April 20, 2014

Homework Help: math

Posted by haylo on Tuesday, October 24, 2006 at 12:39am.

Can someone help me with prime and composite numbers?

Prime numbers are counting numbers that can be divided evenly bt only two numbers:1 and themselves. A prime number can also be described as a counting number with exactly two factors, 1 and itself. So, 1 because it has only one factor ( itself), is not a prime number.Prime numbers to 100:2,3,5,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97

Composite numbers are all counting numbers that are not prime numbers. In other words , composite numbers are numbers that have more than two factors. Again the number 1, because it has only one factor (itself), is not a composite number.

ok true it think

* The Fundamental Theorem of Arithmetic states that every positive integer/number greater than 1 is either a prime or a composite, i.e. can be expressed as a unique product of primes and their exponents, in only one way.

* The number 1 is not considered a prime number, being more traditionally referred to as the unit.
Aristotle regarded the one as not being a number but rather the elemental measure of all numbers.
Euclid stated that a unit is that property of each and every thing in the universe that enables it to be called one, while a number can be considered a multitude of units.

* A prime number is a positive number "p", other than 1, that has only two positive divisors/factors, 1 and "p".
(The strict interpretation of this definition aids in supporting the statement that the number one is not a prime number as it literally has only one divisor/factor whereas a prime has two factors.)

Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, etc., are all primes, being evenly divisible by only 1 and the number itself.

* A composite number is one that has 3 or more factors/divisors.

* A composite number is expressable as a unique product of prime numbers and their exponents, in only one way.
Examples: 210 = 2x3x5x7; 495 = 3^2x5x11.

* A prime factor of a number is a divisor/factor of the number which also happens to be a prime number. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36 but only 2 and 3 are prime factors.

* Any number that can be expressed as the product of two or more primes and their powers, i.e., ab, abc, ab^2c, ab^2c^3d^2, etc., where a, b, c and d are prime numbers, is composite.

* Any number greater than 1 that is not a prime number must be a composite number, and is the result of multiplying primes together.
Examples: 4, 6, 12, 24, 72, etc., are composite, each being divisible by lower prime numbers.

* Every number n > 1 is divisible by some prime.

* With the exception of the number 2, all prime numbers are odd numbers.
The number 2 is the only even prime, thereby making it the oddest prime.

* Two integers, a and b, are said to be relatively prime if their greatest common divisor is 1. Example: 7 and 12 are relatively prime as their g.c.d. is 1.

* Primes differing by 2 are called twin primes. Examples: 3-5, 5-7, 17-19, 1,000,000,009,649-1,000,000,009,651.

* There is only one set of triple primes - 3, 5, and 7.

How to Find Prime Numbers

The Sieve of Eratosthenes

Lets find the primes between 1 and 100.
Write down the sequence of numbers from 1 to 100.
Cross out the 1.
Beginning with the 2, strike out every second number beyond the 2, i.e., 4, 6, 8, 10, etc.
Starting from the first remaining number, 3, cross out every third number beyond the 3, i.e., 3, 6, 9, 12, etc.
Starting from the first remaining number, 5, cross out every fifth number beyond the 5, i.e., 5, 10, 15, 20, etc.
Continue with the 7, crossing out every seventh number beyond the 7, i.e., 7, 14, 21, 28, etc.
Continue the process until you have reached N or 100.
The numbers remaining are the primes between 1 and 100, namely 2, 3, 5, 7, 11, 13,17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. By definition, all the others are composite numbers.

what is the largest number tou will have to check to find the prime number of 100

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