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 bitsize range, no new factors of that bit size are ever discovered, by him or by anyone else. Doing TF for 64bits 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 
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