PrimeQ queries
- To: mathgroup at smc.vnet.net
- Subject: [mg24213] PrimeQ queries
- From: "Greg Keogh" <greg at mira.net>
- Date: Sat, 1 Jul 2000 03:21:45 -0400 (EDT)
- Organization: Pacific Internet (Australia)
- Sender: owner-wri-mathgroup at wolfram.com
Hello from Melbourne Australia, I stumbled across some educational notebooks during the week that teach basic number theory. One of them contained this function that surprised me: primeQ[n_]:=PrimeQ[n] && n!=89*11551*37159 && n<10^15 Further down I discover that the built-in PrimeQ incorrectly reports these numbers as prime: 89*11551*37159 = 38200901201 7309*321553*2828197 = 6646915915638769 I didn't know that PrimeQ had "flaws" in it like this, or that it had an upper limit of reliability around 10^15. Could someone point me to some resources that might explain more on this matter? Some related questions: * What algorithm does Mathematica 2.2 use in PrimeQ? Has it been changed in later releases? * Can someone point me to sample code to implement the Miller-Rabin primality test with selectable numbers of witnesses? Cheers, Greg Keogh <greg at mira.net>
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