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-   -   Odd perfect related road blocks II (https://www.mersenneforum.org/showthread.php?t=11829)

Zeta-Flux 2010-12-12 05:23

Don't forget:
983^79-1:
[code]
prp94 factor: 1000102122253158220136804515506925452640552848715960125028992536708499380888800526693799575059
prp119 factor: 29023570765769453849681787520675402409630111311649476322178663467954992292617669855309548046285560789566509795994872589[/code]

warut 2010-12-14 00:38

From Pascal's t1200.txt
[CODE]C100 of σ(36728082526819661667857337816331659873101014887185199844001421365006816972083681181271048314143381829405266285912997^1) =
3659402566213103404909138110576043729 * P64[/CODE]

wreck 2010-12-14 06:12

I notice these results could be applied to find Multiply Perfect Number, maybe it is more practicable to find a 12-fold perfect number than odd perfect number.

wblipp 2010-12-14 12:39

Another Brent Composite that is also a Mishima Cyclotomic Number and has no known divisors of at least 12 digits. The only previously known factors were two 10 digits primes.

ECM to t50 by yoyo@home
SNFS sieving by RSALS
Post Processing by Jeff Gilchrist

[code]
991^79-1
P102: 201849318340494650600524975102565992103025447755390579255168927940026290453347066962589932525532814429
P114: 111955911757660306248924126583569398234178392319622577900155635873591442919816885706041553256706268531750471285851
[/code]

wblipp 2010-12-14 21:11

Another Brent Composite that is also a Mishima Cyclotomic Number, this one with no known factors.

ECM to 2/9 of size by yoyo@home
SNFS sieving by RSALS
Post Processing by Zetaflux aka Pace
[code]
757^71-1
P91: 1853856977303162056123441618990518309880296757314855102471010834384392698189415867726432077
P112: 1858700531674982701750692070444229381902405282234445674712201923634723119197004047859363846214622467271829313191
[/code]

warut 2010-12-18 20:58

From Pascal's t450.txt
[CODE]By GNFS, C120 of σ(1674289^28) =
2854374493236676390901193322846128273399688595917 * P72[/CODE]
I'll begin factoring all composites < C120 in t450.txt soon.

wblipp 2010-12-22 05:08

Another Brent Composite that is also a Mishima Cyclotomic Number. This one had six previously known factors. The largest was 10 digits.

ECM to t50 by yoyo@home
SNFS sieving by RSALS
Post Processing by Zetaflux aka Pace
[code]
997^79-1
P92: 40544184333690501765237779233180821314618745238777145869243663625849687211741050365307226433
P105: 769737574114047129205933004833243718546571078931147873196560989148588268817236360077794279762487040349383
[/code]

warut 2010-12-22 19:56

From Pascal's t450.txt by GNFS:
[CODE]C115 of 853390763^19-1
= 4027938967897062644522060592327993192417576623 (P46)
* 2371205957205642539669900514634876175041736492264927377008081811790029 (P70)

C118 of 1803647^31-1
= 9163693611379762685171969917143051920717885453324156509 (P55)
* 769794736107205212415435727665901137007985989384334936511898039 (P63)

C118 of 89222701^19-1
= 198314129151251436274644581626332423991723363337573188001 (P57)
* 44564394742103358126045158869632434407051955148384303683329577 (P62)

C119 of 1501489387^17-1
= 1775298787766766475021420265094759755545397007091612709 (P55)
* 27629856352211142136927510769802601805473911476703435101589165893 (P65)[/CODE]

wblipp 2010-12-31 04:53

41^127-1:
ECM to 2/9 of SNFS size by yoyo@home
SNFS sieving by RSALS
Post Processing by Lionel Debroux

1093^79-1:
ECM to 2t50 by yoyo@home
SNFS sieving by RSALS
Post Processing by Pace Nielsen aka Zetaflux

2467^71-1:
ECM to t45 by Richard Dickerson

[code]
41^127-1:
P57: 518655283452900648931029664703840376945085793544369598067
P136: 3965861240059093328548309563332212674524345806905858168068449099985490555378230992902581553255748190806599069084081286578776351758713827

1093^79-1:
P59: 41533887490047118877116011014233342675846633318446966947329
P164: 22791784339703335066067236815215495650313386444804921146073407902230321258799037906128754503995304219927716381259643728095798983975694062230595273607587550586258941

2467^71-1:
P48: 671637019726792059928280139537039790028611205977
C172:
[/code]

wblipp 2011-01-04 02:04

Two more

ECM to t50 by yoyo@home
SNFS Sieving by RSALS
Post Processing by Lionel Debroux

[code]
1009^71-1
P63: 158090386133100277223772971146833557573037803742996676372486081
P138: 134889572351569200979059455239921998603810707636247252256734429815729581477130262232589933056664613142398593539423331540476157955575831791

9181^59-1
P88: 1548413386383055842898295433567369185886595472021948393948301017174957085565048450081273
P143: 45475727734645851166966780395374195256805057694025658533369378328729093206038970372422364519511997230700680148545937394553880623373668912738343
[/code]

wblipp 2011-01-13 08:50

This finished in the ECM qualification stage, saving us an NFS factorization

[code]
547^78-1
P45: 388386719516557534522780653448008927820035473
P102: 113819742239468124744051778339848713380977647914090627659741280637021953614222821061124686337235156939
[/code]


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