fond of a factor? Urn yourself to become remains - Page 49

LaurV · 2012-09-15, 06:17

Quote:

Originally Posted by ET_

(Now that I think about it... which one would be faster?)

The one with a lower B1 is much faster, as for each additional prime to B1 you need to do a new exponentiation (i.e. a couple of squaring operations and multiplications) mod Mp. When extending B2, for each additional cluster of primes that you add to B2 you need to do a (single one) multiplication mod Mp.

ET_ · 2012-09-15, 10:45

Quote:

Originally Posted by LaurV

The one with a lower B1 is much faster, as for each additional prime to B1 you need to do a new exponentiation (i.e. a couple of squaring operations and multiplications) mod Mp. When extending B2, for each additional cluster of primes that you add to B2 you need to do a (single one) multiplication mod Mp.

That is true, but the modular multiplication on B2 are done on a much higher number of bits... That is the reason of my question.

Luigi

c10ck3r · 2012-09-16, 16:38

Chals,
Cohen has nothing to do with it. If you want to play that game, don't quote Jwb. "Everybody Knows" what he said- it is on the same page. Please don't take this as an attack on you personally, but please leave the bard duties to daveiddy!
Just my 2¢.

PageFault · 2012-09-21, 19:36

Found a few lately:

Code:

P-1 found a factor in stage #1, B1=810000.
UID: PageFault/boxen_01, M70002791 has a factor: 10476233014671785173315351

M70002791

k = 3 x 5^2 x 19 x 79 x 761 x 2141 x 407959

M70003481

Code:

P-1 found a factor in stage #1, B1=810000.
UID: PageFault/boxen_01, M70003481 has a factor: 222473048199885240645001

k = 2^2 x 3 x 5^4 x 277 x 2731 x 280069

These aren't very smooth. Both could have been found with a ridiculous B1 of 2750. Perhaps I should start pre-screening for these?

c10ck3r · 2012-09-21, 21:28

Quote:

Originally Posted by PageFault

Found a few lately:

Code:

P-1 found a factor in stage #1, B1=810000.
UID: PageFault/boxen_01, M70002791 has a factor: 10476233014671785173315351

M70002791

k = 3 x 5^2 x 19 x 79 x 761 x 2141 x 407959

M70003481

Code:

P-1 found a factor in stage #1, B1=810000.
UID: PageFault/boxen_01, M70003481 has a factor: 222473048199885240645001

k = 2^2 x 3 x 5^4 x 277 x 2731 x 280069

These aren't very smooth. Both could have been found with a ridiculous B1 of 2750. Perhaps I should start pre-screening for these?

FWIW, in the 84.4M range, there are at least (several tests left) three numbers factored with B1=60000=B2 or less, including M84,400,003. I am taking this 100k range to B1=1M (slowly) and saving files to do B2 on top of.

Jwb52z · 2012-09-22, 15:06

P-1 found a factor in stage #2, B1=530000, B2=9805000.
UID: Jwb52z/Clay, M57744637 has a factor: 256107633532327108861568647

87.727 bits

Jwb52z · 2012-09-22, 17:25

P-1 found a factor in stage #1, B1=530000.
UID: Jwb52z/Clay, M57731417 has a factor: 1322645848375959335562359

80.130 bits

Jwb52z · 2012-09-22, 21:47

P-1 found a factor in stage #1, B1=530000.
UID: Jwb52z/Clay, M57739921 has a factor: 174129453467924169651127

77.205 bits

Jatheski · 2012-09-23, 14:08

P-1 found a factor in stage #2, B1=565000, B2=12006250, E=6.
UID: Jatheski/JTS_2, M56268371 has a factor: 445745465219441846607767554801 (98.492 bits)
k = 3960888304545388799400 = 2^3 × 3 × 5^2 × 47 × 599 × 8573 × 26041 × 1050331

Largest factor I found using P-1

Jatheski · 2012-09-23, 16:07

Quote:

Originally Posted by Jatheski

P-1 found a factor in stage #2, B1=565000, B2=12006250, E=6.
UID: Jatheski/JTS_2, M56268371 has a factor: 445745465219441846607767554801 (98.492 bits)
k = 3960888304545388799400 = 2^3 × 3 × 5^2 × 47 × 599 × 8573 × 26041 × 1050331

Largest factor I found using P-1

Sorry for the double post but i cannot edit my previous reply...

Two weeks ago i found this one:

P-1 found a factor in stage #2, B1=535000, B2=10967500, E=6.
UID: Jatheski/JTS_2, M57252271 has a factor: 68943540478860569348473098497 (95.799 bits)
k = 602103106782092271488 = 2^7 × 11 × 53 × 521 × 1607 × 9636930871

Dubslow · 2012-09-23, 16:46

Quote:

Originally Posted by Jatheski

Sorry for the double post but i cannot edit my previous reply...

Two weeks ago i found this one:

P-1 found a factor in stage #2, B1=535000, B2=10967500, E=6.
UID: Jatheski/JTS_2, M57252271 has a factor: 68943540478860569348473098497 (95.799 bits)
k = 602103106782092271488 = 2^7 × 11 × 53 × 521 × 1607 × 9636930871

That is a monster B-S find... wow. I'm pretty sure you smashed the record.

Could you submit the result here so that it appears on that list?

2012-09-21, 19:36	#532
PageFault Aug 2002 Dawn of the Dead 5×47 Posts	Found a few lately: Code: P-1 found a factor in stage #1, B1=810000. UID: PageFault/boxen_01, M70002791 has a factor: 10476233014671785173315351 M70002791 k = 3 x 5^2 x 19 x 79 x 761 x 2141 x 407959 M70003481 Code: P-1 found a factor in stage #1, B1=810000. UID: PageFault/boxen_01, M70003481 has a factor: 222473048199885240645001 k = 2^2 x 3 x 5^4 x 277 x 2731 x 280069 These aren't very smooth. Both could have been found with a ridiculous B1 of 2750. Perhaps I should start pre-screening for these? Last fiddled with by PageFault on 2012-09-21 at 19:38 Reason: Alcohol is highly suspect

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2012-09-16, 16:38	#531
c10ck3r Aug 2010 Kansas 547 Posts	Chals, Cohen has nothing to do with it. If you want to play that game, don't quote Jwb. "Everybody Knows" what he said- it is on the same page. Please don't take this as an attack on you personally, but please leave the bard duties to daveiddy! Just my 2¢.

2012-09-22, 15:06	#534
Jwb52z Sep 2002 17×47 Posts	P-1 found a factor in stage #2, B1=530000, B2=9805000. UID: Jwb52z/Clay, M57744637 has a factor: 256107633532327108861568647 87.727 bits

2012-09-22, 17:25	#535
Jwb52z Sep 2002 1437₈ Posts	P-1 found a factor in stage #1, B1=530000. UID: Jwb52z/Clay, M57731417 has a factor: 1322645848375959335562359 80.130 bits

2012-09-22, 21:47	#536
Jwb52z Sep 2002 31F₁₆ Posts	P-1 found a factor in stage #1, B1=530000. UID: Jwb52z/Clay, M57739921 has a factor: 174129453467924169651127 77.205 bits

2012-09-23, 14:08	#537
Jatheski Apr 2012 993438: i1090 2×73 Posts	P-1 found a factor in stage #2, B1=565000, B2=12006250, E=6. UID: Jatheski/JTS_2, M56268371 has a factor: 445745465219441846607767554801 (98.492 bits) k = 3960888304545388799400 = 2^3 × 3 × 5^2 × 47 × 599 × 8573 × 26041 × 1050331 Largest factor I found using P-1