Hi everyone,
A few points about publishing known factors.
1) I don't see any particular need to make available files in human-
readable format, provided that we provide a specification for the
file, and also binary executables for common platforms for converting
a machine-readable file to human-readbale format. On the other hand,
it could be that "zipping" a human-readable format file provides near-
optimal compression.
2) Since factors are of the form 2kp+1, it is only neccessary to list
p & k. This saves a significant amount of storage (compared with
listing p and 2kp+1) and the proper factor is easily recovered.
3) If the data was held in variable-length records in a format
similar to
p,n,k1,k2,k3...
where n is the number of known factors and k1, k2, k3,... are the
multipliers for each of the known factors in turn, this would save
much duplication compared with the current format (of factor.txt).
4) For values of p which fit into a (integer) CPU register and
"small" values of k (up to approx. 64K), trial factoring is so fast
that I doubt it would be any faster to search a file than to repeat
the calculation - even if the file is already available locally.
Therefore I suggest that, in order to reduce substantially the size
of the frequently-updated publicly-available known factors file,
"small" values of k are omitted, and a program be provided instead to
generate the data (with binary executables for common platforms).
Perhaps the file should contain a "flag" denoting that factors are
known, but have been omitted for this reason.
We should still have a large master file somewhere, but this need not
be uploaded frequently.
5) Following on from (4), it seems to make sense to record the
highest value of k tested by trial factoring, rather than the maximum
number of bits.
6) PrimeNet trial factoring has moved well into the 10 millions,
however George's factor.zip file contains data only up to 10 million.
I know there is a problem with uploading the large files concerned;
hopefully, the suggestions above will help to reduce the size of the
file, sufficiently to make it feasible to expand the exponent range
to cover (at least) the active Primenet assignments for long enough
for cheap, high-speed Internet connectivity to become widespread.
7) I have several hundred megabytes of disk space available on my ftp
server, which has reasonable Internet access - at least 8 Mbps
connectivity to the Internet core - and would be happy to provide
means for anyone interested to upload factoring data (or anything
else, strictly relevant to Mersenne or closely-related numbers) for
the purpose of making it publicly available.
Regards
Brian Beesley
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