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# prime numbers watch

1. what is a prime number and how to recognise
2. (Original post by aempson17)
what is a prime number and how to recognise
''A number above 0 that can't be divided by 2.''
Rule 1
[with the exception of 2 itself]
3. (Original post by Den987)
A number above 0 that can't be divided by 2.
4. (Original post by Den987)
A number above 0 that can't be divided by 2.
ermm that sounds like the definition of odd numbers ?

5. A prime number is a number that can only be divided by itself and 1. No other numbers.
Essentially they’re 2, 3, 5, 7, 11, 13, 17, 19 and more.
1 is debatable.
6. (Original post by the bear)
ermm that sounds like the definition of odd numbers ?

I was trying to give a clue only .

Rule 2 - *(They can't be divided by any other number except 1 and themselves)
7. (Original post by aempson17)
what is a prime number and how to recognise
A prime number is a positive integer whose only divisors are one and itself. A quick way to check primality is quite complicated and even then subject to errors. All you need to do to validate whether or not a number is prime is check divisors of up to and including (well, floor of sqrt(n) )
8. (Original post by SweetLeilani)
A prime number is a number that can only be divided by itself and 1. No other numbers.
Essentially they’re 2, 3, 5, 7, 11, 13, 17, 19 and more.
1 is debatable.
By the way I’m talking about integers only here.

9. (Original post by Den987)
A number above 0 that can't be divided by 2.
So 9 is a prime number...?

(Original post by aempson17)
what is a prime number and how to recognise
A prime number is a positive integer which is only divisible by and itself.

First few are:

One thing to notice is that prime numbers (with the exception of 2) are all odd. So if you see an even number, you can say straight away it is not prime because it has a divisor (namely 2) that is neither 1 nor the number itself.
Secondly, every odd number (with the exception of 5) is not prime. So numbers like 15, 25, 35, ... are not primes (they are divisible by 5)
Thirdly, if the sum of the digits of your number is a multiple of 3, then your number is not prime.

A common way to test whether an odd number is prime or not is to take its square root, and see whether your number is divisible by any prime up to this square root. If not, then your number is prime.
10. A prime number is an integer, greater than 1, divisible only by 1 and itself.

With small numbers it's easy enough to verify it by brute force, That is, trying to divide by each number up to , rounded down. Obviously, if is a whole number, is not prime, since it is a square number. If it's even, you know that it's not prime right off the bat.

For larger numbers it is far harder to find out whether a number is prime. How best to do so would depend on the problem at hand. (I'm not sure if you'll be interested in this bit, I think the first line would have you covered)

If you're interesting in programming a solution, look up the sieve of sieve of eratosthenes to generate a list of the first primes.
11. (Original post by SweetLeilani)
By the way I’m talking about integers only here.

1 isn't prime by definition. The notion of primality is extended to algebra (prime elements of groups/rings), topology (prime knots) and soo many fields and in all cases the identity element is excluded from the definition.

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