E. Mayer writes:
---
Will Edgington wrote:
>>>
M( 27471827 )G: 288230414480354201 576460748539783185
M( 27471827 )J: 576460748539783185 576460790500150601
The G lines represent these gaps.
<<<
I tested M27471827 to 2^64 using my Mfactor code, with no factor found,
so at least in that case you can replace the multiple factoring-data
lines in your database with the single one:
M( 27471827 )U: 18446744073709551616
---
Actually, this is not enough. My data already included:
M( 27471827 )U: 576460790500150601
G lines ignore U and H lines precisely because they represent gaps in
known trial factoring data. Only J lines "close" gaps and, so far as
I'm aware, only the mersfac* (e.g., mersfacgmp) programs from the mers
package that I maintain know about G and J data.
The other issue is that many (most?) of the exponents with gaps also
have known factors, which means Prime95 cannot be used to close those
gaps since it stops on finding a factor and does not search in numeric
order. This last means that it actually _creates_ gaps when it finds
a factor. I don't seem to have a copy of Mfactor, so I can't check
whether it has similar issues.
(I also tested M32091881 to 65 bits, again with no factor found.)
But it does sound like I can close any gaps related to these two
exponents, since no factors were found.
Will, if you want to start a systematic effort to start closing
gaps in factoring data, I suggest calling for volunteers over at
mersenneforum.org (where most of us hang out these days). Given that
factoring M27471827 to 2^64 takes about an hour on decent 64-bit
hardware (AMD64,Alpha, Itanium), a couple dozen volunteers with such
machinery could get some serious work done.
Actually, I've already got a systematic effort going, it's just that
I'm the only participant ... except for one volunteer who emailed me
directly in response to this same message of mine. As I explained to
him, I already have a server and some Perl scripts that know how to
get work from and report results back to it, but the server,
especially, is simply not ready for public use yet. So, this time, I
just emailed him some of the "biggest" gaps his program can deal with.
And note that many of the gaps are for smaller exponents than those
currently of interest to GIMPS, which means they take more effort, not
less, to close than do gaps of the same numeric size (stop minus
start) for larger exponents.
As for using the forums, I just never seem to get around to them; for
me, email has always been much more useful and easier to use.
Will
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