The plural of "guess" is not "fact"
 

[QUOTE=GP2;467922]also [URL="http://www.mersenneforum.org/showthread.php?t=19014&p=461679"]user TJAOI has covered everything up to 64 bits[/URL].[/QUOTE]It is my understanding that we don't know this for certain. It is merely an assumption that people seem to take as a known truth.

[QUOTE=retina;467936]It is my understanding that we don't know this for certain. It is merely an assumption that people seem to take as a known truth.[/QUOTE]

It's no different than trusting all the other "no factor" TF results.

[QUOTE=Mark Rose;467963]It's no different than trusting all the other "no factor" TF results.[/QUOTE]Maybe. But there is a difference in that we can audit results from users doing TF to compare the expected vs discovered factors. It isn't a perfect test of course. However, there is no equivalent test we can apply to the results from TJAOI.

[QUOTE=retina;467964]Maybe. But there is a difference in that we can audit results from users doing TF to compare the expected vs discovered factors. It isn't a perfect test of course. However, there is no equivalent test we can apply to the results from TJAOI.[/QUOTE]

See [URL="http://www.mersenneforum.org/showthread.php?p=467989"]my post in the "User TJAOI" thread[/URL], where I look at the datestamps for factor discoveries in the PrimeNet database to check how systematic TJAOI's searches are.

Spoiler: from the empirical evidence, it is very systematic. Apart from one glitch almost three years ago, which was quickly fixed, it is indeed true that when TJAOI finishes with a given bit-size range, no new factors of that bit size are ever discovered, by him or by anyone else.

Doing TF for 64-bits or smaller will not find any new factors. Even 65 bits would probably just be a duplication of effort, since we can expect TJAOI to systematically complete that range sometime in 2018.

Here is a graph of the number of factored exponents (at least 1 factor) since November 2008 based on the summary files.

[URL="http://hoegge.dk/mersenne/factored.png"]factored.png[/URL]

The top of the chart 30,850,000 is roughly at 20M unfactored exponents (19,997,534).

Unfortunately the slope has gone down during 2017, the averate rate in the last 6 months is 436 exponents per day, which will give 10.1 years to reach 20M unfactored exponents.

Number of newly factored exponents per day, average over 30 days:

[URL="http://hoegge.dk/mersenne/factoredspeed.png"]factoredspeed.png[/URL]

Yeah I know its a long way away....but I think it will be done before all exponents are tested up to 100M ... or before we find our find a 100M digit prime.

I just find it interesting to watch.
And if I can knock off a couple dozen ranges over the next year it will be fun.

TeeHeeHee

And thanks for the data.

Oct 15, 2017 Update; 1 month later
 

643 more exponents factored in the ranges of interest....0 - 59.9M
(In ranges where there are still more than 1,999 unfactored.

2 more ranges cleared (now below 2,000): 48.9M and 49.1M

November 16, 2017 - 1 month later
 

800 more exponents factored in the ranges of interest....0 - 59.9M
(In ranges where there are still more than 1,999 unfactored.

2 more ranges cleared (now below 2,000): 46.1M and 49.9M

100 days...100 factors for me.
 

...

December 17,2017 - Monthly Update
 

841 more exponents factored in the ranges of interest....0 - 59.9M
(In ranges where there are still more than 1,999 unfactored.

6 more ranges cleared (now below 2,000): 1.8M, 2.1M, 45.4M, 47.0M, 47.6M and 48.0M