Windows 7 Forums
Welcome to Windows 7 Forums. Our forum is dedicated to helping you find support and solutions for any problems regarding your Windows 7 PC be it Dell, HP, Acer, Asus or a custom build. We also provide an extensive Windows 7 tutorial section that covers a wide range of tips and tricks.

Windows 7: What is a prime number?

2 Weeks Ago   #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:

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.
My System SpecsSystem Spec
2 Weeks Ago   #2

Windows 10 Pro x64 x3, Ubuntu

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
My System SpecsSystem Spec
2 Weeks Ago   #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.
My System SpecsSystem Spec

2 Weeks Ago   #4

Windows 10 Pro x64 x3, Ubuntu

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
My System SpecsSystem Spec
2 Weeks Ago   #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.
My System SpecsSystem Spec
2 Weeks Ago   #6
F22 Simpilot

Windows 7 Ultimate x64

I guess that's more clear. Thanks.
My System SpecsSystem Spec
2 Weeks Ago   #7

Windows 7 pro 64-bit sp 1


Learn to pronounce

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.
My System SpecsSystem Spec
2 Weeks Ago   #8
F22 Simpilot

Windows 7 Ultimate x64

So 9 is a composite.
My System SpecsSystem Spec
2 Weeks Ago   #9

Windows 7 pro 64-bit sp 1

I haven't heard it put that way but yes.
My System SpecsSystem Spec
2 Weeks Ago   #10

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.
My System SpecsSystem Spec

Thread Tools

Similar help and support threads
Thread Forum
Prime 95 and troubleshooting questions
So, I've been playing some Payday 2 on steam with a friend when a problem occurred. We played for about 2 hours when it happened. My screen froze, the audio stuttered, and there was absolutely nothing I could do except for turning off the system via power button. I've just run FurMark in 1080p...
Spooky Halloween prime number
I came across this weird prime number in the UK press today (31 Oct). 1000000000000066600000000000001 it's the number of the beast '666' with 13 zero's each side (13 considered unlucky) and a 1 - known to math dudes as Belphegor's Prime. Not only is it a prime number (divisible only by itself...
Chillout Room
new CPU failing Prime 95
Hiya guys, would like to pick your brains if I may. As some of you may or may not know, I recently built my new rig (specs in profile). Now last night, I was running Prime95 to get an idea of my stock temps, and Core 3 failed (expected x, returned y). Fearing the worst, I reran it, and it again...
Hardware & Devices
Not Ready for Prime Time
Realizing this is a beta, I 've had some problems. I want to post the ones I can think of at the moment. These are persistant problems which no amout of "googling" has turned up any fixes for. This is on just ONE system. I need one for every day stablity, and havn't run the 3rd system long enough...
General Discussion
RC not ready for prime time?
With all the problems some folks are having trying to install this perhaps MS should stop allowing downloads till they fix the problem in RC-2. If this product is released to the public as is it will be a disaster. What is shocking is that the beta installed without a hitch but would not install...
Installation & Setup

Our Sites

Site Links

About Us

Find Us

Windows 7 Forums is an independent web site and has not been authorized, sponsored, or otherwise approved by Microsoft Corporation. "Windows 7" and related materials are trademarks of Microsoft Corp.

© Designer Media Ltd

All times are GMT -5. The time now is 15:32.
Twitter Facebook