What are prime numbers?

Answer 1

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 .♥

Answer 2

In mathematics prime numbers 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 79 83 89 97 101 109 and 113.The study of being a prime is called primality and the word prime is also used as an adjective. Since 1 is the onlye even prime number the term odd prime refers to all 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 the primes seem to be randomly distributed but the global distribution of primes follows well-defined laws. The notion of prime numbers has been generalized in many different branches of mathematics. In ring theory a branch of abstract algebra the rerm prime element has a specific meaning. Here a non-zero non-unit ring elemenr a is defined to be prime if whenever a divides b c for ring elements b and c then divides at least one of b or c. With this meaning the additive inverse of any prime number is also prime. In other words when considering the set of intergers Z as a ring -7 is a prime element. Eisenstein primes and Gaussian primes may also be of intersest. In know theory a prime knot is a knot which can not be disaggregated into a smaller prime knot. Ancient Greeks such as Pythagoras are believed to have been the first to study prime numbers and simple sieve method for finding them is attributed to Eratosthenes. Until the 19th century most mathematicians considered the number 1 a prime and there is still a large body of mathematical work that is still valid despite labelling 1 a prime such as the work of Stern and Zeisel. Henri Lebesgue is said to be the last professional mathematician to call 1 prime. The change in label occured so that it can be said each number has a unique factorizaton into primes. For a long time prime numbers were thought as having no possible application outside of number theory this changed in the 1970's when the concepts of public-key cryptography were invented in which prime numbers formed the basis of the first algorithms such as the RSA cryptosystem or the Diffie-Hellman key-exchange algorithm.

Answer 3

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).
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.

There is no known formula for primes which is more efficient at finding primes than the methods mentioned above under "Finding prime numbers".

There is a set of Diophantine equations in 9 variables and one parameter with the following property: the parameter is prime if and only if the resulting system of equations has a solution over the natural numbers. This can be used to obtain a single formula with the property that all its positive values are prime.

There is no polynomial, even in several variables, that takes only prime values. For example, the curious polynomial in one variable f(n) = n2 − n + 41 yields primes for n = 0,..., 40, but f(41) is composite. However, there are polynomials in several variables, whose positive values as the variables take all positive integer values are exactly the primes.

Another formula is based on Wilson's theorem mentioned above, and generates the number two many times and all other primes exactly once. There are other similar formulae which also produce primes.

FOR MORE INFORMATION PL. VISIT:
http://en.wikipedia.org/wiki/Prime_number

Answer 4

Not certain, but I think they're whole numbers which are divisible by only themselves and the number 1. For instance, 13 is a prime number since you can only divide it by 1 or 13. The number 14, however, is not a prime number, since you can not only divide it by 1 and 14, but by 2 and 7 as well.

I could be waaayyy off on this. It's been a while...

Answer 5

prime \'prim\ n [ME, fr. MF, fem. of prin first, L primus; akin to L prior] 1 : first in time : ORIGINAL 2 a : having no factor except itself and one <3 is a ~ number> b : having no common factor except one <12 and 25 are relatively ~> 3 a : first in rank, authority or significance : PRINCIPAL b : having the highest quality or value <~ television time>
Each of Webster's definitions may be applied to this page, but the most operative is 2a: An integer greater than one is prime if its only positive divisors are itself and one (otherwise it is composite). For example: 15 is composite because it has the two prime divisors 3 and 5.

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

Answer 6

Prime numbers are integers that have no factors other than 1 and itself. For example, 3 is a prime number; its factors are 1 and 3. 4 is not a prime number, its factors are 1,2 and 4. The next prime number is 5. All prime numbers are odd.

EDIT that last statement: All prime numbers except 2 are odd.

Answer 7

Prime numbers are those numbers which are only divisible by 1 and themselves. 1 is not considered a prime number by most mathematicians as it has only one factor: itself. Here's a list of all the 25 prime numbers from 1 to 100:
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

Answer 8

Note: Yes, basically everyone has good answers. But, not every even number, is not prime. Ex: 2. The number 2 is the only even, prime number! Read everyone else's answers, but remember that there is one, and only one, even, prime number, which is 2!

Answer 9

they r numbers that can only be divided by themselves or 1 (which is a prime number)

ie: 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, ....139 (my favorite)...etc

Answer 10

Numbers with exactly two factors. One an itself. One is not prime. It is "Special"