does this affect us?

crash893 · 2002-11-05, 00:12

http://www.cse.iitk.ac.in/users/manindra/index.html

i found this at a diffent forums

im really not too math inclined so if some one could break it up into newb for me that would really help

thanks

ewmayer · 2002-11-05, 01:26

The short answer is: no.

There is some discussion and links in the Math thread titled

AKS - A polynomial-time algorithm for testing primality.

The main significance of the AKS algorithm is that it is the first *provably*
polynomial-time scheme for proving primality (or not) of any desired number.
That doesn't mean it's necessarily faster in practice than schemes such
as ECPP, which are polynomial time for nearly all inputs (and many such schemes
are in fact polynomial time for ALL inputs if the Extended Riemann Hypothesis
is true - it probably is, but AKS doesn't need it to be). And for numbers of
special form (e.g. Mersennes, Fermats, Proths, etc.) there are well-known
deterministic primality tests that are not only polynomial time, but also
much faster than AKS, ECPP, etc. So don't expect to replace Prime95 with
anything else just yet. :)

Cheers,
-Ernst

Deamiter · 2002-11-05, 02:26

if that didn't make any sense to you, just think that there are very fast ways that 'special' numbers like mersennes can be checked. The downside is that you can ONLY find mersenne numbers (or other similar numbers) with this special algorithm, but you can still find larger numbers faster.

This new way is an algorithm that'll find if ANY number is prime, but while it's faster than checking all the primes less than the Square Root of the number in question, it's not nearly as fast as P95 at checking mersenne numbers in the special form (2^k)-1.

2002-11-05, 00:12	#1
crash893 Sep 2002 2³×37 Posts	does this affect us? http://www.cse.iitk.ac.in/users/manindra/index.html i found this at a diffent forums im really not too math inclined so if some one could break it up into newb for me that would really help thanks

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2002-11-05, 01:26	#2
ewmayer ∂²ω=0 Sep 2002 República de California 2DDB₁₆ Posts	The short answer is: no. There is some discussion and links in the Math thread titled AKS - A polynomial-time algorithm for testing primality. The main significance of the AKS algorithm is that it is the first provably polynomial-time scheme for proving primality (or not) of any desired number. That doesn't mean it's necessarily faster in practice than schemes such as ECPP, which are polynomial time for nearly all inputs (and many such schemes are in fact polynomial time for ALL inputs if the Extended Riemann Hypothesis is true - it probably is, but AKS doesn't need it to be). And for numbers of special form (e.g. Mersennes, Fermats, Proths, etc.) there are well-known deterministic primality tests that are not only polynomial time, but also much faster than AKS, ECPP, etc. So don't expect to replace Prime95 with anything else just yet. :) Cheers, -Ernst

2002-11-05, 02:26	#3
Deamiter Sep 2002 75₁₆ Posts	if that didn't make any sense to you, just think that there are very fast ways that 'special' numbers like mersennes can be checked. The downside is that you can ONLY find mersenne numbers (or other similar numbers) with this special algorithm, but you can still find larger numbers faster. This new way is an algorithm that'll find if ANY number is prime, but while it's faster than checking all the primes less than the Square Root of the number in question, it's not nearly as fast as P95 at checking mersenne numbers in the special form (2^k)-1.