Date: Wed, 06 Apr 2005 23:00:32 -0400
From: Bruce Dodson <...>
X-Accept-Language: en-us, en
To: Paul Zimmermann <...>, Torbjo"rn Granlund, Sam Wagstaff, Richard Brent
Cc: Peter Montgomery, Paul Leyland, Bruce Dodson
Subject: Re: [www@loria.fr: new Cunningham factor]

Paul Zimmermann wrote:

>Torbjo"rn is challenging Bruce's resources:
>
>10,369- c216 = p43 * c174 Granlund
>
       If that's so, he didn't pick quite the best time to do so.
----------------

Subject:  Sit down before reading!    Date:  April 6, 2005

Dear Arjen,
   ....
  And M963 came out well for once (no p5x this time),
    with p91*p94.  But have a look at what just popped-up in output from
    the new Opteron cluster as the factorization of  3,466+ c180, with snfs
    difficulty 222.3:

GMP-ECM 6.0 [powered by GMP 4.1.90] [ECM]

Input number is 
1802413971039407720781597792978015040177086533038137501450821699
06990204420366728928912748144027605313041315900678619513985483829311951906153713 

242484788070992898795855091601038513 (180 digits)
Using B1=110000000, B2=680270182898, polynomial Dickson(30), 
sigma=1875377824
Step 1 took 961498ms
Step 2 took 331891ms
********** Factor found in step 2: 
709601635082267320966424084955776789770864725
643996885415676682297
Found probable prime factor of 66 digits: 
70960163508226732096642408495577678977
0864725643996885415676682297
Probable prime cofactor 
25400363836963900630494626058015503341642741484107646018
9423633564858960970523044852717009521400767374773786652729 has 114 digits
Report your potential champion to Richard Brent <...>
(see 
ftp://ftp.comlab.ox.ac.uk/pub/Documents/techpapers/Richard.Brent/champs.txt
)

I checked with maple:

 > 
isprime(709601635082267320966424084955776789770864725643996885415676682297); 

                                    true


Wow, the order is very weird;  doesn't use b1=110M (for p55-limits),
largest step 1 prime seems to be just 13.15M, and the step 2 isn't very
large either ---  249.43M, just 2.27*b1.  A whole bunch of smaller step 1
primes,  844K*1.8M*6.0M*7.6M*8.0M*8.1M*13.1M.
-------------------------------

Paul&Richard:

here's the actual order:

[ <2, 2>, <3, 1>, <11243, 1>, <336181, 1>, <844957, 1>, <1866679, 1>, 
<6062029,
1>, <7600843, 1>, <8046121, 1>, <8154571, 1>, <13153633, 1>, <249436823, 
1> ]

Total time: 102.800 seconds

>  
>