## Re: certification of a prime gap

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• Jose Luis Gomez Pardo wrote ... The snappy pace of 8342 bits in 66 hours (1GHz Athlon) in http://groups.yahoo.com/group/primenumbers/message/2259 is about as
Message 1 of 12 , Aug 31, 2001
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Jose Luis Gomez Pardo wrote

> I realize now that the certification of the top and
> bottom requires much more work than what I had assumed

The snappy pace of 8342 bits in 66 hours (1GHz Athlon) in

is about as fast as ECPP gets, to date.

I reckon that the median Primo time (same machine) is
about half a week at 8000 bits. One week, or even two,
might be required if Run 3 appears, and/or there is need of
significant backtracking after discriminant exhaustion.

I wonder what Hans and Giovanni are doing right now?
5k decimal digits by someone, in time for Christmas?

In my bones I feel that, *within operational limits*,
Primo scales more like digts^4 than the asymptotic
estimate digits^6. If 2.5k digits takes half a week,
5k digits might take only only 2 or 3 months,
on a wing and a prayer...

David
• David Broadhurst wrote: [Snip] ... Some less digits from me and some more digits from Giovanni (and from someone else) seem to be likely before Christmas :)
Message 2 of 12 , Sep 1, 2001
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[Snip]
> I wonder what Hans and Giovanni are doing right now?
> 5k decimal digits by someone, in time for Christmas?

Some less digits from me and some more digits from Giovanni
(and from someone else) seem to be likely before Christmas :)

> In my bones I feel that, *within operational limits*,
> Primo scales more like digts^4 than the asymptotic
> estimate digits^6. If 2.5k digits takes half a week,
> 5k digits might take only only 2 or 3 months,
> on a wing and a prayer...

In my bones I'm feeling the same, but too much depends on the
*individual* number being tested. You'll know what a certain
5k-+ number takes to be proven prime with Tx/Po on a certain
PC using certain methods this year, that's for sure.

Hans

PS: I indeed don't know what Giovanni is testing at present,
I only know what I am working on with Primo.
• On Thu, 30 Aug 2001 21:30:16 -0400, Nathan Russell ... Now finished. cert_val quick-check passed, though i didn t clean out all the headers and didn t change
Message 3 of 12 , Sep 12, 2001
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On Thu, 30 Aug 2001 21:30:16 -0400, Nathan Russell
<nrussell@...> wrote:

>On Thu, 30 Aug 2001 18:35:11 -0000, d.broadhurst@... wrote:
>
>>of the top and bottom PrPs for his gap.
>>My experience is that a 8000 bit PrP takes
>>between 3 and 4 days to certify, running
>>Primo on a 1GHz Athlon, if the chain of elliptic
>>curves never hits "Run 3". So with a bit of luck
>>Jose Luis' gap could be certified in a week.
>>I have no spare machine, at present, but I think
>>that someone here surely has! (Greg?)
>>The top and bottom would then be archivable as
>>ECPP primes, for a while.
>>David
>
>I will do the bottom prime of this gap, devoting my P3-600 with Win98
>and 384 MB of 133 MHz memory completely to it until it is finished.

Now finished.

cert_val \quick-check passed, though i didn't clean out all the
headers and didn't change any test numbers. I don't know if that's
important to anyone...

I'm running a full cert_val now, and I'll send out the certificate (in
compressed form, of course) to Jose and anyone else who expresses an
interest after that passes. It's about 2/3 of a megabyte.

Nathan
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