Difference between revisions of "Prime number"
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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]]. | ||
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| + | == Famous Primes == | ||
| + | === Fermat Primes === | ||
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| + | === Mersenne Primes === | ||
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| + | === 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
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.
