Can someone please explain to me what a prime number is?

Question

I still dont fully understand, can some1 show me how i can find out in an example or something hoe i can find out if a number is prime or not

Answer 1

Hi!!!
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.

eg: If you have the number 2, you can divide it by only numbers 1 & 2. So 2 is a prime number

-- If you have the number 3, you can divide it by only numbers 1 & 3 and not by 2. So 3 is a prime number

But take the number 4, you can divide it by 1,2 & 4. SO it is not a prime number...

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.


I hope this helps you!!!!!!!!!!!!!

Answer 2

All "normal" numbers (1, 2, 3, 4, 5, etc.) are either prime or composite. Prime numbers cannot be divided by any other numbers apart from themselves and 1. Composite numbers can be formed by multiplying two other numbers together. The number 1 is considered "special" and is neither prime or composite.

Examples:

1) 3 can only be divided by 1 and 3 and is prime
2) 6 can be evenly divided by 2 and 3, in addition to 1 and 6, and is composite

You cannot easily test if a number is prime. But there is an ancient algorithm for deriving prime numbers called the Sieve of Eratosthenes (apologies if the name is spelled incorrectly). You can try this as follows:

1. Write down all the numbers from 1 to 100 (or as many as you like)
2. Cross out all the numbers that can be divided by 2 (2, 4, 6, 8...)
3. Cross out all the numbers that can be divided by 3 (3, 6, 9, 12...)
4. No need to cross out number that can be divided by 4, as these are already crossed out because they can be divided by 2
5. Cross out all the numbers that can be divided by 5
6. Keep going until you stop crossing off any numbers
7. The remaining numbers are prime

The numbers that you actually need to divide using this method are all prime (2, 3, 5, etc.) but it doesn't matter if you try dividing by other numbers.

You should end up with: 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

As you can imagine, testing if a very large number is prime takes ages and this is the basis for many forms of encryption e.g. making websites secure. These use two enormous numbers that it would take years for a computer to figure out...

Answer 3

For example, we ask: is 179 prime?

Method: the square root of 179 is 13 and a bit, so we will test it by dividing it by all primes up to and including 13.

179 / 2 = something, remainder 1
179 / 3 = something else, remainder 2.
179 / 5 = another thing, remainder 4.
179 / 7 = different thing, remainder 4.
179 / 11 = still other thing, remainder 3.
179 / 13 = something or other, remainder 10.

None of the remainders were zero, therefore 179 is prime. It is not the product of any two whole numbers which are both greater than 1.

If we start again with 187, we get a remainder when we divide it by 2, 3, 5 or 7, but a remainder of zero when we divide it by 11, therefore 187 is not prime. It is a product of two whole numbers, 11 times 17.

This method is quite okay on a computer for numbers up to maybe 10 or 11 digits long. After that, cleverer methods are needed to make the test go quickly enough.

Answer 4

A number which is divisible by 1 & itself is called a prime number.Prime numbers begin from 2, and 2 is the on & only even prime.
Some simple tricks to use are any number ending with, 0,2,4,5,6,8 will never be prime. So this will reduce the numbers of questions you have to work out.
2,3,5,7,11,13,17,19 .etc are some prime numbers.
You can express all numbers are a product of some powers of prime numbers.

Answer 5

A prime number is a number that can be divided by itself and 1 only.

The lowest prime number is 2.

The first few prime numbers are:-
2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29, 31,-------

Answer 6

A number that can be divided only by itself and one. (These are the building blocks of other numbers. ie., any natural number can br factored into a product of primes--->concept used in cryptography)
the opposite kind are the composite ie., those that ve factors on top of one and themselves. 1 is aspecial case being neither of these. and 2 is the only even prime.

Regarding your other question of finding whether a number is prime or not.u can either do a brute force (which really is not required) or u can use the fact that any composite number has atleast one prime factor

Answer 7

Try finding divisors of the number given. If you can find any other than 1 & the number itself, then the number is prime.

Some simple tricks to use are any number ending with, 0,2,4,5,6,8 will never be prime. So this will reduce the numbers of questions you have to work out.
2,3,5,7,11,13,17,19 .etc are some prime numbers.
You can express all numbers are a product of some powers of prime numbers.

Answer 8

A prime number is a number that can only be divided by itself and one.

like 1, 3, 5, 7, 11, 13, 17, 19 etc.

Answer 9

a prime number is a number that can only be divided by itself and by one.

take the number 3. it's divisible by 3, you get 1. and it's divisible by 1, you get 3. but that's it. so it's prime.

Answer 10

A prime number is a number which is divisible only by 1 and itselves.Here divisible means the anwers of division should be an integer.
eg.2,3,5,7,11,13........
1 is neither prime nor composite