[QUOTE=alpertron;468274]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.[/QUOTE]

Maybe I defined them differently in my parsing program. What I call 64 bit factors are between 2^64 and 2^65, so 64.xxx bits.


[QUOTE=petrw1;468271]How hard would it be to note how many "FIRST" factors he found?[/QUOTE]

You mean factors for exponents with no known previous factors?

[QUOTE=ATH;468277]Maybe I defined them differently in my parsing program. What I call 64 bit factors are between 2^64 and 2^65, so 64.xxx bits.[/QUOTE]

except that 2^0 doesn't have 0 bits it has 1 bit. in fact generally 2^n has n+1 bits.

[QUOTE=ATH;468277]Maybe I defined them differently in my parsing program. What I call 64 bit factors are between 2^64 and 2^65, so 64.xxx bits.




You mean factors for exponents with no known previous factors?[/QUOTE]

Yes

[QUOTE=alpertron;468274]Are you sure that these numbers are OK? TJAOI finished finding 64-bit prime factors and is now finding 65-bit prime factors.[/QUOTE]

There's a simple explanation:

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

So he used archived data that doesn't include 2017 results, such as the completion of the 64-bit range as of June 2017.

[QUOTE] 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.[/QUOTE]

It's normal that there are fewer 64-bit prime factors shown, since this doesn't include 2017 results, as mentioned above.

Regarding the decreasing numbers of 62-bit, 61-bit, 60-bit, etc. factors, remember that this data comes from XML archives, which shows factors reported to [STRIKE]PrimeNet[/STRIKE] GIMPS. For some of the smaller-sized factors, [STRIKE]they may have been found in the early days of GIMPS, or[/STRIKE] they may have been found historically by other researchers before GIMPS started. So the XML archive data won't have any record of them.

[STRIKE]Also, the XML archives probably only extend as far back as the introduction of Primenet v5 (in 2008?), so again, any factors found earlier won't be represented.[/STRIKE]

Edit:

[QUOTE=Madpoo;422636](available for years going back to 1997)[/QUOTE]

[QUOTE=GP2;468303]he used archived data that doesn't include 2017 results, such as the completion of the 64-bit range as of June 2017.
[/QUOTE]
Note that above the table he wrote:
[QUOTE]
I found the links for the daily xml backup files as well, so I updated this up tuesday 2017-09-18:[/QUOTE]

[QUOTE=alpertron;468304]Note that above the table he wrote:[/QUOTE]

Ah, OK. Then the explanation is that he mislabeled 65-bit factors as 64-bit factors, etc., and everything is off-by-one, as mentioned in the posts above.

The first factors I can find that was not reported by type F (trialfactoring) was P-1 on April 17th 2007 (exponent 1200 ???) and April 23rd 2007, and by ECM on August 1st 2007:

Only these 4 was found by P-1 in 2007 while 461 was found by ECM.

[CODE]<result exponent="1200"><UserName>ANONYMOUS</UserName><ComputerName>UNKNOWN</ComputerName><ResultType>F-PM1</ResultType><DateReceived>2007-04-17 07:59</DateReceived><GHzDays>0.0000</GHzDays><Message>Factor: 13411442880309433733448109292499785853376890789048899839491431454436064036618343692769897730327375</Message></result>
<result exponent="41844091"><UserName>ANONYMOUS</UserName><ComputerName>v4_computers</ComputerName><ResultType>F</ResultType><DateReceived>2007-04-23 00:00</DateReceived><GHzDays>0.0000</GHzDays><Message>Factor: 56882683315410041087</Message></result>
<result exponent="46000231"><UserName>James Heinrich</UserName><ComputerName>WHS</ComputerName><ResultType>F-PM1</ResultType><DateReceived>2007-11-23 19:30</DateReceived><AssignmentAge>1.6</AssignmentAge><GHzDays>1.4583</GHzDays><Message>Factor: 64450044967347486511</Message></result>
<result exponent="46000613"><UserName>Team_Bundu</UserName><ComputerName>bundu3</ComputerName><ResultType>F-PM1</ResultType><DateReceived>2007-12-08 21:23</DateReceived><AssignmentAge>7.5</AssignmentAge><GHzDays>1.3932</GHzDays><Message>Factor: 281729255818247573438807</Message></result>

<result exponent="171719"><UserName>George Woltman</UserName><ComputerName>D_P4Debug</ComputerName><ResultType>F-ECM</ResultType><DateReceived>2007-08-01 21:13</DateReceived><AssignmentAge>0.0</AssignmentAge><GHzDays>0.0000</GHzDays><Message>Factor: 7554878084919728140007</Message></result>
<result exponent="166987"><UserName>George Woltman</UserName><ComputerName>D_P4Debug</ComputerName><ResultType>F-ECM</ResultType><DateReceived>2007-08-01 19:25</DateReceived><AssignmentAge>0.0</AssignmentAge><GHzDays>0.0000</GHzDays><Message>Factor: 460116060108723937</Message></result>
<result exponent="163973"><UserName>George Woltman</UserName><ComputerName>D_P4Debug</ComputerName><ResultType>F-ECM</ResultType><DateReceived>2007-08-01 15:26</DateReceived><AssignmentAge>0.0</AssignmentAge><GHzDays>0.0000</GHzDays><Message>Factor: 742837306591069995407</Message></result>
[/CODE]

[QUOTE=ATH;468329]The first factors I can find that was not reported by type F (trialfactoring) was P-1 on April 17th 2007 (exponent 1200 ???) and April 23rd 2007, and by ECM on August 1st 2007:

Only these 4 was found by P-1 in 2007 while 461 was found by ECM.

[CODE]<result exponent="1200"><UserName>ANONYMOUS</UserName><ComputerName>UNKNOWN</ComputerName><ResultType>F-PM1</ResultType><DateReceived>2007-04-17 07:59</DateReceived><GHzDays>0.0000</GHzDays><Message>Factor: 13411442880309433733448109292499785853376890789048899839491431454436064036618343692769897730327375</Message></result>
<result exponent="41844091"><UserName>ANONYMOUS</UserName><ComputerName>v4_computers</ComputerName><ResultType>F</ResultType><DateReceived>2007-04-23 00:00</DateReceived><GHzDays>0.0000</GHzDays><Message>Factor: 56882683315410041087</Message></result>
<result exponent="46000231"><UserName>James Heinrich</UserName><ComputerName>WHS</ComputerName><ResultType>F-PM1</ResultType><DateReceived>2007-11-23 19:30</DateReceived><AssignmentAge>1.6</AssignmentAge><GHzDays>1.4583</GHzDays><Message>Factor: 64450044967347486511</Message></result>
<result exponent="46000613"><UserName>Team_Bundu</UserName><ComputerName>bundu3</ComputerName><ResultType>F-PM1</ResultType><DateReceived>2007-12-08 21:23</DateReceived><AssignmentAge>7.5</AssignmentAge><GHzDays>1.3932</GHzDays><Message>Factor: 281729255818247573438807</Message></result>

<result exponent="171719"><UserName>George Woltman</UserName><ComputerName>D_P4Debug</ComputerName><ResultType>F-ECM</ResultType><DateReceived>2007-08-01 21:13</DateReceived><AssignmentAge>0.0</AssignmentAge><GHzDays>0.0000</GHzDays><Message>Factor: 7554878084919728140007</Message></result>
<result exponent="166987"><UserName>George Woltman</UserName><ComputerName>D_P4Debug</ComputerName><ResultType>F-ECM</ResultType><DateReceived>2007-08-01 19:25</DateReceived><AssignmentAge>0.0</AssignmentAge><GHzDays>0.0000</GHzDays><Message>Factor: 460116060108723937</Message></result>
<result exponent="163973"><UserName>George Woltman</UserName><ComputerName>D_P4Debug</ComputerName><ResultType>F-ECM</ResultType><DateReceived>2007-08-01 15:26</DateReceived><AssignmentAge>0.0</AssignmentAge><GHzDays>0.0000</GHzDays><Message>Factor: 742837306591069995407</Message></result>
[/CODE][/QUOTE]
I don't think TJAOI does TF on the lower millions exponents (<10M??) ? as it would take too long. But I'm unsure where his cutoff exactly is. He does a lot of ECM on low exponents though.

Ok, so I tried again searching for all factors including P-1 and ECM, and I rounded up the bitlevel instead of down.

I also added checks that rejected factors where (factor-1)!=0 (mod 2*exponent) and where exponent is not a prime, and finally I removed duplicate factors.

So the total factors for TJAOI 5.7M fits pretty well with what the server reports, but the rest of us found much more than 3.8M factors, I'm not sure where the rest are, but I do not think I missed millions of factors.

[CODE]
Others TJAOI
Total 3816202 5736806

15 1
16 1
17 3
18 10
19 29
20 58
21 107
22 179
23 313
24 600
25 1100
26 1808
27 3446
28 5896
29 10396
30 15287
31 21437
32 24634
33 28018
34 33139
35 50303
36 60902
37 72906
38 75704
39 80148
40 83690 38
41 85732 453
42 82882 6565
43 71764 18833
44 87760 38012
45 57070 71809
46 54041 74795
47 50617 77168
48 44481 82727
49 39660 92413
50 33334 97976
51 22108 120260
52 25567 149602
53 25554 222679
54 15953 364134
55 19868 412526
56 22164 412589
57 20692 414657
58 20925 416043
59 23162 416701
60 22003 417979
61 22095 415855
62 44905 414941
63 149475 413842
64 266728 420583
65 314670 150609
66 351650 578
67 341738 622
68 329854 587
69 213951 615
70 161612 621
71 63423 663
72 47395 645
73 21555 633
74 15367 608
75 11022 636
76 7001 633
77 5619 621
78 5176 557
79 4554 548
80 4081 475
81 3607 449
82 3375 409
83 2908 417
84 2602 341
85 2424 315
86 2168 254
87 1981 260
88 1756 223
89 1563 235
90 1401 162
91 1364 133
92 1170 123
93 1029 99
94 925 100
95 908 69
96 769 63
97 646 48
98 657 43
99 548 43
100 449 27
101 423 26
102 405 23
103 359 16
104 327 17
105 259 13
106 252 13
107 230 8
108 179 4
109 203 8
110 180 5
111 156 4
112 155 1
113 143 3
114 139 1
115 107 3
116 111 3
117 89
118 95
119 92 1
120 89
121 96
122 65 3
123 73
124 74
125 64
126 53
127 62
128 54
129 59
130 59
131 43
132 54 1
133 48
134 48
135 43
136 52
137 52
138 50
139 58
140 42
141 55
142 55
143 42
144 61
145 53
146 57
147 43
148 51
149 50
150 58
151 44
152 50
153 39
154 36
155 34
156 38
157 35
158 35
159 33
160 43
161 28
162 34
163 27
164 30
165 19
166 20
167 29
168 19
169 21
170 16
171 21
172 17
173 17
174 16
175 12
176 11
177 16
178 9
179 10
180 9
181 7
182 12
183 9
184 13
185 10
186 5
187 6
188 4
189 2
190 6
191 2
192 4
193 6
194 5
195 6
196 5
197 3
198 7
199 5
200 5
201 8
203 3
204 2
206 4
207 1
208 2
209 2
210 3
211 1
212 1
213 1
215 1
217 1
218 2
220 1
221 2
222 1
224 1
226 2
228 2
230 3
231 2
232 1
236 1
240 1
241 2
245 1
246 1
249 1
250 1
251 1
255 1
256 2
260 1
263 1
264 1
273 1
293 1
303 1
313 1
321 1
342 1
346 1
422 1
460 1
474 1
[/CODE]

Thanks a lot for your statistics Gepeto! :razz: Subscribing to what the man said below.

[QUOTE=kladner;468003]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]

That was never in discussion, if the work is valid or not. As long as a single factor is reported, the work is valid. His resources, his money. What was in discussion was, in the beginning, the method, and along the period, from time to time, the utility, of what he is doing. The method became clear after not long (what I have called "search by k", for me it was very transparent from the beginning, as I was playing exactly with the same method, but lacking the resources). The utility is still unclear. For the project itself, what he does is futile. For the math community in general, what he does may have some value, but it is above our knowledge (as amateur mathematicians and mostly cranks) to judge if the work is useful or futile.

[QUOTE=petrw1;468271]How hard would it be to note how many "FIRST" factors he found?[/QUOTE]
The answer is simple: none. (this has to be verified! do not take it for granted!)
When he started, most of the ranges were already over the 64-65 bits, except for the small exponents (first million) and even there, a lot of ECM was done to have almost zero chances to find a new factor. He may have some "new" factors however, found by ECM or P-1, which he also does a lot! (this is admiringly, it is not intended as irony or reproach!)

[QUOTE=VictordeHolland;468342]I don't think TJAOI does TF on the lower millions exponents (<10M??) ? as it would take too long. But I'm unsure where his cutoff exactly is. He does a lot of ECM on low exponents though.[/QUOTE]
No, he does not look for factors of the lower millions especially, see above. But the effect is that he has higher probability to find factors for lower mersenne, assuming no ECM done in the range. He does "search by k", just run this line in pari:

[CODE]q=10^3;while(q<10^5,v=factorint(q-1)~[1,];for(i=1,#v,if(v[i]<10^9&&Mod(2,q)^v[i]==1,print(q" divide 2^"v[i]"-1");break)); until(Mod(q,8)==1||Mod(q,8)==7, q=nextprime(q+1)))[/CODE]

You can start and stop everywhere, use powers of 10 or powers of two, etc, and this will find always all the factors in range.
With some sieving and a clever split into classes (to avoid the nextprime() and modularity tests), this can be very fast, and when combined with a lot of computing power... As it is written, the method is totally inefficient over ~2^45 or so, you can try it around 2^40 to see how fast it is, but as you go higher, it will spit factors rarely and rarely; you need to implement it at least 1000 times faster, to have it worth the time. Possibly, avoid factoring q-1, which takes the most of the time, or implemented it in a more clever way than pari does (you need to have a very efficient method to factor numbers with less than 100 bits, or ~30 digits). This can be done, and again, with sieving and a lot of resources... You can split it in a hundred ranges, in a hundred computers (easy paralelizable) and have a local server that assigns you ranges. The work he does takes the same amount of time, regardles the exponent, it only depends on the size of the factor, and it doubles with every bitlevel.

This is what TJAOI is doing. He is reliable, valid, reasonable fast up to now. And maybe useful from the math point of view. Hopefully he can find some "first time" factors in the future, caused by GIMPS missing factors, due to hardware errors or due to idiots who intentionally report "no factors in range..." for credit reasons, or just to cause mischief. Here is where TJAOI can be useful, as he/she/them decrease the probability of errors (missing first-time factors) in the DB.

But on the other hand, GIMPS will always be a step (a handful of steps!) ahead him, because all the larger exponents are easy to factor to higher bits, they already reached over 2^75 or so, and they will reach 2^80 soon, and in the lower ranges where TF "by p" is difficult to do, there LL is faster, and all exponents had LL done and DC-ed, so finding a "first" factor has only "pride" importance.

[QUOTE]But on the other hand, GIMPS will always be a step (a handful of steps!) ahead him, because all the larger exponents are easy to factor to higher bits...[/QUOTE]
This is necessary, if their aim is "filling in the gaps" or "mapping the terrain." As a non-math type, I can still see the value of adding more values to the knowledge base.

I wish my long-deceased math-loving friend could have joined this discussion, and many others, here.