. | Note that <math>1</math> is usually defined as being neither prime nor composite because it is its only factor among the [[natural number|natural numbers]]. | ||
+ | |||
+ | |||
+ | == Famous Primes == | ||
+ | === Fermat Primes === | ||
+ | |||
+ | === Mersenne Primes === | ||
+ | |||
+ | === Twin Primes === | ||
+ | Two primes that differ by exactly 2 are known as [[twin primes]]. The following are the smallest examples: | ||
+ | 3, 5 | ||
+ | 5, 7 | ||
+ | 11, 13 | ||
+ | 17, 19 | ||
+ | 29, 31 | ||
+ | 41, 43 | ||
+ | |||
+ | |||
== Advanced Definition == | == Advanced Definition == | ||
When the need arises to include negative divisors, a '''prime''' is defined as an integer p whose only divisors are 1, -1, p, and -p. | When the need arises to include negative divisors, a '''prime''' is defined as an integer p whose only divisors are 1, -1, p, and -p. |
Revision as of 23:34, 19 June 2006
A prime number (or simply prime) is a positive integer whose only positive divisors are 1 and itself. Note that is usually defined as being neither prime nor composite because it is its only factor among the natural numbers.
Contents
[hide]Famous Primes
Fermat Primes
Mersenne Primes
Twin Primes
Two primes that differ by exactly 2 are known as twin primes. The following are the smallest examples: 3, 5 5, 7 11, 13 17, 19 29, 31 41, 43
Advanced Definition
When the need arises to include negative divisors, a prime is defined as an integer p whose only divisors are 1, -1, p, and -p.