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mod function and AKS paper

• To: mathgroup at smc.vnet.net
• Subject: [mg65368] mod function and AKS paper
• From: "Kai Gauer" <kai.g.gauer at gmail.com>
• Date: Tue, 28 Mar 2006 04:05:53 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

The celebrated "Primes is in P" paper (
http://www.cse.iitk.ac.in/users/manindra/primality_v6.pdf ) seems to
call in a special-purpose version of mod at its formula (2) on page 2
(notice the 2 arguments). Is this similar to the call of the
Mathematica version of Mod or PowerMod? If not, is there a way that I
can write mod in terms of some Mathematica calls?

Of course, I may also have not read the paper carefully enough to find
this version of the mod definition. The remaining portion of the
algorithm's notation on page 3 seems to make sense.

Also, I've since heard that there are better guesses for the bounds,
being ~ O[(ln^(6+epsilon)) p] and ~O[(ln^(4+epsilon)) p], the latter
having a small probability of ambiguous return (
http://mathworld.wolfram.com/AKSPrimalityTest.html ). Which tricks in
the code would one change to apply the quicker bounds of AKS-test?
Apologies if this has been asked and answered in a previous thread.

Thanks,
Kai G. Gauer