The early days of trial factoring .....

[bayanne]

At the moment all factoring (as given out by PrimeNet) is at a minimum of 57 bit.

However at what level of starting bit depth did these exponents used to be handed out?

Was much factoring done before the days of PrimeNet?

How would I find out the starting bit depth of exponents going back some number of years?

I am trying to set up a stats page and it would help me immensely if there was a way of finding out this information.

[cheesehead]

You could probably find some answers in the early postings to the Mersenne mailing list. There was discussion of trial factoring right from the beginning.

I can send you zip files of any you want, all the way back to the start on April 21, 1996. Mersenne Digest number 1 came out July 8, 1996, but the mailing list started on April 21 and I have the pre-Digest postings (109KB zipped) as well as all the Digests. PM me your e-addr if interested.

[Mr. P-1]

Originally Posted by cheesehead

You could probably find some answers in the early postings to the Mersenne mailing list. There was discussion of trial factoring right from the beginning.

I can send you zip files of any you want, all the way back to the start on April 21, 1996. Mersenne Digest number 1 came out July 8, 1996, but the mailing list started on April 21 and I have the pre-Digest postings (109KB zipped) as well as all the Digests. PM me your e-addr if interested.

I would appreciate this too. Thanks

Regards

Daran - daranSPAMg@lineone.net

[edit - munged addy - this was meant to be an instant message. ops: ]

[bayanne]

It would seem that in years gone by, the starting bit was 53 bit, but I don't know when this started being used, or when it was changed to a higher level. There is nothing I have specifically found in the archives which helps. The only way perhaps would be if someone had the source code for a really old version.

[cheesehead]

Originally Posted by bayanne

At the moment all factoring (as given out by PrimeNet) is at a minimum of 57 bit.

... because people, especially the Lone Mersenne Hunters (see their forum), have put a lot of work into trial-factoring all exponents in the GIMPS range up to that level. It was fairly recently that the LMH finished bringing all TF up to 2^57, and maybe a year earlier they had completed all to 2^56.

However at what level of starting bit depth did these exponents used to be handed out?

Whatever bit depth to which the exponent had previously been trial-factored, whether by GIMPS or by others (and reported to GIMPS), as recorded in file nofactor.cmp. :)

Part of the early GIMPS work was collecting and combining data bases of work that had previously been done. However, it's important to note that even with a now-modest 90MHz Pentium (what George had when he started the project), it was quite feasible to simply TF all the way up to limits in the 2^40s in a relatively short time, without bothering to skip what anyone had done before. (And that may be exactly what he did.) TFing to 2^40 on even a small exponent is pretty fast, almost instantaneous on larger ones.

Was much factoring done before the days of PrimeNet?

Depends on your definition of "much". The total time devoted to trial factoring by all efforts before PrimeNet may have been a noticeable fraction of what has been done since then, but one needs also to take into account the increases in average speed of the CPUs doing the work. TFing to 2^56 on a 1000 MHz machine now takes about as long as TFing to 2^49 did when the speed was 8-10 Mhz (disregarding differences in TFing efficiency between 386s and Pentia).

How would I find out the starting bit depth of exponents going back some number of years?

At http://home.planet.nl/~tha/mersenne/index.html are graphs of the status of trial-factoring depth since early 2001. Looking at the oldest graph, from 3/6/2001, at http://home.planet.nl/~tha/mersenne/...ew20010306.gif, we see that there were then a few exponents that had been trial-factored to only 2^50. More had been TFed to only 2^52, 2^53, 2^54, or 2^55.

It would seem that in years gone by, the starting bit was 53 bit, but I don't know when this started being used, or when it was changed to a higher level. There is nothing I have specifically found in the archives which helps. The only way perhaps would be if someone had the source code for a really old version.

Keep in mind that you will not find any starting bit level coded into Prime95. The starting bit level is specified for each exponent in the worktodo.ini file, and Prime95 simply accepts that value then continues from there.

What you will find coded in Prime95 are the default endiing bit levels for each range of exponent. There have been minor changes in those default ending levels, but I think all of them are still within 1 bit of what they were in the first version of Prime95.