- I wrote:

> Chris Caldwell has to screen out such PrP impostors.

To save others a waste of time probing Milton Brown's false

claim (viz p37) of a proof by PrimeForm, here is how far

it is from BLS, according to PFGW:

C:\pfgw>pfgw -t -q10^20000+56149

PFGW Windows Release Version 20001129.6 (c) 1998-2000,

The OpenPFGW project.

Primality testing 10^20000+56149 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 2

Calling Brillhart-Lehmer-Selfridge with factored part 0.04%

10^20000+56149 is PRP! (177.250000 seconds)

C:\pfgw>pfgw -tp -q10^20000+56149

PFGW Windows Release Version 20001129.6 (c) 1998-2000,

The OpenPFGW project.

Primality testing 10^20000+56149 [N+1, Brillhart-Lehmer-Selfridge]

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

Running N+1 test using discriminant 3, base 4+sqrt(3)

Running N+1 test using discriminant 3, base 9+sqrt(3)

Running N+1 test using discriminant 3, base 11+sqrt(3)

Calling Brillhart-Lehmer-Selfridge with factored part 0.05%

10^20000+56149 is Lucas PRP! (2554.370000 seconds)

[Interesting how long it took to find a Lucas test.

Timing on an 900 Mhz Athlon.]

On the bright side, it's notable that not a single

other person in the world seems to cheat in this game,

as far as I know. We make mistakes; but we don't

wilfully misrepresent our findings. Consensual honesty

is taken for granted here, though it may be rare

in other circles.

Of course, it could just be that Milton merely forgot all

our advice, as he may have done when submitting a previous

rogue PrP in 3 succesive weeks.

If so, my apology for cynicism will follow his for amnesia.

David - On Fri, 02 February 2001, d.broadhurst@... wrote:
> C:\pfgw>pfgw -t -q10^20000+56149

In order to try to extract some pearls from the swine's ear (*) I pose a little pre-weekend teaser, which probably has been asked and answered before, but I've never seen the answered:

> Calling Brillhart-Lehmer-Selfridge with factored part 0.04%

> C:\pfgw>pfgw -tp -q10^20000+56149

> Calling Brillhart-Lehmer-Selfridge with factored part 0.05%

1) For _totally_ arbitrary number A of size log(A) digits,

what is the expected factorisation ratio if wheel factorisation is tried to F, where F << A?

2) If instead of arbitrary numbers we take 'primorially doped' numbers which cannot have any factors less than or equal to P, where P << F. This can include P=2 - i.e the odd numbers!

3) If instead of arbitrary numbers we take numbers which we know can have factors only of the form 2xk+1 for some fixed k?

All of the above look as if they should crack given the right brain with the right insight. However presently I have neither!

Phil

(* I make no apologies for my abuse of metaphors)

(PS. log=base 10, << = much less than)

Mathematics should not have to involve martyrdom;

Support Eric Weisstein, see http://mathworld.wolfram.com

Find the best deals on the web at AltaVista Shopping!

http://www.shopping.altavista.com - The retoric seems a little strong here.

I am sure you did not mean to accuse me

of being dishonest, as your message implies.

But, I do appreciate helpful suggestions,

as you have done in the past.

Milton L. Brown

miltbrown@...

d.broadhurst@... wrote:

> I wrote:

>

> > Chris Caldwell has to screen out such PrP impostors.

>

> To save others a waste of time probing Milton Brown's false

> claim (viz p37) of a proof by PrimeForm, here is how far

> it is from BLS, according to PFGW:

>

> C:\pfgw>pfgw -t -q10^20000+56149

> PFGW Windows Release Version 20001129.6 (c) 1998-2000,

> The OpenPFGW project.

> Primality testing 10^20000+56149 [N-1, Brillhart-Lehmer-Selfridge]

> Running N-1 test using base 2

> Calling Brillhart-Lehmer-Selfridge with factored part 0.04%

> 10^20000+56149 is PRP! (177.250000 seconds)

>

> C:\pfgw>pfgw -tp -q10^20000+56149

> PFGW Windows Release Version 20001129.6 (c) 1998-2000,

> The OpenPFGW project.

> Primality testing 10^20000+56149 [N+1, Brillhart-Lehmer-Selfridge]

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

> Running N+1 test using discriminant 3, base 4+sqrt(3)

> Running N+1 test using discriminant 3, base 9+sqrt(3)

> Running N+1 test using discriminant 3, base 11+sqrt(3)

> Calling Brillhart-Lehmer-Selfridge with factored part 0.05%

> 10^20000+56149 is Lucas PRP! (2554.370000 seconds)

>

> [Interesting how long it took to find a Lucas test.

> Timing on an 900 Mhz Athlon.]

>

> On the bright side, it's notable that not a single

> other person in the world seems to cheat in this game,

> as far as I know. We make mistakes; but we don't

> wilfully misrepresent our findings. Consensual honesty

> is taken for granted here, though it may be rare

> in other circles.

>

> Of course, it could just be that Milton merely forgot all

> our advice, as he may have done when submitting a previous

> rogue PrP in 3 succesive weeks.

>

> If so, my apology for cynicism will follow his for amnesia.

>

> David

>

>

>

> Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com

> The Prime Pages : http://www.primepages.org