macbook:~ languasc$ gp2c-run -pmy_ -g -W /Users/languasc/Desktop/Msum-progressions130.gp /Users/languasc/Desktop/Msum-progressions130.gp.c: In function `my_mertenssum': /Users/languasc/Desktop/Msum-progressions130.gp.c:81: warning: unused variable `my_rows' /Users/languasc/Desktop/Msum-progressions130.gp.c:81: warning: unused variable `my_lines' /Users/languasc/Desktop/Msum-progressions130.gp.c:81: warning: unused variable `my_col' /Users/languasc/Desktop/Msum-progressions130.gp.c:81: warning: unused variable `my_j' /Users/languasc/Desktop/Msum-progressions130.gp.c:81: warning: unused variable `my_u' /Users/languasc/Desktop/Msum-progressions130.gp.c:81: warning: unused variable `my_a' /Users/languasc/Desktop/Msum-progressions130.gp.c: In function `my_chibern': /Users/languasc/Desktop/Msum-progressions130.gp.c:701: warning: unused variable `my_r' /Users/languasc/Desktop/Msum-progressions130.gp.c: In function `my_bernpol': /Users/languasc/Desktop/Msum-progressions130.gp.c:726: warning: unused variable `my_j' /Users/languasc/Desktop/Msum-progressions130.gp.c: In function `my_LEuler': /Users/languasc/Desktop/Msum-progressions130.gp.c:754: warning: unused variable `my_i' /Users/languasc/Desktop/Msum-progressions130.gp.c:754: warning: unused variable `my_j' /Users/languasc/Desktop/Msum-progressions130.gp.c: In function `my_rootnumber': /Users/languasc/Desktop/Msum-progressions130.gp.c:814: warning: unused variable `my_j' /Users/languasc/Desktop/Msum-progressions130.gp.c: In function `my_Smchi': /Users/languasc/Desktop/Msum-progressions130.gp.c:1123: warning: unused variable `my_v' /Users/languasc/Desktop/Msum-progressions130.gp.c:1123: warning: unused variable `my_k' /Users/languasc/Desktop/Msum-progressions130.gp.c:1123: warning: unused variable `my_i' /Users/languasc/Desktop/Msum-progressions130.gp.c:1123: warning: unused variable `my_a' /Users/languasc/Desktop/Msum-progressions130.gp.c:1123: warning: unused variable `my_j' /Users/languasc/Desktop/Msum-progressions130.gp.c: In function `my_genchar': /Users/languasc/Desktop/Msum-progressions130.gp.c:1256: warning: unused variable `my_k' /Users/languasc/Desktop/Msum-progressions130.gp.c:1256: warning: unused variable `my_i' /Users/languasc/Desktop/Msum-progressions130.gp.c:1256: warning: unused variable `my_l' /Users/languasc/Desktop/Msum-progressions130.gp.c:1256: warning: unused variable `my_u' /Users/languasc/Desktop/Msum-progressions130.gp.c: In function `my_gencharmodprime': /Users/languasc/Desktop/Msum-progressions130.gp.c:1568: warning: unused variable `my_k' /Users/languasc/Desktop/Msum-progressions130.gp.c:1568: warning: unused variable `my_j' /Users/languasc/Desktop/Msum-progressions130.gp.c: In function `my_gencharcyclic': /Users/languasc/Desktop/Msum-progressions130.gp.c:1680: warning: unused variable `my_a' /Users/languasc/Desktop/Msum-progressions130.gp.c:1680: warning: unused variable `my_k' /Users/languasc/Desktop/Msum-progressions130.gp.c:1680: warning: unused variable `my_l' /Users/languasc/Desktop/Msum-progressions130.gp.c: In function `my_gencharpowersoftwo': /Users/languasc/Desktop/Msum-progressions130.gp.c:1823: warning: unused variable `my_j2' /Users/languasc/Desktop/Msum-progressions130.gp.c:1823: warning: unused variable `my_j1' /Users/languasc/Desktop/Msum-progressions130.gp.c:1823: warning: unused variable `my_a' /Users/languasc/Desktop/Msum-progressions130.gp.c:1823: warning: unused variable `my_k' GP/PARI CALCULATOR Version 2.3.5 (released) i386 running darwin (x86-64/GMP-5.0.1 kernel) 64-bit version compiled: May 27 2010, gcc-4.2.1 (Apple Inc. build 5659) (readline v6.1 enabled, extended help available) Copyright (C) 2000-2006 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 8000000, primelimit = 500000 ? mertenssum(100) ************ A. LANGUASCO & A. ZACCAGNINI ************* ****** COMPUTATION OF THE MERTENS CONSTANTS FOR THE SUM MOD 100 ******* ****** WITH A PRECISION OF AT LEAST 130 DECIMAL DIGITS ******* q= 100 precomputations (quite long); depends on phi(q). Main parameters: for their meaning see the paper A= 3200 K= 34 N= 31100 T= 120 ********** ERRORS ************** Errors: see the paper for their definitions and estimations err1= 6.93258941307095088706786128973270027388204496406711147718562367580534864061228226102939855619747819639946280071783422828847898759627471876841763879759 E-139 U = 0.430408940964004038889433232950605425424570682540289654757006103992561215461131961361490264697219955406330542783242653563637061235142911834438694912209 err3= 3.25765555621635059354822190739914894477929875222238805096246184509471318100253651948599775425246871393387995653492952766410921676879011734311144977491 E-137 totalerr= 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 used level of primes: B= min(A*q,9600) = 9600 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 1 is = -0.0327328506433100964865591320930048072116438944230580812123969878411668305666432779058159373870616632469149389219354796589435060666487892035718217873925 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 3 is = 0.296796051280987294742970937513218999433325601239321356892232047773962084736794303587697038184312968741046908428311550682108314418228512185814609522938 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 7 is = 0.109164660582488612007924295113635623988824110708222892563560968656152306277518563610826956502528604956207588722080350206287073587318617088315942281639 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 9 is = -0.0317072585110717311614975891439776768183338182503369107750009738720300343420972220122589012325102372688889071984157440962950487510585867551184519202181 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 11 is = 0.0525392593617032986211242722948319599868308022971932509427005952209928022291289982022603850380106786565197770606901748805760744623937223940482361839045 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 13 is = 0.0426109269250587204358452633135599416192357324245437172834703756014952013688853608925704955282478993133346571074457600200815279082134799290612405113824 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 17 is = 0.0150314878146081597086876326404899084997994990199612843462168889064803550490083230918214280321926721787298859184277895547952444473857970476350834054356 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 19 is = 0.0109334390998046805514799425989118847223839795741349842084312433122734160655203037595963028420462413570596672376585264935009371617797326720700074729392 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 21 is = -0.0417987666199882381554101070045008003381487531805600975523878180039230858196302235656253797830373191616953674729603120999080562507877095699491499544669 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 23 is = 0.00429980733850639333208812186069401128116915699348246617141047798817040453762193285902463341836647089195115507728847566775982371098680720261523750977953 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 27 is = -0.0341176432026934031798118897841360406727175517993793376884864059556879259837133958935214866013236601483299529423674988857556007229283776150753328028601 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 29 is = -0.00684556550845667228277778030463854728375793923422527354916808650949702410907799026613193419319878989711435385277761437968248940561579972644133884268144 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 31 is = -0.000882019747089267191689451734045295106533287619236174773020817566409194489590899552019467854901157970631230058009645211540616655559817506675118024772577 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 33 is = -0.0398162557586811487218938785343754046573555818959406283146822724901401059496759353744927958293554690023722370287004243249402784082699977733593324982342 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 37 is = -0.0102279906317679444335912720164744293764558048990475039302884280614981794081982643974150883523589601353706711212898333714345802821100192321429488327433 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 39 is = -0.0321595332963616451080367909504231097305999133684914348622917500796534432626879721026712661910249376449870826554815360731330369048798166591494065712901 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 41 is = -0.0174449250429062421986041546085092898562048212570655213998527490583655005960687478561088743402085027527269455554486821425573629607832809646696053799588 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 43 is = -0.0211360658221425540355687928175262101048822207383699351503859306267612949104547137611977567578819332834762452273108596440895609150991187093063974760897 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 47 is = -0.0204531829766119508711316300183053778265915710908097387335274555231812426195606139016419850746285688170957870912089063200131390410267047480795002622719 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 49 is = -0.0366254740517904877152631123883871179081152057919444361549484792898196995999374244958859644167239276685344360793325474743966314524739307927089879062793 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 51 is = -0.0351434786950777268987719834938725009588029958572354007673240324009063727900325636416481626443088305493772336656968837173458149320132130502746269565729 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 53 is = -0.0226972066993157647309792376402909270586316096081411123036241598565913796393917259322979452776305606038125579335685484448632675759563467766191851425166 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 57 is = -0.0325765749024211602755096901379087165722110325763499330143698983697775611640085788035090563921728599468216937898749461568121311089217525332839731241471 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 59 is = -0.0255972500173944737573300788977412693450547816527269774329641314670480954987063024252686826569450208294041164666797055416328815523619275692904228334058 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 61 is = -0.0278286463430071239161270301682991077533575587261217818741249652711993097567322510709369304053300945036413356408079012202473850964386642334016485618504 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 63 is = -0.0335981132403069486459144502313207373190111663759397837651621329964643563356665778936948693359647683261959202383896027165664223991779765394955812477910 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 67 is = -0.0215622199307553304269482499263860330611608283824490222680448081698435594665783769604302759934475971674845573342006464114637311647129327045986330373043 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 69 is = -0.0425884782618983166596496197101822785384127993507272767348175726565791342019871014976242480049024428717732247362747955014734548534306415568144304803176 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 71 is = -0.0281279461582123388760458288494394727596857103723780656130996327603893880747767454505691547630829301597841499582259610309148890238853203581962826432787 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 73 is = -0.0242942021393837676448545674808807411661745595581368268861597494129926328085557880202457801790921732593930655889514848110631560468102962622674461506165 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 77 is = -0.0403016818292845344264159233808642777486104026960193440007596505037316748622741678183780453179030018600247570208326034289775868328481133803111256125901 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 79 is = -0.0258608096502094405172333084018448635774209954760710635781321048885967738076186542713920725214721231729358897410952025779581974975174729447067902265140 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 81 is = -0.0382936433211064890956609925860194834407109213463456897416664475021448135348394117206912316011516049681152827764139219558860765229882479594434695180546 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 83 is = -0.0266126795143592885540643412538428925936537283459286198855340428842290207314921833082858361852329847769143118719537892751869749677608905305210379334580 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 87 is = -0.0412427727572622471627739267758883931022346126834504991917311844751862875105689902159660736986203532099681253425198680241294032689420800896689921599127 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 89 is = -0.0340854865585412017841720068124490112177507676171172246971874453810296105419947000154941366243558251159080727046307358474167001472878837371621738252018 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 91 is = -0.0391214327782647589416235354311767335466234788518395944921607850772238365854496509926165638950119872089792658331427168065065265985927061145516180504673 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 93 is = -0.0369018583285861763311254259678182751760400661597029348458943962919753530323607396697845860495980121542689337967621422359084522854313806781588513826467 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 97 is = -0.0276176058143249827783865174148928153613240611206033456003353665956627926716780840170735879716274742451221573663735064377243003655729391259832389632759 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** FINAL RESULT ******** M(q,a) with q = 100 and a = 99 is = -0.0398788008029309226792713307672238332917897936899111754264277216948965446950603014789605305793931131151691036637825596825583453141438886940199493768645 with error <= of 3.24380691408838359985842800728906404883016622181648268659096012980644750072344285854388444631908240850042771992855517319831915647863404291752573550882 E-137 number of the correct decimal digits = 134 ****** SUM VERIFICATION ******** The sum of these constants is = -0.438502787152357216244573161391304140948433351738800793807935786075075489102631790285857368565753348948382271123513978002216609675729955575456512598028 The error from its expected value is = 1.7900017754880496185 E-154 ****** COMPUTATION TIME ******** Elapsed time for the precomputation: 8 min, 21 sec, 209 millisec Elapsed time for the final computation: 0 min, 0 sec, 47 millisec Total elapsed time: 8 min, 21 sec, 256 millisec ****** END PROGRAM ********