[QUOTE=GP2;467989]How systematic is TJAOI? Let's try to answer that question.
.....
We conclude that TJAOI's methodology is indeed systematic, and trial-factoring for ranges below 65 bits will almost certainly be completely fruitless. We might expect TJAOI to complete the 65-bit range sometime in 2018.[/QUOTE]
This is a welcome analysis, given how much discussion on this forum TJAOI's work stimulates. I don't quite understand the dating differences, but my overall impression is that TJAOI is doing valid work in their chosen pursuit.

[QUOTE=Mark Rose;467995]What is the lowest exponent for which TJAOI found a factor?[/QUOTE]

40151 for ECM

57653 for TF???

[QUOTE=kladner;468003]I don't quite understand the dating differences,[/QUOTE]

The question examined was:

Each time the people who follow TJAOI's activity (like alpertron) posted a message to say that he had finished a given bit range, was that bit range truly finished? Or did TJAOI ever miss some factors?

To answer it, we look at the date someone posted "TJAOI finished this bit range" versus the date that the last factor in that bit range was actually reported to PrimeNet. That's the date difference.

The answer is, yes, each time TJAOI finished a bit range, that bit range was indeed finished, and no additional factors in that range have ever been discovered, except for a couple of stragglers just a few days later, and one actual glitch three years ago where he did miss a handful of factors (eight in total), which TJAOI promptly fixed a couple of days after someone else found one of the missed factors.

[QUOTE=Prime95;468005]40151 for ECM

57653 for TF???[/QUOTE]

Note that if you manually report "Mnnnnnnn has a factor: xxxxxxxxxxx", with no further information in parentheses about B1 and B2 or TF, then the server assumes you used ECM with ridiculously low B1 and awards you 0.0000 GHz-days credit.

So some of his "ECM" discoveries might not actually involve ECM. His factoring for [M]M40151[/M] was reported as running only one ECM curve, so that might be the case here.

[QUOTE=GP2;468007]So some of his "ECM" discoveries might not actually involve ECM. His factoring for [M]M40151[/M] was reported as running only one ECM curve, so that might be the case here.[/QUOTE]
But at 74 bits, TF is unlikely. P-1 with a B2 bound of 20.4e9 is sufficient (doable with GMP-ECM), but child's play for ECM.

[QUOTE=GP2;468006]The question examined was:

Each time the people who follow TJAOI's activity (like alpertron) posted a message to say that he had finished a given bit range, was that bit range truly finished? Or did TJAOI ever miss some factors?

To answer it, we look at the date someone posted "TJAOI finished this bit range" versus the date that the last factor in that bit range was actually reported to PrimeNet. That's the date difference.

The answer is, yes, each time TJAOI finished a bit range, that bit range was indeed finished, and no additional factors in that range have ever been discovered, except for a couple of stragglers just a few days later, and one actual glitch three years ago where he did miss a handful of factors (eight in total), which TJAOI promptly fixed a couple of days after someone else found one of the missed factors.[/QUOTE]
Thanks for all of your educational efforts, as well as for your patience with previously-answered questions. That is, I read your original post, and didn't really try to sort out what was clearly there. :redface:

[QUOTE=GP2;467989]
[B]44[/B] 2014-01-10
[B]45[/B] 2014-01-13
[B]46[/B] 2014-01-31
[B]47[/B] 2014-02-21
[B]48[/B] 2014-03-21
[B]49[/B] 2014-10-06 (actually 2014-04-17 for all but one factor)
[B]50[/B] 2014-10-06 "[URL="http://www.mersenneforum.org/showthread.php?t=19014&p=373637"]2014-05-16[/URL]"
[B]51[/B] 2014-06-13
[B]52[/B] 2014-07-18 "[URL="http://www.mersenneforum.org/showthread.php?t=19014&p=378875"]2014-07-18[/URL]"
[B]53[/B] 2014-08-31 "[URL="http://www.mersenneforum.org/showthread.php?t=19014&p=381803"]2014-08-31[/URL]"
[B]54[/B] 2014-10-26 "[URL="http://www.mersenneforum.org/showthread.php?t=19014&p=386171"]2014-10-26[/URL]"
[B]55[/B] 2014-12-30 "[URL="http://www.mersenneforum.org/showthread.php?t=19014&p=391247"]2014-12-30[/URL]"
[B]56[/B] 2015-02-27
[B]57[/B] 2015-05-15 "[URL="http://www.mersenneforum.org/showthread.php?t=19014&p=402532"]2015-05-18[/URL]"
[B]58[/B] 2015-07-31 "[URL="http://www.mersenneforum.org/showthread.php?t=19014&p=407169"]2015-08-03[/URL]"
[B]59[/B] 2015-10-19 "[URL="http://www.mersenneforum.org/showthread.php?t=19014&p=412849"]2015-10-16[/URL]"
[B]60[/B] 2015-12-30 "[URL="http://www.mersenneforum.org/showthread.php?t=19014&p=420515"]2015-12-30[/URL]"
[B]61[/B] 2016-03-22 "[URL="http://www.mersenneforum.org/showthread.php?t=19014&p=429782"]2016-03-22[/URL]"
[B]62[/B] 2016-06-18 "[URL="http://www.mersenneforum.org/showthread.php?t=19014&p=436527"]2016-06-18[/URL]"
[B]63[/B] 2016-11-28 "[URL="http://www.mersenneforum.org/showthread.php?t=19014&p=447614"]2016-11-23[/URL]"
[B]64[/B] 2017-06-21 "[URL="http://www.mersenneforum.org/showthread.php?t=19014&p=461679"]2017-06-21[/URL]"
[/QUOTE]
It would be interesting to complete the table with the number of factors found by TJAOI and the number of factors found by anyone else by number of bits of the exponent.

I parsed all the xml archive files up to 2016-12-31 looking for factors found trial factoring only and by TJAOI and by others:

Edit: I found the links for the daily xml backup files as well, so I updated this up tuesday 2017-09-18:

[CODE]
bits others TJAOI
20 107
21 179
22 314
23 600
24 1023
25 1742
26 3250
27 5669
28 10116
29 15009
30 21111
31 24320
32 27686
33 32799
34 49933
35 60500
36 72539
37 75321
38 79739
39 83286 38
40 85335 453
41 82472 6565
42 71417 18833
43 88730 38012
44 58400 71809
45 55532 74795
46 52157 77168
47 46026 82727
48 41114 92413
49 34667 97976
50 22799 120260
51 25912 149602
52 26584 222679
53 16828 364121
54 22091 412441
55 24264 412382
56 21388 414466
57 22059 415806
58 24597 416440
59 23404 417641
60 23026 415455
61 46037 414538
62 150335 413400
63 267814 420124
64 315365 150059
65 352070
66 341299
67 328409
68 211655 2
69 158534 4
70 60280
71 43971 3
72 18412
73 12205
74 7501
75 3041
76 1913
77 1732
78 1336
79 1085
80 927
[/CODE]

Thanks for this effort.

Could you please prepare another table including factors found by ECM, P-1 and trial factor and the sum of them for each bit range?

[QUOTE=ATH;468161]I parsed all the xml archive files up to 2016-12-31 looking for factors found trial factoring only and by TJAOI and by others:
[/QUOTE]

How hard would it be to note how many "FIRST" factors he found?

[QUOTE=ATH;468161]
[CODE]
bits others TJAOI
....
60 23026 415455
61 46037 414538
62 150335 413400
63 267814 420124
64 315365 150059
65 352070
66 341299
...
[/CODE][/QUOTE]
Are you sure that these numbers are OK? TJAOI finished finding 64-bit prime factors and is now finding 65-bit prime factors. Another problem that I see is that there are lot more 63-bit prime factors found than 64-bit prime factors or 62-bit prime factors, when I expect that the number of factors should not decrease.