20120803, 00:24  #1 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{3}·7·163 Posts 
Hot tuna!  a p75 and a p79 by Sam Wagstaff!
A new ECM record by Sam Wagstaff!
Code:
970 p75 336842026814486816413712532665671525518487238461533945786937785048474675329 11^304+1 1G 3885593015 20120802 Sam Wagstaff [ <2, 2>, <3, 1>, <5, 2>, <13, 1>, <41, 1>, <11971, 1>, <14923, 1>, <15887, 1>, <16333, 1>, <119129, 1>, <970961, 1>, <3408437, 1>, <10882111, 1>, <38612713, 1>, <173109949, 1>, <1584686398147, 1> ] Interestingly, the default B2 value for B1=173109999 is 1589274236566, which is just enough. (a minimalistic test in progress: ecm sigma 3885593015 173109999 < c227 > ECp75.txt ... and surely ... Code:
GMPECM 6.4.2 [configured with GMP 5.0.2, enableasmredc] [ECM] Input number is 6604857068189252819730948667846433708170919682317463967174714319350148535968504700215131814737582542911409411528095995619903696877100287394595437895996885419119698970679814635893121 (181 digits) Using B1=173109999, B2=1589274236566, polynomial Dickson(30), sigma=3885593015 Step 1 took 1208795ms Step 2 took 278537ms ********** Factor found in step 2: 336842026814486816413712532665671525518487238461533945786937785048474675329 Found probable prime factor of 75 digits: 336842026814486816413712532665671525518487238461533945786937785048474675329 Probable prime cofactor has 107 digits Last fiddled with by Batalov on 20120803 at 01:38 
20120803, 00:59  #2 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
21040_{8} Posts 
I thought that you brought a P75 online in the hunt for primes.

20120803, 01:56  #3  
Mar 2006
730_{8} Posts 
Quote:
Now all we need is a p71 and a p74 ecm find to have all digit levels up to p75 represented. 

20120803, 11:48  #4  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
not the main tables? Meets the Brent condition of 2.2*factor < C181. Still short of 256bits? Guess now we can keep records for the PS3 assisted ECM. Hot Tuna for sure. Bruce 

20120804, 16:24  #5 
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
3×419 Posts 
A p75 ecm factor from a 181 digit number? In my own opinion, it could have been done by using GNFS itself, rather than the effort needed, required to find away a 75 digit factor, away by using ecm.
As such, such a huge factor would have been productive enough to be able to have been ratherworthwhile although if in case that it had been emerged away, popped from a larger enough, hardertoNFS number, finding away candidate like, such as the p70 digit factor from the 3,607+ 
20120804, 23:54  #6 
Bemusing Prompter
"Danny"
Dec 2002
California
2^{2}·577 Posts 
In other news, M1061 was factored today, setting a new SNFS record. If two new records in one day isn't awesome, then I don't know what is.

20120805, 01:27  #7  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
reasonably estimate that Sam would have spent no more than the effort to find a p60; and certainly less than needed for 181digit gnfs. Finding ecm factors like this p75 (and my p70) is due to a large number of curves, spread over a lot of input numbers; not by a disproportionate effort on a single number. It is quite possible that no more than a t55 effort was spent on this specific number before the p75 showed up (just lotsandlots of t55 efforts ...). bdodson 

20120805, 14:43  #8  
Jun 2005
lehigh.edu
2000_{8} Posts 
Quote:
2^247 < p75 < 2^248. Guess that means Arjen's 1024bit RSA key as a product of four 256bit primes is still secure. bd In other late breaking news, Sam's agreed to have the base11 and base5 main table extensions effective August 1. We may now welcome the newest Cunningham Champion! 

20120812, 21:23  #9  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{3}·7·163 Posts 
And another one, this time a p79!
Quote:
Code:
p:=2302872188505279576573535015926441913945044975483579529517513795897664211127797; time GroupOrder(p, 3648110021); [ <2, 2>, <3, 3>, <5, 1>, <17, 1>, <29, 1>, <31, 1>, <127, 1>, <197, 1>, <673, 1>, <3947, 1>, <18481, 1>, <938939, 1>, <19305469, 1>, <26324929, 1>, <46026329, 1>, <97707917, 1>, <138483313, 1>, <764489238641, 1> ] Last fiddled with by Batalov on 20120812 at 22:56 

20120824, 10:26  #10 
Oct 2004
Austria
7·353 Posts 

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