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Windows 7: What is a prime number?

05 Jan 2020   #1
F22 Simpilot

Windows 7 Ultimate x64
 
 
What is a prime number?

So I have read many times over that somehow prime numbers are used to help decrypt encryption, but I don't understand what a prime number is.

From Wikipedia:

Quote:
No even number n {\displaystyle n} greater than 2 is prime because any such number can be expressed as the product 2 × n / 2 {\displaystyle 2\times n/2} . Therefore, every prime number other than 2 is an odd number, and is called an odd prime.[8] Similarly, when written in the usual decimal system, all prime numbers larger than 5 end in 1, 3, 7, or 9. The numbers that end with other digits are all composite: decimal numbers that end in 0, 2, 4, 6, or 8 are even, and decimal numbers that end in 0 or 5 are divisible by 5.[9]
So why isn't 9 prime? It's greater than 2 and not even.

And how do prime numbers help in decryption? Does this have something to do with "collisions?"

It's been at least 25 years since I was in school so I don't remember any of this stuff.
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05 Jan 2020   #2
Barman58

Windows 10 Pro x64 1909 - 18363.657 XP/Vista/Win7/Win8.1 in VM for testing
 
 

A prime number is any number that is only divisible by 1 or itself to give a whole number

9 is not a prime number as it is divisible by 1, 9, and 3 to give a whole number, no even number is a prime as it always gives a whole number if divided by 1, itself or 2

Prime numbers have long been used in cryptography - you may find this site interesting (though not entertaining) Learn Cryptography - Prime Factorization
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05 Jan 2020   #3
F22 Simpilot

Windows 7 Ultimate x64
 
 

It's the part about only divisible by 1 or its self that confuses me. What exactly does that mean?

That link helped me understand salting and rainbow tables, but most of the other stuff I already knew about.
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05 Jan 2020   #4
Barman58

Windows 10 Pro x64 1909 - 18363.657 XP/Vista/Win7/Win8.1 in VM for testing
 
 

It's basic mathematics 101 -

all numbers are divisible by 1 when they give a result of themselves 9/1=9
All Numbers are divisible by themselves when they give a result of 1 9/9=1
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05 Jan 2020   #5
blue skies

Windows 7 Home Premium 64 bit
 
 

Quote   Quote: Originally Posted by F22 Simpilot View Post
...I don't understand what a prime number is...

So why isn't 9 prime? It's greater than 2 and not even.
Nine isn't a prime number because:
In addition to the usual one times the number in question, in this case --> 1x9=9 you also have 3x3=9 and because of that, it does not qualify as a prime number.

Contrast that with the Prime number seven... you have 1x7=7 but no other combinations of whole number factors. You can't divide 7 by 2 and get a whole number, nor divide 7 by 3 or 4 or 5 or 6 and get a whole number.

Same thing with the Prime number three for another example. You have 1x3=3 but other than that, you don't have any other two whole number factors that can equal 3.

Same with the Prime number 5 etc. -- only 1x5=5.

You can see the difference with number 15 however, which unlike 5 is not a Prime number because in addition to 1x15=15, you also have 5x3=15.

I hope that makes sense to you. I wrote it slightly different than the previous explanation in case that makes in a little more clear.

I have no idea about the cryptography part. I haven't looked at the link, but I'm assuming it's way over my head.
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05 Jan 2020   #6
F22 Simpilot

Windows 7 Ultimate x64
 
 

I guess that's more clear. Thanks.
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07 Jan 2020   #7
townsbg

Windows 7 pro 64-bit sp 1
 
 

Quote:
di·vis·i·ble

/dəˈvizəb(ə)l/
Learn to pronounce



adjective
adjective: divisible


  1. capable of being divided.
    "the marine environment is divisible into a number of areas"
    • Mathematics
      (of a number) capable of being divided by another number without a remainder.
      "24 is divisible by 4"
Does that help? 9 is divisible by 3 because it can be divided by 3 without a remainder. So it isn't a prime number. 7 is prime because it is only divisible by itself and 1. If it was divisible by any other whole number it wouldn't be prime.
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07 Jan 2020   #8
F22 Simpilot

Windows 7 Ultimate x64
 
 

So 9 is a composite.
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07 Jan 2020   #9
townsbg

Windows 7 pro 64-bit sp 1
 
 

I haven't heard it put that way but yes.
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08 Jan 2020   #10
iko22

Windows 7 x64, Vista x64, 8.1 smartphone
 
 

Write out the first n numbers along with the factors of n and watch the pattern :
n factors of n
1 has factor of 1
2 has factors of 1 and 2
3 has factors 1 and 3
4 has factors 1, 2 and 4
5 has factors 1 and 5
6 has factors 1, 2, 3, 6
7 has factors 1, 7
8 has factors 1,2, 4, 8
9 has factors of 1, 3, 9
10 has factors 1, 2, 5, 10
11 has factors 1, 11
12 has factors 1, 2, 3, 4, 6, 12
13 has factors 1 and 13
14 has factors 1, 2, 7, 14
15 has factors 1, 3, 5, 15

Any number n, that has only factors of 1 and n, is a prime number.
So, 1, 2, 3, 5, 7, 11 and 13 are prime numbers.
A composite number is a positive number that has to have at least three possible factors.
So, 4, 6, 8, 9, 10, 12, 14 and 15 are composite numbers.
In algebra, a factor is any whole number that divides into another number an exact number of times.
If you continue the sequence:
16 has factors of 1,2, 4, 8 and 16 so 16 is a composite number.
17 has factors of 1 and 17 and therefore 17 is another prime number.
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