[QUOTE=wblipp;324691]If I understand correctly, when Pascal adapted Kevin Hare's method of working around roadblocks, he also got the phenomenon that there are no longer absolute limits. Both proofs can always go a little bit higher by adding more roadblock circumvention calculations. But the roadblock circumvention calculations are much bulkier that the factor chains possible when factors are known. Extending the proofs becomes a management of resources problem - deciding when it is more efficient to make more roadblock circumvention calculations versus when to factor some of the roadblocks.

Since Bob isn't posting much anymore, I'll take the time to acknowledge that at some point there is not much new mathematics in this allocation of resources. Pascal doesn't seem to feel we have reached that point yet, but even if the professional mathematicians lose interest there is still fun, and there are potential benefits from the accumulated factorizations.

Pascal recently asked for help with these level six and level five roadblocks that we have been tracking here. Offlist, Ryan Propper has recently factored over 30 of Pascal's most heavily weighted roadblocks below 200 digits.[B] I'll post more about this in the not-too-distant future.[/B].[/QUOTE]

Are we there yet?

Kudos to Ryan Propper for clearing out OPN Roadblocks. It started as a clearing of roadblocks under 200 digits, but quickly expanded to include larger numbers, too. Some of them are larger than we normally see factored by an individual. The largest, 2801^83-1, has a thread of it’s own. The good news is that so many roadblocks have been cleared that Pascal is exploring the expansion of his thresholds. The sad news is that the community project I had planned for this will not happen; Ryan cleared the roadblocks faster than I could prep them, so I never was able to announce a new list of SNFS-ready roadblocks to the community at large. I’m not positive I got them all, but here is a list of the roadblocks. Some of these roadblocks are finished and already in the factordb, others are still in progress.

2801^83-1
101^127-1
3001^73-1
3191^71-1
21673^37-1
337^73-1
307^101-1
2521^53-1
2087^53-1
152943249629^13-1
124118720954255306504926792543^7-1
3281533^23-1
761^67-1
(89^109-1)/88+1
11467^43-1
27809^31-1
17519^37-1
17393^37-1
27527^31-1
17209^37-1
27271^31-1
467316307^17-1
16901^37-1
27059^31-1
26951^31-1
15877^37-1
15331^37-1
73^149-1
1549^79-1
1597^79-1
398341412240537151131351^11-1
36209^29-1
30841^31-1
35963^29-1
2123^37-1
20101^37-1
19949^37-1
35509^29-1
35129^29-1
19009^37-1
29209^31-1
29123^31-1
29101^31-1
231^29-1)
18311^37-1
28631^31-1
33809^29-1
33391^29-1
6421^47-1
26539^31-1
26339^31-1
30403^29-1
30391^29-1
30319^29-1
25633^31-1
30071^29-1
29567^29-1
27437^29-1
13591^37-1
150099253^19-1
151421761^17-1
23753^31-1
23773^31-1
14197^37-1
24103^31-1
24169^31-1
14537^37-1
14699^37-1
24749^31-1
14447^37-1
2465227^29-1
6427^43-1
26759^29-1
26927^29-1
23203^31-1
25793^29-1
12637^37-1
142265257^19-1
12919^37-1
13003^37-1
13037^37-1
21089^31-1
21121^31-1
58887991^19-1
64213507^19-1
22171^31-1
12517^37-1
9949^37-1
10289^37-1
11383^37-1
20443^31-1
23879^29-1
20663^31-1
9719^37-1
19141^31-1
241393^23-1
19457^31-1
23279^29-1
19889^31-1
86927653^17-1
7211^37-1
146736883^17-1
9109^37-1

Today, when I search news.google.com for the keyword "Mersenne", the following is the first hit:

[url]http://blogs.scientificamerican.com/roots-of-unity/2013/01/10/odd-perfect-numbers/[/url]

I have no idea what was going on or whether anybody from this forum was involved, but it seems rather embarrassing. Maybe an OPN honcho should talk to the SA blogger?

t450 cleared
 

Ryan Propper has finished Pascal's t450 list. There were 37 numbers on the list as of Feb 9th. The t lists, available on [URL="http://www2.lirmm.fr/~ochem/opn/"]Pascal's site[/URL], are "First Composites" encountered in the factor chain proofs. Completion of this list means it now possible to construct a proof there are no OPNs less the 10^450 in which every component is fully factored. This has a aesthetic appeal - Richard Brent's two papers on OPNs ([URL="http://maths-people.anu.edu.au/~brent/pub/pub100.html"]100 [/URL]and [url=http://maths-people.anu.edu.au/~brent/pub/pub116.html]116[/url]) both regretted the incompleteness of some factorizations. It also has a practical effect of postponing the point at which road block circumvention techniques must be employed, making it feasible to construct proofs to higher levels.

Thanks, Ryan

523^113-1 is factored
 

I just found my first non-trivial GPU-ECM factor.

[CODE]Input number is (523^113-1)/((523-1)*227) (303 digits)
Using B1=4900000-4900000, B2=11416155670, polynomial Dickson(12), sigma=3:887554791
Step 1 took 0ms
Step 2 took 33462ms
********** Factor found in step 2: 11581456209668458770811390483767555203365868641
Found probable prime factor of 47 digits: 11581456209668458770811390483767555203365868641
Probable prime cofactor ((523^113-1)/((523-1)*227))/11581456209668458770811390483767555203365868641 has 257 digits[/CODE]

P35 for [URL="http://factordb.com/index.php?id=1100000000212988394"]809^2213-1[/URL]

This completes the search for two explicit large factors of 809^224055185-1. This is a part of the [URL="http://oddperfect.org/FermatQuotients.html"]Vanishing Fermat Quotients[/URL] project that supports some of Zeta-Flux's OPN work. Yoyo's ECM queues are currently stocked with moderately long tasks in support of the [URL="http://www.seti-germany.de/boinc_pentathlon/22_en_Welcome.html#"]BOINC Pentathalon[/URL]. Some of those long tasks are these Vanishing Fermat Quotient composites.

A nice split from OPN's [URL="http://oddperfect.org/composites.html"]Composite Page[/URL] via GNFS.

746739942764461557811^11-1 (C136 remain)

[CODE]prp68 factor: 14940569223633060623013972442226275836365428230226383755684158173461
prp69 factor: 115727850067186724139333070599790801929567660189931939023508002705101[/CODE]

29^193-1 is factored
 

Factors:
98077203985215563327661270646204385764952723400824363798768294532999335907157553726123
320425190121109347341687742161867395230640027836273695424556536016342459

Poly used:
c0: 11918583039386136356512310543606665785
c1: 92543034719470933101609178744230
c2: -152630928846043961598467393
c3: -71517680292659419598
c4: 521218120548
c5: 3837240
Y0: -1522843067282449973585257178416
Y1: 294347831770073809

[QUOTE=lorgix;344018]Factors:
98077203985215563327661270646204385764952723400824363798768294532999335907157553726123
320425190121109347341687742161867395230640027836273695424556536016342459

Poly used:
c0: 11918583039386136356512310543606665785
c1: 92543034719470933101609178744230
c2: -152630928846043961598467393
c3: -71517680292659419598
c4: 521218120548
c5: 3837240
Y0: -1522843067282449973585257178416
Y1: 294347831770073809[/QUOTE]

Be sure to send it to Richard Brent.

[QUOTE=R.D. Silverman;344034]Be sure to send it to Richard Brent.[/QUOTE]
I think Jonathan Crombie keeps track of the Brent numbers now. ([URL="http://maths-people.anu.edu.au/~brent/factors.html"]See here.[/URL])

[QUOTE=lorgix;344043]I think Jonathan Crombie keeps track of the Brent numbers now. ([URL="http://maths-people.anu.edu.au/~brent/factors.html"]See here.[/URL])[/QUOTE]


Thanks, but someone :bow wave: is already submitting the opn numbers.:smile:

(And that emoticon is really ironic today, considering the name of the major river flooding my city today.)