[EMAIL PROTECTED] writes:
Using the wonderful modpwr() from Paul Pollack's NTH library for
the TI-92, I have quickly verified the following results I found on
Entropia.com: [...]
Good.:)
For each of them, the TI-92 quickly returned that 2^exponent mod
factor = 1, and very quickly too (yay!). A calculator factoring
program is a real possibility. I'll get to work coding a
"front-end" right away. However, I think I recently read that some
people had their computers race ahead and factor large exponents
(like 25million) up to some small number, like 2^40. Have those
results been posted anywhere? If this TI-92 program is distributed
far and wide, repeating already-done work would be a waste. Thanks.
I have that data, including some that Brian Beesley just sent me, but
I do not have enough space on the web to store it. I do, however,
create an pre-Primenet DATABASE file that contains enough data to
support this kind of effort: finding new first factors of prime
exponent Mersennes. It is the DATABASE file in:
http://www.garlic.com/~wedgingt/mersdata.tgz
mersdata.zip
The extract program of the mers package can print DATABASE files in a
simple human readable format; grab mers.tgz or mers.tar.gz as well to
get extract.c.
I have just updated my web pages, including this DATABASE file, so it
now includes the new data from Brian on prime exponent Mersenne
numbers with just over 10 million digits.
[EMAIL PROTECTED] writes:
I hacked up a quick TI-92 factoring program. It is slower than I
wanted. :-( It's "testing" 2^25,000,009 - 1 right now. It can test
one factor every 1.3 seconds. AUGH! At that rate it would take 95
*billion* years to trial divide by all odd numbers under
2^62. Noooo.
Hm. Are you forgetting that factors of prime exponent Mersennes must
be 1 or 7 mod 8 and 2*k*p + 1 where p is the prime exponent? And the
Prime95 and mersfac* programs also do some sieving of the possible
factors, so they don't try ones that themselves have small factors.
However, a semi-reasonable task would be to test numbers for
factors up to 2^16. Pitiful, I know, but a TI could test a single
number in 12 hours (running constantly - hah, no multitasking
here).
If it really is that bad, then it's probably not worth doing. I once
tested all the prime exponent Mersennes with exponents from about 10
million thru about 21 million for factors smaller than 2^33 or so,
using mersfacgmp on a Pentium 90MHz, in a couple of days.
A) Where would the numbers start that haven't been factored at ALL,
to ANY extent?
There are some prime exponents in this category between 21.5 and 22
million, but not many. And, now that I have more disk space, I'm
likely to "cure" this sometime soon, by factoring to 2^33 or more all
the way past the next likely GIMPS limit (exponents less than 41
million).
B) To Mr. Woltman or Mr. Kurowski - how "useful" would factoring
(most likely very large) exponents to only 2^16 be? Or have "real"
computers already quickly scanned very high for such small factors?
Actually, I believe that George and Scott are not concerned with the
larger exponents (above the current GIMPS limit near 20.5 million).
Certainly, George has known for a long time that I have some data for
larger exponents and hasn't asked for it yet.
Will
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