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Old 2020-12-26, 10:15   #1
drmurat
 
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minus A Study About Fermat Primability Test

The primability test of Fermat
• P is prime
• ( n p – n ) / p is integer p is psodoprime or probably prime .
• n p - 1 mod p = 1 is must be true equation
in this equation
• ( n p – n ) / p = ( n * ( n p – 1 – 1 ) ) / p is getted
İf n is not equal to p or n is not equal to p * d than n is not devided by p so ( n p – 1 – 1 ) must be devided by p
Lets get n = 2 and p is one of the mersenne number

• n =2
• p = 231 – 1
• if ( ( 2 ) ^ ( 231 – 1 ) -2 ) / ( 231 – 1 ) is integer
• 231 – 1 is probably prime or psodoprime
• ( ( 2 ) ^ ( 231 – 1 ) -2 ) / ( 231 – 1 )
• = (2* ( 2 ) ^ ( 231 – 2 ) -1 ) / ( 231 – 1 )
• Lets find 2n which is equal to 1 according to mod( 231 – 1 )
• 231 mod ( 231 – 1 ) = 1
• İn this case 231*2 = 262 , 231*3 =293 , 231*a mod ( 2^31 – 1) is equal to 1
• İf ( 2 ) ^ ( 231 – 2 ) / 231 is integer also is equal to 1 for mod ( 231 – 1)
• ( 231 – 2 ) / 31 is integer
• P is probably prime or psodoprime

• n =2
• p = 231 + 1
• lets find 2n mod ( 231 + 1 ) = 1
• 2n + 1 , 2n + 2 , … 2n + b
• 2n + b mod 231 + 1 = 1
• ( ( 2 ) ^ ( 231 + 1 ) -2 ) / ( 231 +1 )
• = (2* ( 2 ) ^ ( 231 ) -1 ) / ( 231 + 1 )
• if ( 231 ) / ( n + b ) is integer
• P is probably prime or psodoprime
.
• n =2
• p = 231 + c
• lets find 2n mod 231 + c = 1
• 2n + 1 , 2n + 2 , … 2n + b sayısı 231 + c
• 2n + b mod 231 + c = 1
• ( ( 2 ) ^ ( 231 + c ) -2 ) / ( 231 +c )
• = (2* ( 2 ) ^ ( 231+c-1 ) -1 ) / ( 231 + c )
• İf ( 231+c-1 ) / ( n + b ) is integer
• P is probably prime or psodoprime

N can be different from 2

I Dont know this study adds something to Fermat Primability Test
Please write your comments

Last fiddled with by drmurat on 2020-12-26 at 10:25
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Old 2020-12-26, 10:22   #2
Batalov
 
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Quote:
Originally Posted by drmurat View Post
The primability test of Fermat
• P is prime
• ( n p – n ) / p is integer p is psodoprime or probably prime .
• n p – 1 mod p = 1 is must be true equation <<< ??
There is an error in the 3rd line.
Rework, try again.
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Old 2020-12-26, 10:25   #3
drmurat
 
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Quote:
Originally Posted by Batalov View Post
There is an error in the 3rd line.
Rework, try again.
np-1 mod p = 1
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Old 2020-12-26, 14:22   #4
drmurat
 
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I dont know forum rules well. What is the meanimg of Red labeled minus sign on post and who putted it there
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Old 2020-12-26, 17:20   #5
Uncwilly
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Quote:
Originally Posted by drmurat View Post
I dont know forum rules well. What is the meanimg of Red labeled minus sign on post and who putted it there
It is not a minus sign. It is like the road sign that is nearly universal, meaning "Do Not Enter"
https://en.wikipedia.org/wiki/File:K...not_Enter).svg

A moderator would have added it as a statement about the value of the thread.

Green plus symbols have been added to threads to indicate that they are important or high value.

Last fiddled with by Uncwilly on 2020-12-26 at 17:22
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Old 2020-12-27, 02:41   #6
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Quote:
Originally Posted by Uncwilly View Post
It is not a minus sign. It is like the road sign that is nearly universal, meaning "Do Not Enter"
https://en.wikipedia.org/wiki/File:K...not_Enter).svg
I thought it was a minus too, especially since there was a plus icon in opposition. I'm so used to seeing the "Do Not Enter" sign with words. The American version is https://commons.wikimedia.org/wiki/File:MUTCD_R5-1.svg.

Last fiddled with by Happy5214 on 2020-12-27 at 02:44 Reason: Detail
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Old 2020-12-27, 09:54   #7
drmurat
 
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Quote:
Originally Posted by Happy5214 View Post
I thought it was a minus too, especially since there was a plus icon in opposition. I'm so used to seeing the "Do Not Enter" sign with words. The American version is https://commons.wikimedia.org/wiki/File:MUTCD_R5-1.svg.
Maybe small note can be helpfull for us which is related with this sign. İt can be non sende no it clear wroong etc...
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Old 2020-12-28, 05:26   #8
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Quote:
Originally Posted by drmurat View Post
Maybe small note can be helpfull for us which is related with this sign. İt can be non sende no it clear wroong etc...
To be fair, whether you interpret it as a minus or a Do Not Enter sign, the implication of a "bad", "poor quality", or "no-go" thread is the same (and I understood that part already), so the difference is immaterial.

Last fiddled with by Happy5214 on 2020-12-28 at 05:27 Reason: Article
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Old 2020-12-28, 05:38   #9
Batalov
 
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Quote:
Originally Posted by drmurat View Post
I Dont know this study adds something to Fermat Primability Test
So, that's the thing.
What you posted doesn't add. It subtracts.

The reader comes in being in some state in time-knowledge space.
He goes away with less, in both.
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