--- In

primeform@yahoogroups.com, "paulunderwooduk" <paulunderwood@...> wrote:

>

>

>

> --- In primeform@yahoogroups.com, "djbroadhurst" <d.broadhurst@> wrote:

> >

> > --- In primeform@yahoogroups.com,

> > "djbroadhurst" <d.broadhurst@> wrote:

> >

> > > I imagine that other such easily found PRPs at

> > > http://donovanjohnson.com/lucas.html

> > > will soon yield to fervent users of Primo.

> >

> > As predicted, Bernardo has promoted Donovan's PRP to a prime:

> > http://primes.utm.edu/primes/page.php?id=103784

> >

> > The next one on Donovan's list is

> > http://donovanjohnson.com/lucas.html

> > > V(39769)/(2863369*6334883549)

> >

>

> I find it hard to believe that all the larger numbers given on:

> http://donovanjohnson.com/lucas.html

> http://donovanjohnson.com/fibonacci.html

> were tested with "a Miller-Rabin primality test in 10 randomly chosen bases (ispseudoprime test in PARI/GP)." It must have taken a long time,

>

I ran some tests on the biggest of the numbers with a 2.4Ghz core2:

$ time echo "ispseudoprime(fibonacci(348307)/(1393229*14759160817),1)" | gp -q

1

real 56m44.939s

user 56m41.673s

sys 0m1.692s

Next my own 2-selfridge algorithm ( which is currently verified for n<6.2*10^11), which is stored in my .bashrc file and pipes into gp -q:

$ time S1 fibonacci\(348307\)/\(1393229*14759160817\)

LIKELYprime

real 114m9.782s

user 112m59.832s

sys 0m6.720s

Then I ran some PFGW tests:

$ time ./pfgw64 -q"F(348307)/(1393229*14759160817)"

PFGW Version 3.4.4.64BIT.20101104.x86_Dev [GWNUM 26.4]

F(348307)/(1393229*14759160817) is 3-PRP! (544.9254s+0.0110s) 1/28.00

real 9m4.948s

user 6m56.506s

sys 0m0.100s

$ time ./pfgw64 -tp -q"F(348307)/(1393229*14759160817)"

PFGW Version 3.4.4.64BIT.20101104.x86_Dev [GWNUM 26.4]

Primality testing F(348307)/(1393229*14759160817) [N+1, Brillhart-Lehmer-Selfridge]

Running N+1 test using discriminant 7, base 7+sqrt(7)

Calling Brillhart-Lehmer-Selfridge with factored part 0.01%

F(348307)/(1393229*14759160817) is Lucas PRP! (2034.5473s+0.0111s)

real 33m54.567s

user 25m4.678s

sys 0m2.004s

$ time ./pfgw64 -tc -q"F(348307)/(1393229*14759160817)"

PFGW Version 3.4.4.64BIT.20101104.x86_Dev [GWNUM 26.4]

Primality testing F(348307)/(1393229*14759160817) [N-1/N+1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 7

Running N+1 test using discriminant 23, base 3+sqrt(23)

Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.04% proof)

F(348307)/(1393229*14759160817) is Fermat and Lucas PRP! (2702.0909s+0.0114s)

real 45m2.111s

user 32m20.409s

sys 0m3.904s

So if my 2-selfridge algorithm was implemented in PFGW it would take ~14 minutes for this number,

Paul