> 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.
The factoring program I used to trial-factor the 10 million plus
digit Mersenne numbers with exponents up to 36 million up to 2^40
takes only 20 _seconds_ to trial factor all 159,975 numbers to a
depth of 2^32 on a PII-350. That's including the disk I/O involved in
reading the exponents from a file & writing the results. Possible
factors were checked for +/-1 (mod 8) and screened for divisibility
by the smallest 10 primes before passing to the factoring routine,
which was called 1,267,515 times.
The slower your factoring routine is, the more sieving out of trial
factors helps the execution speed. Though there is always a cutoff
point - executing even just a Fermat test to base 2 (to determine
whether the trial factor is probably prime, with low confidence)
takes longer than the actual trial factoring (the code involved is
pretty well the same, but 2kp+1 > p).
>
> 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).
v19 has FFT sizes up to 2^22 (4 million), it should be capable of
handling exponents up to approx. 80 million. Which is more than
makes sense with current hardware.
> 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?
Sorry, but useless. Since the smallest possible factor of 2^p-1 (when
p is prime) is 2p+1, only exponents less than 2^15 can have factors
less than factors less than 2^16. We probably know almost all of the
factors of 2^p-1 for prime p < 16384 that it would be possible to
find with a TI-92, any remaining will likely have at least 15 digits.
Regards
Brian Beesley
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