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• ... 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
Message 1 of 4 , Feb 2, 2001
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On Fri, 02 February 2001, d.broadhurst@... wrote:
> C:\pfgw>pfgw -t -q10^20000+56149
> 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%

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:

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;
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• 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
Message 1 of 4 , Feb 2, 2001
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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@...

> 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
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