A Study About Fermat Primability Test

[drmurat]

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 ) ^ ( 2^{31 – 1} ) -2 ) / ( 2³¹ – 1 ) is integer
• 2³¹ – 1 is probably prime or psodoprime
• ( ( 2 ) ^ ( 2^{31 – 1} ) -2 ) / ( 2³¹ – 1 )
• = (2* ( 2 ) ^ ( 2^{31 – 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 2^31*2 = 2⁶² , 2^31*3 =2⁹³ , 2^31*a mod ( 2^31 – 1) is equal to 1
• İf ( 2 ) ^ ( 2^{31 – 2} ) / 2³¹ is integer also is equal to 1 for mod ( 2³¹ – 1)
• ( 2^{31 – 2} ) / 31 is integer
• P is probably prime or psodoprime

• n =2
• p = 2³¹ + 1
• lets find 2ⁿ mod ( 2³¹ + 1 ) = 1
• 2^{n + 1} , 2^{n + 2} , … 2^{n + b}
• 2^{n + b} mod 2³¹ + 1 = 1
• ( ( 2 ) ^ ( 2^{31 + 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
• 2^{n + 1} , 2^{n + 2} , … 2^{n + b} sayısı 2³¹ + c
• 2^{n + b} mod 2³¹ + c = 1
• ( ( 2 ) ^ ( 2^{31 + c} ) -2 ) / ( 2³¹ +c )
• = (2* ( 2 ) ^ ( 2^31+c-1 ) -1 ) / ( 2³¹ + c )
• İf ( 2^31+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

[Batalov]

Originally Posted by drmurat

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.

[drmurat]

Originally Posted by Batalov

There is an error in the 3rd line.
Rework, try again.

n^p-1 mod p = 1

[drmurat]

I dont know forum rules well. What is the meanimg of Red labeled minus sign on post and who putted it there

[Uncwilly]

Originally Posted by drmurat

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.

[Happy5214]

Originally Posted by Uncwilly

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.

[drmurat]

Originally Posted by Happy5214

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...

[Happy5214]

Originally Posted by drmurat

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.

[Batalov]

Originally Posted by drmurat

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.