ElevenSmooth Searching for factors of the Mersenne number M(3326400) = 23326400-1

Italian Operation Billion Digits

Operation Billion Digits

History
Instructions

Operation Billion Digits is a whimsical Distributed Computing Project that is searching for a Billion Digit Mersenne prime. There isn't hope of really finding such a prime with today's technology and algorithms. A Lucas-Lehmer primality test is estimated to require 852 years. Perhaps much longer because many of us won't use modern hardware on a whimsical project; I'm using a Pentium Pro 180 and Luigi is using a P2 250. P-1, P+1, and ECM tests are also unfeasible because they require operations modulo the billion digit number. The only part of this project that can be undertaken today is trial factoring, and even that cannot be done with the efficient Prime95 program. Luigi, aka "ET_" on the MersenneForum.org boards, has written a trial factoring program that can handle these numbers.

# Progress is Now at Level 19.06

Level 20 will be twenty candidates trial factored to at least 86 bits.
Level 19 is nineteen candidates trial factored to at least 85 bits.
Level 18 is eighteen candidates trial factored to at least 84 bits.

There will be twenty-one steps from Level 19 to Level 20: getting a twentieth candidate to 85 bits and getting each candidate from 85 to 86 bits. Each of these steps will be indicated with a decimal point (19.01, 19.02, through 19.20, then 20.00).

 Exponentunknown Bits Exponentcomposite Bits Factors Searcher 3321928097 80 6158854691839 41457662650561 7771207163883536443921 dsouza123 Luigi Oliver 3321928109 76 408676883681617 William 3321928121 76 684317192927 502959849088127 William Luigi 3321928171 84 3321928189 76 312261249767 43284724302671 William William 3321928217 76 1166521668825287 William 3321928219 80 670475084138875461500081 Oliver 3321928241 83 3321928243 76 619406102645311603441 Carlo 3321928307 83 3321928319 83 3321928373 83 3321928381 83 3321928391 76 260093705301737 578015540034001 Luigi Luigi 3321928417 83 3321928439 76 468552214000564196383 MrHappy 3321928483 83 3321928501 76 391987563119 Luigi 3321928513 76 14749362597721 256998380021105500319 Luigi Patrick Schmeer 3321928531 76 437571069960383 Luigi 3321928567 76 6378501480068041 3650224967587337351 74195408962462535089 Luigi Rde Patrick Schmeer 3321928601 83 3321928607 76 59794714927 Luigi 3321928619 76 797262868561 48684837137044687 59077344656726951 Luigi Luigi Luigi 3321928661 76 19931571967 Luigi 3321928679 75 325549010543 Luigi 3321928697 84 3321928699 84 3321928703 76 2577816673529 558801558703849 80064692506573275079 Luigi Luigi Patrick Schmeer 3321928777 84 3321928787 76 108855788204768513089 thomasn 3321928849 76 9415489101590057 Luigi 3321928919 76 797189858123783 Luigi 3321928921 76 2126624089497447084199 Carlo 3321928927 84 3321928949 76 1375278584887 218868942175952957527 Luigi Patrick Schmeer 3321928963 84 3321928991 75 945422219952326671 Luigi 3321928993 75 18791328475010737 Luigi 3321928999 77 97924979511078172425361 Oliver 3321929029 75 42168567094127 Uncwilly 3321929041 84 3321929053 84 3321929059 84 3321929113 84 3321929129 75 1063017321281 406550974523537 446771855975579753 Uncwilly Uncwilly Uncwilly 3321929173 84 3321929179 84 3321929197 84 3321929209 84 3321929257 75 1275434806649609 Uncwilly 3321929339 75 5106177450128969 Uncwilly 3321929357 75 26575434857 6350799856004899669463 Uncwilly Oliver 3321929393 75 5921511883350937 35018683424306311 Uncwilly Uncwilly 3321929411 84 3321929461 75 190321952205082414447 Andres Aitsen 3321929477 75 595324177467781721 40584264169612484969 Uncwilly Patrick Schmeer 3321929509 75 1455005124943 Uncwilly 3321929519 84 3321929531 75 2074963555230407 4584880631672767 Uncwilly Uncwilly 3321929551 75 8174238826850191 Uncwilly 3321929563 84 3321929573 84 3321929579 75 1055548986560900822153 Rde 3321929587 75 2853464432782087 Uncwilly 3321929599 75 11719767625273 Uncwilly 3321929603 75 6643859207 Uncwilly 3321929617 84 3321929621 84 3321929683 75 53150874929 Uncwilly 3321929701 84 3321929749 75 471714024359 Uncwilly 3321929759 75 4103086300931724495689 thomasn 3321929777 75 425207011457 13219240369219034113 Uncwilly Rde 3321929789 84 3321929827 82 73716630445294762224353 Andres Aitsen 3321929843 80 6643859687 3195696508967 524208687885094409 132697127323609301207 2947492197366428673583 Uncwilly Uncwilly Rde Patrick Schmeer Oliver 3321929861 75 12413327709847303 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26684570938036205809 Uncwilly Uncwilly Uncwilly Rde Rde 3321931981 75 623234030420949559 Uncwilly 3321931993 83 3321932063 75 1175963950303 2742985743060361 Uncwilly Uncwilly 3321932093 83 3321932099 75 483792398236284953 51043506150165031487 Uncwilly Patrick Schmeer 3321932111 83 3321932123 83 3321932143 83 3321932149 75 1785252843922687 Uncwilly 3321932161 86 3321932179 75 9700207262025227041 Curtis 3321932189 75 558084607753 Uncwilly 3321932249 75 129581933168993 Uncwilly 3321932353 75 372056423537 Uncwilly 3321932359 86 3321932377 75 817195364743 Uncwilly 3321932407 75 11241419265289 Uncwilly 3321932423 75 4092620745137 830728928749303 Uncwilly Uncwilly 3321932443 75 1143949670281329107993 Luigi 3321932473 75 79726379353 5768855748580684424359 Uncwilly Oliver 3321932479 75 132877299161 6856468636657 Uncwilly Uncwilly 3321932491 86 28126803354429776910329417 aketilander 3321932567 86 3321932591 75 444143875642500769 Uncwilly 3321932597 75 3743412761042167 Uncwilly 3321932701 75 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3321933253 83 3321933271 75 5215435235471 Uncwilly 3321933281 75 247169243036792441 20842680057158059318249 Uncwilly Oliver 3321933287 75 8637026546201 Uncwilly 3321933289 83 3321933313 83 3321933337 83 3321933341 75 6879458194543721 620045604917690104273 Uncwilly Luigi 3321933361 83 3321933367 83 3321933379 75 7467706235993 Uncwilly 3321933389 83 3321933397 81 558084810697 16104733108657 974759534169131831 Uncwilly Uncwilly Patrick Schmeer 3321933451 83 3321933469 75 31007997831543599089 Patrick Schmeer 3321933473 75 487044233056784479 501613681828405961 5883891163931472673 278312000858867160103 Uncwilly Uncwilly Luigi Luigi 3321933541 83 3321933551 83 3321933577 83 3321933607 75 65488599128399 Uncwilly 3321933613 83 3321933661 83 3321933679 83 3321933689 75 44258400890014668689 Patrick Schmeer 3321933691 75 3248851149799 Uncwilly 3321933697 75 418563645823 25865392960531463 697364784792616751641 Uncwilly Patrick Schmeer Luigi 3321933709 75 79726409017 2524696194309673 Uncwilly Uncwilly 3321933721 75 132877348841 Uncwilly 3321933781 75 1913433857857 97612971199608343 Uncwilly Patrick Schmeer 3321933829 75 14277645021571369 Uncwilly 3321933893 76 36285087986156170392041 lavalamp 3321933917 75 285686316863 Uncwilly 3321933931 75 55739579843335337 Uncwilly 3321933971 75 6643867943 Uncwilly 3321934003 83 3321934051 83 3321934069 75 3262139255759 Uncwilly 3321934081 75 19931604487 Uncwilly 3321934097 75 607276128404377 15812406301721 615056098059551 Uncwilly Uncwilly Uncwilly 3321934129 83 3321934163 83 3321934193 83 3321934199 79 308387132301983065210409 Christenson 3321934207 76 47533991797717340492791 Aillas 3321934211 75 391782276976919 Uncwilly 3321934223 75 3885952146986279 Uncwilly 3321934237 75 59688514370417 19931605423 Uncwilly Uncwilly 3321934241 83 3321934243 84 3321934247 84 3321934271 75 7334830870369 Uncwilly 3321934307 83 8549101696397212690851457 aketilander 3321934379 84 3321934391 75 75670848426616433 Uncwilly 3321934403 75 194148940484324943191 gjmccrac 3321934433 75 1893290023006289 6342547534666724263 Uncwilly gjmccrac 3321934463 75 23306692192409 35717439346177 Uncwilly Uncwilly 3321934471 75 1337729723733817 68440096871362946921 Uncwilly gjmccrac 3321934537 84 3321934579 75 3980838549161824437481 firejuggler 3321934591 75 11593551722591 Uncwilly 3321934607 84 3321934633 75 116728996875129123113 gjmccrac 3321934687 75 59794824367 Uncwilly 3321934697 84 3321934709 75 378121774679999658041 1839558484365372097673 gjmccrac & Rodrigo Rodrigo 3321934739 75 367778038824169 Uncwilly 3321934741 75 7746884766484204303 gjmccrac 3321934751 75 983292686297 216297815507113 36323492823707124479 84474066559669972439 Uncwilly Uncwilly gjmccrac gjmccrac 3321934757 84 3321934769 75 428278227684768847 113096593114556228647 200343264327196739657 Uncwilly gjmccrac gjmccrac 3321934783 84 3321934801 84 3321934807 75 21579288506273 Uncwilly 3321934817 75 51500586635566231 6697894572190743799 11153949230292921599 Uncwilly gjmccrac gjmccrac 3321934831 84 3321934843 75 177665502036166583753 gangho 3321934849 75 4222013096336551 Uncwilly 3321934907 75 2174538590122201 Uncwilly 3321934909 83 3321934937 75 186028356473 862161705809233 Uncwilly Uncwilly 3321934951 83 3321935017 83 3321935021 83 3321935033 75 4889888368577 Uncwilly 3321935117 75 259110939127 Uncwilly 3321935119 75 79726442857 Uncwilly 3321935179 75 37627165053551160863 gjmccrac 3321935203 75 385457429344903 1857446781016639 Uncwilly Uncwilly 3321935209 79 493977517166390327987471 firejuggler 3321935213 83 3321935237 75 1450649254775057 643749876865272623 Uncwilly gjmccrac 3321935249 77 139473106885101315506711 Rodrigo 3321935263 75 1807132783073 658657646944513310407 Uncwilly firejuggler 3321935321 83 3321935327 80 675711084621646309671833 Rodrigo 3321935341 75 527729292141943 279389697599393137 Uncwilly gjmccrac 3321935387 75 9057934700146700447 gjmccrac 3321935437 75 294562127559994081 1695317956952380524487 Uncwilly firejuggler 3321935567 83 3321935569 81 1937278552181490609610657 Luigi 3321935581 75 2344665191939006081543 gjmccrac 3321935627 75 26575485017 7557397518789901369 Uncwilly gjmccrac 3321935629 75 823837079469290191 Uncwilly 3321935633 75 2331998814367 Uncwilly 3321935647 75 21187305556567 5049235881499297 Uncwilly Uncwilly 3321935651 75 495127864910249 68014863882259892809 Uncwilly gjmccrac 3321935689 77 118924509745675004089871 bloodIce 3321935741 75 298814763774433 Uncwilly 3321935759 75 6643871519 3727211921599 Uncwilly Uncwilly 3321935783 75 6643871567 Uncwilly 3321935791 75 1866927914543 Uncwilly 3321935797 83 3321935801 83 3321935833 75 10676232922599356300327 monst 3321935843 75 88211853696438737 Uncwilly 3321935849 75 79726460377 Uncwilly 3321935857 75 590826223782593 Uncwilly 3321935861 83 3321935891 83 9573316202778896180247937 Rodrigo 3321935959 75 132877438361 Uncwilly 3321935963 83 3321936043to 3321999991 Not Yet Open 60 Many, available directly or from Will Edgington Uncwilly

# History

On 3 April 2004 and the following days several proposals were discussed for balancing the depth and breadth of trial factoring. The consensus was to use a method that went one candidate broader with each bit deeper, starting with the then achieved result of one candidate trial factored to 67 bits.

 Level 20 Twenty Candidates to 86 bits In Progress Level 19 Nineteen Candidates to 85 bits 26 Aug 2012 Level 18 Eighteen Candidates to 84 bits 12 June 2012 Level 17 Seventeen Candidates to 83 bits 22 July 2011 Level 16 Sixteen Candidates to 82 bits 4 July 2011 Level 15 Fifteen Candidates to 81 bits 26 Nov 2010 Level 14 Fourteen Candidates to 80 bits 15 June 2010 Level 13 Thirteen Candidates to 79 bits 6 June 2010 Level 12 Twelve Candidates to 78 bits 16 Sept 2009 Level 11 Eleven Candidates to 77 bits 28 May 2009 Level 10 Ten Candidates to 76 bits 16 May 2009 Level 9 Nine Candidates to 75 bits 3 Dec 2007 Level 8 Eight Candidates to 74 bits 10 May 2006 Level 7 Seven Candidates to 73 bits 28 Jan 2005 Level 6 Six Candidates to 72 bits 23 July 2004 Level 5 Five Candidates to 71 bits 22 May 2004 Level 4 Four Candidates to 70 bits 03 May 2004 Level 3 Three Candidates to 69 bits 12 Apr 2004 Level 2 Two Candidates to 68 bits 07 Apr 2004 Level 1 One Candidate to 67 bits 26 Mar 2004

You need Luigi's factor program. The latest and fastest is factor5, although memory limited machines may prefer the older factor3_2.

You also need some Cygwin files. If you install Cygwin it has a system to help you keep current with the files you are using. Alternatively, you can get just the two files that are needed here: cygwin1.dll and cyggmp-3.dll are both in this zip file.

# Instructions

Find the next unassigned exponent in the table below, and post a message on the Operation Billion Digit thread to let people know it's now taken.

Open a DOS box and start the factor3_2 (or whichever you downloaded) program. It will prompt for your Mersenne exponent and your beginning and ending factoring exponents. Our plan is to start at 67 digits and extend one digit deeper for every prime broader. So if you are the fourth person joining, we would all attempt to reach 70 digits.

Seriously consider going to the task manager and changing the priority to low.

If the program ends, the next time use the restart flag "factor3_2 -r"