## Re: PFGW

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• ... On this theme, I remember seeing several years ago in Mathematics of Compuation (?) where someone had computed upper limits on random integers passing a
Message 1 of 4 , May 30, 2006
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<paulunderwood@...> wrote:
>
> --- In primenumbers@yahoogroups.com, "Paul Underwood"
> <paulunderwood@> wrote:
> >
> > --- In primenumbers@yahoogroups.com, "Kermit Rose" <kermit@> wrote:
> > >
> > >
> > >
> > > How or where may I get the algorithm or source code for
> > >
> > > PFGW or proth prime number testing algorithms.
> > >
> > > I've written my own prime number testing subroutine, and do not know
> > over
> > > what range it is valid.
> > >
> > > My algorithm is :
> > >
> > > to test if z is prime,
> > >
> > > for B = 2 to 101
> > >
> > > c = mod(B^ [ ( z-1)/2 ] , z )
> > >
> > > if c = 0 return composite
> > > if c = 1 continue loop
> > > if c = -1 continue loop
> > > else return composite
> > >
> > > next B
> > >
> > > return probably prime
> > >
> >
> > The OpenPFGW source code is available here:
> > http://groups.yahoo.com/group/primeform/
> >
> > Your algorithm looks a little bit like a "strong PRP" test. There are
> > composite numbers that will pass your test.
> >
> > See:
> > http://primes.utm.edu/glossary/page.php?sort=StrongPRP
> >
> > HTH
> >
>
> Also see: http://primes.utm.edu/glossary/page.php?sort=Pseudoprime
>
> where it states: "Arnault found a 337 digit number which passed strong
> PRP tests for each of the first 200 primes [Arnault95]."
>

On this theme, I remember seeing several years ago in Mathematics of
Compuation (?) where someone had computed upper limits on random
integers passing a certaing number of prp tests (probably was
Miller-Rabin) for various bit sizes. The key point was that for
general numbers this quickly becomes *much* smaller than the 1/4
tests passed by some numbers. Does anyone know if these bounds have
been improved or extended on in recent years?

Andrew
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