mersenneforum.org  

Go Back   mersenneforum.org > Factoring Projects > Factoring

Reply
 
Thread Tools
Old 2005-12-06, 12:57   #1
AntonVrba
 
AntonVrba's Avatar
 
Jun 2005

2·72 Posts
Default 160 digit factor found of 366 digit (PRP-1)

I am trying to prove the following number prime
p=(2^607-1)*(2^607-169662)+169661

p-1 has following prime factors
2
3 ^ 4
7 ^ 2
13
607
2663
117210 040608 611501
and 160 digit composite factor:
2077 722215 701465 989903 905378 105865 831121
690269 515432 941764 890410 612443 142155 675750
703708 696614 154976 284846 472630 448131 063469
226632 172413 531787 662918 734708 751011
and a remaining 178 digit composite factor

Is finding a 160 digit composite factor a noteworthy record?

Congratulations to Dario Alpern's http://www.alpertron.com.ar/ECM.HTM

The Java applet is now stuck on the 160 digit factor so I installed ecm-6.0.1. Any pointers for the best command line - never used ecm before.


regards
Anton

Last fiddled with by AntonVrba on 2005-12-06 at 12:58
AntonVrba is offline   Reply With Quote
Old 2005-12-06, 13:20   #2
akruppa
 
akruppa's Avatar
 
"Nancy"
Aug 2002
Alexandria

2,467 Posts
Default

Not if it is an algebraic factor - which it undoubtedly is. Before continuing with ECM, try to find all algebraic factors of your number. It will make your job very much easier.

Alex
akruppa is offline   Reply With Quote
Old 2005-12-06, 13:47   #3
R.D. Silverman
 
R.D. Silverman's Avatar
 
Nov 2003

22·5·373 Posts
Default

Quote:
Originally Posted by AntonVrba
I am trying to prove the following number prime
p=(2^607-1)*(2^607-169662)+169661

p-1 has following prime factors
2
3 ^ 4
7 ^ 2
13
607
2663
117210 040608 611501
and 160 digit composite factor:
2077 722215 701465 989903 905378 105865 831121
690269 515432 941764 890410 612443 142155 675750
703708 696614 154976 284846 472630 448131 063469
226632 172413 531787 662918 734708 751011
and a remaining 178 digit composite factor

Is finding a 160 digit composite factor a noteworthy record?

Congratulations to Dario Alpern's http://www.alpertron.com.ar/ECM.HTM

The Java applet is now stuck on the 160 digit factor so I installed ecm-6.0.1. Any pointers for the best command line - never used ecm before.


regards
Anton

You are trying to kill an ant with a sledgehammer.

ECPP or Cyclotomy methods will prove this prime (if it is) in just a few minutes. Why waste factoring a 160-digit composite?
R.D. Silverman is offline   Reply With Quote
Old 2005-12-06, 15:28   #4
John Renze
 
John Renze's Avatar
 
Nov 2005

24×3 Posts
Default

Quote:
Originally Posted by R.D. Silverman
ECPP or Cyclotomy methods will prove this prime (if it is) in just a few minutes.
For the record:

(2^607 - 1)*(2^607 - 169662) + 169661 - 1 == 2(2^303 - 1)(2^303 + 1)(2^607 - 169661)

The algebraic factors 2^303-1 and 2^303+1 have each been completely factored, as revealed by quick check of the Cunningham project tables. This is enough for a classical proof, so you don't even have to bother with 2^607-169661.

The algebraic factorization is not a coincidence. How did you choose to study this form?

John
John Renze is offline   Reply With Quote
Old 2005-12-06, 15:57   #5
akruppa
 
akruppa's Avatar
 
"Nancy"
Aug 2002
Alexandria

2,467 Posts
Default

Thanks for the factorisation, John.

2^607 - 169661 is a fairly easy SNFS number. Anton, you probably won't need this factored any more for your proof, but if want it done, let me know.

Alex
akruppa is offline   Reply With Quote
Old 2005-12-06, 16:35   #6
AntonVrba
 
AntonVrba's Avatar
 
Jun 2005

11000102 Posts
Default

Quote:
Originally Posted by akruppa
Thanks for the factorisation, John.

2^607 - 169661 is a fairly easy SNFS number. Anton, you probably won't need this factored any more for your proof, but if want it done, let me know.

Alex
Thanks all

BTW, Marcel Martin's Primo has done the job of prooving p=(2^607-1)*(2^607-169662)+169661 prime

regards
Anton

Last fiddled with by AntonVrba on 2005-12-06 at 16:37
AntonVrba is offline   Reply With Quote
Old 2005-12-06, 21:56   #7
alpertron
 
alpertron's Avatar
 
Aug 2002
Buenos Aires, Argentina

22·3·5·23 Posts
Default

My applet also declares that the original number is prime by using the APRT-CLE algorithm. So no external programs were needed in this case to prove primality.

Notice that the applet cracked p-1 by using Lehman factorization. This is because it is a product of two similar numbers.
alpertron is offline   Reply With Quote
Old 2005-12-06, 22:02   #8
alpertron
 
alpertron's Avatar
 
Aug 2002
Buenos Aires, Argentina

101011001002 Posts
Default

If you had entered ((2^607 - 1)*(2^607 - 169662) + 169661 - 1)/2/(2^607 - 169661) in the upper box the applet would have completed the factorization. This is because it search in the Web server known factorizations of Cunningham numbers.
alpertron is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
New 70 digit factor R.D. Silverman Cunningham Tables 16 2016-01-23 22:16
73 digit ECM factor akruppa Factoring 103 2010-11-27 20:51
44-digit factor found using ECM w/ B1=1e6 & B2=1e8 WVU Mersenneer Factoring 8 2010-04-24 17:01
Probability of n-digit factor? roger Factoring 3 2007-05-09 22:51
when will the 10M Digit prime be found? Deamiter Lounge 12 2003-08-26 17:33

All times are UTC. The time now is 00:24.


Tue Oct 19 00:24:52 UTC 2021 up 87 days, 18:53, 0 users, load averages: 1.15, 1.16, 1.18

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.