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Somebody please explain me the Miller Rabin Primality test

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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It is a probabilistic test for determining primality belonging to the field of computational number theory.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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Yes, how to do it?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

For once Wiki actually did a good job explaining something!!!!

```
Input: n > 3, an odd integer to be tested for primality;
Input: k, a parameter that determines the accuracy of the test
Output: composite if n is composite, otherwise probably prime
Go:
write n − 1 as 2^s·d with d odd by factoring powers of 2 from n − 1
WitnessLoop: repeat k times:
pick a random integer a in the range [2, n − 2]
x ← ad mod n
if x = 1 or x = n − 1 then do next WitnessLoop
repeat s − 1 times:
x ← x^2 mod n
if x = 1 then return composite
if x = n − 1 then do next WitnessLoop
return composite
return probably prime
```

Can not do any better than that except to do some filling in.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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And what does this method actually rely on?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
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A whole lot of number theory and a thing called a strong pseudo prime.

**In mathematics, you don't understand things. You just get used to them.**

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Mainly fermat's little theorem?

And what ensures it is strong?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Offhand I never remember that definition of them but I could look it up.

More to the point is the test itself and the fact that it is a non deterministic test.

**In mathematics, you don't understand things. You just get used to them.**

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Not the definition but I am asking what gives them a **HIGH ** probability of being prime?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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That I do not remember. I am sorry.

**In mathematics, you don't understand things. You just get used to them.**

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Thats okay.

Once I know that a number is probably prime, how do I make sure?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Three of your countryman developed the AKS algorithm which is deterministic and fast. Or you can use Miller Rabin.

**In mathematics, you don't understand things. You just get used to them.**

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Three of my countrymen? Who are they?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

Manindra Agrawal, Neeraj Kayal, and Nitin Saxena

**In mathematics, you don't understand things. You just get used to them.**

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I did not know them.

I shall google it

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

Are they all three Indians?

**In mathematics, you don't understand things. You just get used to them.**

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The names sound so, but how does it matter?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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It matters in the sense that I like to differ from the rest of my kind.

**In mathematics, you don't understand things. You just get used to them.**

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Would that change the method essentially?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Change the method? I am not understanding you.

**In mathematics, you don't understand things. You just get used to them.**

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Me neither

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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The AKS proves a number is prime while the Miller Rabin tells the probability it is prime.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,796

Or we could just wait for someone to solve the P vs NP problem.

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Who will bell the cat?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

Did you have anymore questions about MIller Rabin?

**In mathematics, you don't understand things. You just get used to them.**

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