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# Windows 7: What is a prime number?

 05 Jan 2020 #1 F22 Simpilot Windows 7 Ultimate x64 3,234 posts Near a 400 KHz transmitter 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. My System Specs
 05 Jan 2020 #2 Barman58 Windows 10 Pro x64 1909 - 18363.657 XP/Vista/Win7/Win8.1 in VM for testing 24,507 posts Newport, South Wales, UK 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 Specs
 05 Jan 2020 #3 F22 Simpilot Windows 7 Ultimate x64 3,234 posts Near a 400 KHz transmitter 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 Specs
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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 24,507 posts Newport, South Wales, UK 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 Specs
 05 Jan 2020 #5 blue skies Windows 7 Home Premium 64 bit 119 posts Quote: Originally Posted by F22 Simpilot ...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 Specs
 05 Jan 2020 #6 F22 Simpilot Windows 7 Ultimate x64 3,234 posts Near a 400 KHz transmitter I guess that's more clear. Thanks. My System Specs
 07 Jan 2020 #7 townsbg Windows 7 pro 64-bit sp 1 1,292 posts Quote: di·vis·i·ble /dəˈvizəb(ə)l/ Learn to pronounce adjective adjective: divisible 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 Specs
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 07 Jan 2020 #8 F22 Simpilot Windows 7 Ultimate x64 3,234 posts Near a 400 KHz transmitter So 9 is a composite. My System Specs
 07 Jan 2020 #9 townsbg Windows 7 pro 64-bit sp 1 1,292 posts I haven't heard it put that way but yes. My System Specs
 08 Jan 2020 #10 iko22 Windows 7 x64, Vista x64, 8.1 smartphone 2,160 posts 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 Specs