20171107, 22:05  #1 
Oct 2006
Berlin, Germany
266_{16} Posts 
P73 found by a yoyo@home user
A yoyo@home user found a P73 for R1186 (10^593+1):
Code:
GMPECM 7.0.5dev [configured with GMP 6.1.2, enableasmredc] [ECM] Input number is 9090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909091 (592 digits) [Tue Nov 07 18:14:21 2017] Using MODMULN [mulredc:4, sqrredc:4] Using B1=110000000, B2=829850101096, polynomial Dickson(30), sigma=0:16299314430696221325 dF=120960, k=5, d=1291290, d2=17, i0=69 Expected number of curves to find a factor of n digits: 35 40 45 50 55 60 65 70 75 80 34 134 608 3119 17689 110056 743875 5417128 4.2e+07 3.6e+08 Writing checkpoint to checkpnt at p = 20333393 Writing checkpoint to checkpnt at p = 40506859 Writing checkpoint to checkpnt at p = 60560629 Writing checkpoint to checkpnt at p = 80690453 Writing checkpoint to checkpnt at p = 101083799 Writing checkpoint to checkpnt at p = 110000000 Step 1 took 3247765ms Estimated memory usage: 1.64GB Initializing tables of differences for F took 1984ms Computing roots of F took 63375ms Building F from its roots took 27093ms Computing 1/F took 12141ms Initializing table of differences for G took 2609ms Computing roots of G took 51422ms Building G from its roots took 26860ms Computing roots of G took 55781ms Building G from its roots took 27016ms Computing G * H took 6610ms Reducing G * H mod F took 9781ms Computing roots of G took 56922ms Building G from its roots took 26859ms Computing G * H took 6766ms Reducing G * H mod F took 9797ms Computing roots of G took 57312ms Building G from its roots took 26594ms Computing G * H took 6750ms Reducing G * H mod F took 9829ms Computing roots of G took 57171ms Building G from its roots took 27079ms Computing G * H took 6422ms Reducing G * H mod F took 9390ms Computing polyeval(F,G) took 57781ms Computing product of all F(g_i) took 344ms Step 2 took 644328ms ********** Factor found in step 2: 2909076542620598524499532435958736860811671130747534094532375046661903161 Found prime factor of 73 digits: 2909076542620598524499532435958736860811671130747534094532375046661903161 Probable prime cofactor 3125015432807993452395038634013309617867717582914358894173268713097150537376427232621985983364362381037572308793912508473244215581788783050366433021306602205095695585123360825687037384480936324147844060907653636389193668837605678869741546508709934354266735495475343271268446929051785779649633066534259397463567093895758026730277823815590724554798361272711560580416081789809541777798773606334712701416644206700894936206530047039287732255861170965984971136826555598096883703505206688714709410112221639166983114001153395131 has 520 digits Report your potential champion to Richard Brent <champs@rpbrent.com> (see http://wwwmaths.anu.edu.au/~brent/ftp/champs.txt) Peak memory usage: 1469MB 
20171107, 22:40  #2 
Mar 2006
11×43 Posts 

20171107, 23:50  #3 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3·5·17·37 Posts 
Very smooth find! Congrats!
Code:
G.o. = 2^4 · 3^2 · 73 · 9013 · 38639 · 380983 · 857743 · 934441 · 2221907 · 2747597 · 6117583 · 13622467 · 16300793 · 313788197 
20171108, 15:20  #4 
"Victor de Hollander"
Aug 2011
the Netherlands
2^{3}·3·7^{2} Posts 
Nice find!
Hopefully the user can also appreciate the find and is not only interested in the BOINC credits 
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