*To*: mathgroup@smc.vnet.net*Subject*: [mg10715] Trouble Proving Primes*From*: Ersek_Ted%PAX1A@mr.nawcad.navy.mil*Date*: Fri, 30 Jan 1998 04:24:51 -0500

Try this: Open the package for ProvablePrimeQ[n] with the following line. In[1]:= <<NumberTheory`PrimeQ` Now try to use ProvablePrimeQ[n] on any of the following numbers. 25000007273 25000007507 25000009733 25000012901 25000014107 25000015493 25000018973 25000021073 You will get a string of messages that say something like; Together::modm: Modulus 25000007273 is too large for this implementation. Then the program seems to get stuck working on it forever. I let my computer work on the smallest case above for 14 hours, and never got an answer. When it does work ProvablePrimeQ[n] can prove that a Prime on the order of (10^11) is Prime in a few minutes. ProvablePrimeQ has several Options (see below). Does anyone know of a way to specify Options that will give better performance? Next suppose I want to use ProvablePrimeQ for numbers on the order of 10^20. Then how do I figure out what Option values are needed? In[12]:= Options[ProvablePrimeQ] Out[12]= {SmallPrime -> 10000000000, Certificate -> False, PrimeQMessages -> False, PollardPTest -> Automatic, PollardRhoTest -> Automatic, TrialDivisionLimit -> Automatic} Thanks, Ted Ersek