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MathGroup Archive 1998

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Trouble Proving Primes




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




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