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# Can someone please explain in detail what a prime number is and why?

Question #77791. Asked by rixbix. (Mar 25 07 10:05 AM)

Diamondlance

I hope this isn't a homework question, but a prime number p is an integer for which |p| > 1 and such that the only divisors of p are 1, -1, p, and -p. Some examples are 2, 3, 5, and 7.

Some sources restrict p to being a positive integer.

...as for 'why', numbers with this property are very important in number theory and have found practical use in modern disciplines such as cryptology.

 Mar 25 07, 10:59 AM
greenkiwi

A prime number is any number that can be divided by itself and the number 1 only.... that is what makes it by definition "A Prime Number"

 Mar 25 07, 12:20 PM
Sofie

In mathematics, a prime number (or a prime) is a natural number that has exactly two (distinct) natural number divisors, which are 1 and the prime number itself. There exists an infinitude of prime numbers, as demonstrated by Euclid in about 300 B.C.. The first 30 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, and 113 (sequence A000040 in OEIS); see the list of prime numbers for a longer list.

The property of being a prime is called primality, and the word prime is also used as an adjective. Since 2 is the only even prime number, the term odd prime refers to all prime numbers greater than 2.

The study of prime numbers is part of number theory, the branch of mathematics which encompasses the study of natural numbers. Prime numbers have been the subject of intense research, yet some fundamental questions, such as the Riemann hypothesis and the Goldbach conjecture, have been unresolved for more than a century. The problem of modelling the distribution of prime numbers is a popular subject of investigation for number theorists: when looking at individual numbers, the primes seem to be randomly distributed, but the "global" distribution of primes follows well-defined laws.

http://en.wikipedia.org/wiki/Prime_number

 Mar 25 07, 4:34 PM

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