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## #1 2013-04-06 03:47:40

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,775
Website

### Miller-Rabin

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'
I'm not crazy, my mother had me tested.

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## #2 2013-04-06 03:49:04

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Miller-Rabin

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #3 2013-04-06 03:59:50

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,775
Website

### Re: Miller-Rabin

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'
I'm not crazy, my mother had me tested.

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## #4 2013-04-06 04:03:23

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Miller-Rabin

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]
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #5 2013-04-06 04:07:31

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,775
Website

### Re: Miller-Rabin

And what does this method actually rely on?

'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'
I'm not crazy, my mother had me tested.

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## #6 2013-04-06 04:11:26

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Miller-Rabin

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #7 2013-04-06 04:14:47

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,775
Website

### Re: Miller-Rabin

Mainly fermat's little theorem?
And what ensures it is strong?

'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'
I'm not crazy, my mother had me tested.

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## #8 2013-04-06 04:21:42

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Miller-Rabin

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #9 2013-04-06 04:32:09

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,775
Website

### Re: Miller-Rabin

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

'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'
I'm not crazy, my mother had me tested.

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## #10 2013-04-06 04:37:16

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Miller-Rabin

That I do not remember. I am sorry.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #11 2013-04-06 04:54:02

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,775
Website

### Re: Miller-Rabin

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

'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'
I'm not crazy, my mother had me tested.

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## #12 2013-04-06 04:58:45

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Miller-Rabin

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #13 2013-04-06 05:07:04

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,775
Website

### Re: Miller-Rabin

Three of my countrymen? Who are they?

'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'
I'm not crazy, my mother had me tested.

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## #14 2013-04-06 05:10:34

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Miller-Rabin

Manindra Agrawal, Neeraj Kayal, and Nitin Saxena

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #15 2013-04-06 05:26:47

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,775
Website

### Re: Miller-Rabin

I did not know them.

'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'
I'm not crazy, my mother had me tested.

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## #16 2013-04-06 05:33:22

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Miller-Rabin

Are they all three Indians?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #17 2013-04-06 05:45:33

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,775
Website

### Re: Miller-Rabin

The names sound so, but how does it matter?

'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'
I'm not crazy, my mother had me tested.

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## #18 2013-04-06 05:46:42

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Miller-Rabin

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #19 2013-04-06 05:54:48

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,775
Website

### Re: Miller-Rabin

Would that change the method essentially?

'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'
I'm not crazy, my mother had me tested.

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## #20 2013-04-06 05:59:57

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Miller-Rabin

Change the method? I am not understanding you.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #21 2013-04-06 06:02:07

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,775
Website

### Re: Miller-Rabin

Me neither

'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'
I'm not crazy, my mother had me tested.

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## #22 2013-04-06 06:09:18

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Miller-Rabin

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #23 2013-04-06 13:08:59

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Miller-Rabin

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

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #24 2013-04-06 15:48:29

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,775
Website

### Re: Miller-Rabin

Who will bell the cat?

'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'
I'm not crazy, my mother had me tested.

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## #25 2013-04-06 19:39:53

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Miller-Rabin

Did you have anymore questions about MIller Rabin?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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