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 2018-12-17, 06:24 #59 GP2     Sep 2003 5·11·47 Posts As mentioned before, there are good reasons to believe that we have already discovered all factors of size 65 bits or less of all Mersenne numbers with prime exponent less than 1 billion. (We can expect TJAOI to complete the 66-bit level by August 2019). Therefore this subset of all known factors is unchanging and complete, and can be suitable for various forms of analysis without any selection bias. In the table below: The 1st column is the starting point of the exponent range, in millions. Obviously we only consider prime exponents. The 2nd column is the average number of factors (of size 65 bits or less) of an exponent in this exponent range. The 3rd column is the total number of exponents in this exponent range. The subsequent columns show how many exponents in this range have 0, 1, 2, 3, 4, 5 or 6 factors (of size 65 bits or less). In each range there are a few exponents with 7 or more such factors, but this is omitted in the display table. We might expect the columns to form a Poisson distribution where k is the number of factors and the second column represents λ. Based on the heuristics in the 1983 paper by Wagstaff, we expect exponents with p=1 (mod 4) to have slightly fewer factors than exponents with p=3 (mod 4), and we see that below. (Divisors of Mersenne numbers ; Math. Comp. 40 (1983), 385-397 ; https://doi.org/10.1090/S0025-5718-1983-0679454-X ) However, neither those heuristics nor the data in the table below can explain the much stronger prevalence of p=1 (mod 4) vs. p=3 (mod 4) among the 50 known Mersenne primes with odd exponent: 31 of them are p=1, and 19 of them are p=3. Code: ******** For exponents with p = 2 (mod 4) 000 0.0000 1 [(0, 1)] ******** For exponents with p = 1 (mod 4) 000 1.0152 332180 [(0, 120212), (1, 122532), (2, 61818), (3, 21017), (4, 5273), (5, 1099), (6, 195)] ... 010 0.9229 302990 [(0, 119978), (1, 111570), (2, 51420), (3, 15736), (4, 3542), (5, 639), (6, 88)] ... 020 0.8993 293609 [(0, 119111), (1, 107759), (2, 48503), (3, 14406), (4, 3188), (5, 558), (6, 74)] ... 030 0.8794 287908 [(0, 119039), (1, 105783), (2, 45990), (3, 13634), (4, 2890), (5, 488), (6, 69)] ... 040 0.8608 283765 [(0, 119754), (1, 103583), (2, 44414), (3, 12765), (4, 2759), (5, 418), (6, 66)] ... 050 0.8561 280218 [(0, 118645), (1, 102342), (2, 43836), (3, 12264), (4, 2626), (5, 444), (6, 52)] ... 060 0.8462 278048 [(0, 118877), (1, 101523), (2, 42676), (3, 11995), (4, 2536), (5, 381), (6, 54)] ... 070 0.8379 275655 [(0, 118771), (1, 100479), (2, 42016), (3, 11598), (4, 2349), (5, 392), (6, 47)] ... 080 0.8287 274020 [(0, 119116), (1, 99895), (2, 41031), (3, 11303), (4, 2226), (5, 391), (6, 50)] ... 090 0.8247 272111 [(0, 119052), (1, 98674), (2, 40528), (3, 11228), (4, 2209), (5, 370), (6, 45)] ... 100 0.8200 270854 [(0, 119277), (1, 97805), (2, 40087), (3, 11072), (4, 2229), (5, 340), (6, 32)] ... 110 0.8146 269117 [(0, 118643), (1, 97812), (2, 39589), (3, 10548), (4, 2112), (5, 352), (6, 56)] ... 120 0.8132 268389 [(0, 118642), (1, 97280), (2, 39395), (3, 10535), (4, 2173), (5, 315), (6, 42)] ... 130 0.8100 267056 [(0, 118414), (1, 96779), (2, 39002), (3, 10361), (4, 2109), (5, 332), (6, 49)] ... 140 0.8032 266064 [(0, 118936), (1, 95887), (2, 38674), (3, 10197), (4, 2020), (5, 306), (6, 38)] ... 150 0.8023 264739 [(0, 118160), (1, 95821), (2, 38400), (3, 10058), (4, 1946), (5, 312), (6, 36)] ... 160 0.7970 264226 [(0, 118717), (1, 95378), (2, 37800), (3, 10081), (4, 1920), (5, 288), (6, 36)] ... 170 0.7983 263745 [(0, 118226), (1, 95421), (2, 37804), (3, 10056), (4, 1894), (5, 296), (6, 43)] ... 180 0.7949 262664 [(0, 118482), (1, 94497), (2, 37494), (3, 9858), (4, 1986), (5, 301), (6, 40)] ... 190 0.7901 261462 [(0, 118347), (1, 94226), (2, 36974), (3, 9664), (4, 1898), (5, 301), (6, 48)] ... 200 0.7842 261268 [(0, 118945), (1, 93783), (2, 36953), (3, 9480), (4, 1802), (5, 274), (6, 26)] ... 210 0.7868 260763 [(0, 118426), (1, 93748), (2, 36811), (3, 9661), (4, 1806), (5, 271), (6, 37)] ... 220 0.7828 259931 [(0, 118565), (1, 93368), (2, 36473), (3, 9311), (4, 1878), (5, 297), (6, 33)] ... 230 0.7781 259477 [(0, 118751), (1, 93317), (2, 36091), (3, 9240), (4, 1760), (5, 275), (6, 37)] ... 240 0.7788 258715 [(0, 118349), (1, 92997), (2, 36029), (3, 9308), (4, 1705), (5, 284), (6, 42)] ... 250 0.7780 258403 [(0, 118461), (1, 92649), (2, 35963), (3, 9250), (4, 1757), (5, 270), (6, 48)] ... 260 0.7761 258126 [(0, 118567), (1, 92505), (2, 35778), (3, 9220), (4, 1729), (5, 286), (6, 37)] ... 270 0.7752 257244 [(0, 118461), (1, 91846), (2, 35685), (3, 9179), (4, 1763), (5, 270), (6, 33)] ... 280 0.7759 256730 [(0, 117902), (1, 92028), (2, 35602), (3, 9167), (4, 1742), (5, 247), (6, 41)] ... 290 0.7700 256241 [(0, 118610), (1, 91515), (2, 35054), (3, 8954), (4, 1774), (5, 294), (6, 34)] ... 300 0.7707 256288 [(0, 118497), (1, 91365), (2, 35465), (3, 8940), (4, 1734), (5, 265), (6, 17)] ... 310 0.7690 255394 [(0, 118102), (1, 91408), (2, 34975), (3, 8953), (4, 1660), (5, 251), (6, 40)] ... 320 0.7663 254928 [(0, 118407), (1, 90886), (2, 34735), (3, 8896), (4, 1738), (5, 234), (6, 32)] ... 330 0.7632 254683 [(0, 118347), (1, 91163), (2, 34536), (3, 8692), (4, 1690), (5, 225), (6, 29)] ... 340 0.7613 254161 [(0, 118365), (1, 90866), (2, 34317), (3, 8740), (4, 1634), (5, 201), (6, 34)] ... 350 0.7656 253755 [(0, 117855), (1, 90650), (2, 34424), (3, 8847), (4, 1691), (5, 261), (6, 24)] ... 360 0.7599 253710 [(0, 118354), (1, 90528), (2, 34347), (3, 8656), (4, 1556), (5, 244), (6, 24)] ... 370 0.7590 253403 [(0, 118345), (1, 90378), (2, 34241), (3, 8576), (4, 1599), (5, 232), (6, 28)] ... 380 0.7559 253077 [(0, 118639), (1, 90175), (2, 33835), (3, 8559), (4, 1601), (5, 241), (6, 26)] ... 390 0.7571 252490 [(0, 118123), (1, 90175), (2, 33842), (3, 8434), (4, 1624), (5, 264), (6, 25)] ... 400 0.7542 252255 [(0, 118514), (1, 89424), (2, 34196), (3, 8339), (4, 1527), (5, 227), (6, 24)] ... 410 0.7542 251924 [(0, 118274), (1, 89627), (2, 33848), (3, 8336), (4, 1572), (5, 233), (6, 32)] ... 420 0.7544 251590 [(0, 118026), (1, 89648), (2, 33732), (3, 8341), (4, 1578), (5, 239), (6, 25)] ... 430 0.7498 251025 [(0, 118361), (1, 89018), (2, 33731), (3, 8187), (4, 1494), (5, 194), (6, 37)] ... 440 0.7513 251535 [(0, 118405), (1, 89461), (2, 33629), (3, 8207), (4, 1568), (5, 227), (6, 32)] ... 450 0.7476 250626 [(0, 118200), (1, 89381), (2, 33186), (3, 8106), (4, 1496), (5, 230), (6, 22)] ... 460 0.7505 250429 [(0, 117838), (1, 89132), (2, 33605), (3, 8093), (4, 1510), (5, 224), (6, 21)] ... 470 0.7469 250328 [(0, 118193), (1, 89184), (2, 33029), (3, 8247), (4, 1427), (5, 207), (6, 35)] ... 480 0.7465 249898 [(0, 118291), (1, 88608), (2, 33068), (3, 8194), (4, 1489), (5, 221), (6, 25)] ... 490 0.7463 249591 [(0, 118181), (1, 88536), (2, 32964), (3, 8121), (4, 1538), (5, 227), (6, 20)] ... 500 0.7416 249413 [(0, 118510), (1, 88427), (2, 32795), (3, 8023), (4, 1425), (5, 210), (6, 21)] ... 510 0.7480 249280 [(0, 117800), (1, 88391), (2, 33159), (3, 8213), (4, 1494), (5, 202), (6, 16)] ... 520 0.7418 249065 [(0, 118347), (1, 88300), (2, 32711), (3, 8071), (4, 1395), (5, 212), (6, 26)] ... 530 0.7436 248897 [(0, 118158), (1, 88102), (2, 32885), (3, 8051), (4, 1491), (5, 182), (6, 25)] ... 540 0.7387 248580 [(0, 118364), (1, 88319), (2, 32333), (3, 7900), (4, 1417), (5, 215), (6, 28)] ... 550 0.7386 248341 [(0, 118335), (1, 87991), (2, 32474), (3, 7903), (4, 1427), (5, 187), (6, 22)] ... 560 0.7384 247962 [(0, 118180), (1, 88031), (2, 32136), (3, 7924), (4, 1463), (5, 201), (6, 26)] ... 570 0.7392 248316 [(0, 118431), (1, 87840), (2, 32403), (3, 7906), (4, 1522), (5, 182), (6, 30)] ... 580 0.7350 247663 [(0, 118698), (1, 87323), (2, 32110), (3, 7898), (4, 1408), (5, 203), (6, 22)] ... 590 0.7380 247605 [(0, 118160), (1, 87670), (2, 32163), (3, 7953), (4, 1449), (5, 187), (6, 21)] ... 600 0.7346 247249 [(0, 118476), (1, 87317), (2, 31960), (3, 7843), (4, 1430), (5, 194), (6, 27)] ... 610 0.7373 246725 [(0, 117915), (1, 87117), (2, 32254), (3, 7724), (4, 1503), (5, 179), (6, 32)] ... 620 0.7348 246873 [(0, 118224), (1, 87135), (2, 32093), (3, 7835), (4, 1376), (5, 189), (6, 17)] ... 630 0.7369 246609 [(0, 117684), (1, 87348), (2, 32269), (3, 7643), (4, 1444), (5, 203), (6, 16)] ... 640 0.7337 246608 [(0, 118104), (1, 87199), (2, 32058), (3, 7627), (4, 1400), (5, 186), (6, 33)] ... 650 0.7316 246038 [(0, 118042), (1, 87172), (2, 31553), (3, 7624), (4, 1401), (5, 232), (6, 14)] ... 660 0.7324 246119 [(0, 118289), (1, 86676), (2, 31867), (3, 7583), (4, 1461), (5, 206), (6, 37)] ... 670 0.7355 246091 [(0, 117651), (1, 87136), (2, 31963), (3, 7678), (4, 1443), (5, 199), (6, 20)] ... 680 0.7290 245793 [(0, 118326), (1, 86794), (2, 31405), (3, 7708), (4, 1356), (5, 188), (6, 15)] ... 690 0.7291 245481 [(0, 118155), (1, 86683), (2, 31476), (3, 7573), (4, 1385), (5, 181), (6, 26)] ... 700 0.7299 245622 [(0, 118226), (1, 86584), (2, 31609), (3, 7585), (4, 1389), (5, 204), (6, 22)] ... 710 0.7266 245171 [(0, 118232), (1, 86502), (2, 31453), (3, 7447), (4, 1316), (5, 194), (6, 24)] ... 720 0.7266 244938 [(0, 118206), (1, 86279), (2, 31459), (3, 7446), (4, 1317), (5, 205), (6, 26)] ... 730 0.7296 244738 [(0, 117833), (1, 86206), (2, 31517), (3, 7643), (4, 1323), (5, 195), (6, 19)] ... 740 0.7270 244396 [(0, 117892), (1, 86232), (2, 31194), (3, 7504), (4, 1359), (5, 191), (6, 22)] ... 750 0.7265 244705 [(0, 118039), (1, 86388), (2, 31265), (3, 7454), (4, 1328), (5, 206), (6, 23)] ... 760 0.7256 244807 [(0, 118018), (1, 86500), (2, 31518), (3, 7227), (4, 1329), (5, 191), (6, 21)] ... 770 0.7237 244132 [(0, 118332), (1, 85671), (2, 31214), (3, 7343), (4, 1344), (5, 200), (6, 26)] ... 780 0.7274 244460 [(0, 117872), (1, 86037), (2, 31604), (3, 7469), (4, 1272), (5, 171), (6, 32)] ... 790 0.7255 243975 [(0, 117583), (1, 86375), (2, 31171), (3, 7337), (4, 1294), (5, 189), (6, 19)] ... 800 0.7254 244097 [(0, 118032), (1, 85933), (2, 31048), (3, 7565), (4, 1293), (5, 195), (6, 29)] ... 810 0.7244 243536 [(0, 117913), (1, 85563), (2, 31131), (3, 7377), (4, 1317), (5, 213), (6, 20)] ... 820 0.7202 243656 [(0, 118302), (1, 85700), (2, 30833), (3, 7383), (4, 1250), (5, 170), (6, 18)] ... 830 0.7220 243486 [(0, 118020), (1, 85767), (2, 30805), (3, 7372), (4, 1322), (5, 175), (6, 24)] ... 840 0.7233 243081 [(0, 117853), (1, 85418), (2, 30815), (3, 7446), (4, 1329), (5, 203), (6, 15)] ... 850 0.7207 243037 [(0, 117767), (1, 85957), (2, 30526), (3, 7269), (4, 1280), (5, 209), (6, 26)] ... 860 0.7243 242782 [(0, 117445), (1, 85590), (2, 30783), (3, 7422), (4, 1310), (5, 201), (6, 31)] ... 870 0.7192 242938 [(0, 118238), (1, 85159), (2, 30795), (3, 7272), (4, 1255), (5, 192), (6, 25)] ... 880 0.7187 242350 [(0, 117888), (1, 85246), (2, 30439), (3, 7289), (4, 1285), (5, 175), (6, 24)] ... 890 0.7204 242536 [(0, 117603), (1, 85718), (2, 30420), (3, 7243), (4, 1335), (5, 196), (6, 19)] ... 900 0.7145 242910 [(0, 118873), (1, 84791), (2, 30619), (3, 7195), (4, 1241), (5, 171), (6, 18)] ... 910 0.7155 242624 [(0, 118434), (1, 85167), (2, 30354), (3, 7200), (4, 1266), (5, 172), (6, 27)] ... 920 0.7205 241813 [(0, 117625), (1, 84725), (2, 30654), (3, 7262), (4, 1341), (5, 190), (6, 14)] ... 930 0.7210 242235 [(0, 117740), (1, 84975), (2, 30609), (3, 7418), (4, 1281), (5, 193), (6, 15)] ... 940 0.7191 242177 [(0, 117781), (1, 85187), (2, 30427), (3, 7270), (4, 1305), (5, 175), (6, 31)] ... 950 0.7175 241702 [(0, 117544), (1, 85039), (2, 30641), (3, 7030), (4, 1258), (5, 171), (6, 16)] ... 960 0.7142 241850 [(0, 118124), (1, 84915), (2, 30221), (3, 7167), (4, 1253), (5, 151), (6, 19)] ... 970 0.7153 241371 [(0, 118063), (1, 84337), (2, 30313), (3, 7171), (4, 1292), (5, 172), (6, 23)] ... 980 0.7129 241561 [(0, 118240), (1, 84655), (2, 30084), (3, 7159), (4, 1226), (5, 178), (6, 16)] ... 990 0.7137 241289 [(0, 118130), (1, 84436), (2, 30076), (3, 7179), (4, 1271), (5, 177), (6, 19)] ... ******** For exponents with p = 3 (mod 4) 000 1.0599 332398 [(0, 114506), (1, 122927), (2, 64753), (3, 22756), (4, 5993), (5, 1186), (6, 239)] ... 010 0.9691 303038 [(0, 114718), (1, 111577), (2, 54225), (3, 17468), (4, 4152), (5, 765), (6, 116)] ... 020 0.9358 293643 [(0, 114611), (1, 108364), (2, 50821), (3, 15500), (4, 3590), (5, 645), (6, 91)] ... 030 0.9187 287887 [(0, 114200), (1, 106406), (2, 48621), (3, 14664), (4, 3269), (5, 603), (6, 108)] ... 040 0.9085 283715 [(0, 113773), (1, 104537), (2, 47578), (3, 14032), (4, 3114), (5, 592), (6, 81)] ... 050 0.8942 280763 [(0, 114118), (1, 103300), (2, 46445), (3, 13383), (4, 2933), (5, 516), (6, 60)] ... 060 0.8857 277901 [(0, 114063), (1, 102191), (2, 45080), (3, 13147), (4, 2838), (5, 511), (6, 62)] ... 070 0.8781 275663 [(0, 113923), (1, 101225), (2, 44494), (3, 12825), (4, 2683), (5, 452), (6, 54)] ... 080 0.8710 273552 [(0, 113932), (1, 100403), (2, 43569), (3, 12417), (4, 2752), (5, 421), (6, 51)] ... 090 0.8649 272390 [(0, 114342), (1, 99657), (2, 42895), (3, 12422), (4, 2572), (5, 436), (6, 58)] ... 100 0.8585 271000 [(0, 114214), (1, 99527), (2, 42251), (3, 11982), (4, 2519), (5, 447), (6, 53)] ... 110 0.8563 269222 [(0, 113782), (1, 98725), (2, 41828), (3, 11954), (4, 2451), (5, 411), (6, 61)] ... 120 0.8509 268150 [(0, 114190), (1, 97748), (2, 41697), (3, 11588), (4, 2448), (5, 409), (6, 62)] ... 130 0.8484 266956 [(0, 113618), (1, 97700), (2, 41454), (3, 11391), (4, 2350), (5, 374), (6, 61)] ... 140 0.8433 266133 [(0, 113951), (1, 97188), (2, 40961), (3, 11310), (4, 2277), (5, 396), (6, 46)] ... 150 0.8378 265323 [(0, 114048), (1, 97288), (2, 40167), (3, 11098), (4, 2304), (5, 362), (6, 49)] ... 160 0.8363 264399 [(0, 113697), (1, 96983), (2, 40125), (3, 10982), (4, 2176), (5, 385), (6, 46)] ... 170 0.8326 263557 [(0, 114295), (1, 95776), (2, 39910), (3, 10924), (4, 2266), (5, 326), (6, 52)] ... 180 0.8320 262424 [(0, 113602), (1, 95734), (2, 39743), (3, 10753), (4, 2168), (5, 378), (6, 40)] ... 190 0.8309 262002 [(0, 113579), (1, 95417), (2, 39823), (3, 10552), (4, 2208), (5, 385), (6, 34)] ... 200 0.8251 261421 [(0, 113902), (1, 95306), (2, 39138), (3, 10565), (4, 2170), (5, 294), (6, 41)] ... 210 0.8234 260151 [(0, 113789), (1, 94362), (2, 39008), (3, 10547), (4, 2065), (5, 344), (6, 33)] ... 220 0.8188 260102 [(0, 114289), (1, 94281), (2, 38687), (3, 10474), (4, 2012), (5, 321), (6, 35)] ... 230 0.8194 259494 [(0, 113915), (1, 94106), (2, 38782), (3, 10204), (4, 2126), (5, 322), (6, 34)] ... 240 0.8152 259059 [(0, 114084), (1, 94119), (2, 38358), (3, 10057), (4, 2088), (5, 307), (6, 39)] ... 250 0.8155 258139 [(0, 113480), (1, 94108), (2, 38058), (3, 10114), (4, 2002), (5, 328), (6, 42)] ... 260 0.8143 257398 [(0, 113585), (1, 93464), (2, 37699), (3, 10248), (4, 2059), (5, 298), (6, 43)] ... 270 0.8080 257441 [(0, 114004), (1, 93771), (2, 37506), (3, 9823), (4, 1985), (5, 305), (6, 40)] ... 280 0.8086 256864 [(0, 113869), (1, 93314), (2, 37358), (3, 10037), (4, 1932), (5, 299), (6, 48)] ... 290 0.8082 256421 [(0, 113590), (1, 93089), (2, 37763), (3, 9702), (4, 1907), (5, 324), (6, 41)] ... 300 0.8060 255908 [(0, 114030), (1, 92360), (2, 37327), (3, 9917), (4, 1932), (5, 295), (6, 43)] ... 310 0.8059 255291 [(0, 113703), (1, 92248), (2, 37195), (3, 9890), (4, 1892), (5, 319), (6, 36)] ... 320 0.8031 255341 [(0, 113915), (1, 92496), (2, 36860), (3, 9819), (4, 1916), (5, 290), (6, 42)] ... 330 0.8001 254447 [(0, 113444), (1, 92501), (2, 36923), (3, 9417), (4, 1857), (5, 273), (6, 28)] ... 340 0.7999 254760 [(0, 114245), (1, 91806), (2, 36770), (3, 9701), (4, 1889), (5, 315), (6, 29)] ... 350 0.7984 254007 [(0, 113595), (1, 92267), (2, 36503), (3, 9440), (4, 1844), (5, 323), (6, 29)] ... 360 0.7964 253407 [(0, 113855), (1, 91601), (2, 36179), (3, 9579), (4, 1879), (5, 280), (6, 30)] ... 370 0.7988 253565 [(0, 113536), (1, 91690), (2, 36738), (3, 9394), (4, 1893), (5, 272), (6, 38)] ... 380 0.7930 252760 [(0, 113893), (1, 91206), (2, 36203), (3, 9344), (4, 1802), (5, 279), (6, 29)] ... 390 0.7943 252626 [(0, 113646), (1, 91307), (2, 36155), (3, 9390), (4, 1809), (5, 271), (6, 47)] ... 400 0.7958 252132 [(0, 113456), (1, 90766), (2, 36314), (3, 9490), (4, 1784), (5, 283), (6, 36)] ... 410 0.7888 251842 [(0, 113865), (1, 90927), (2, 35836), (3, 9157), (4, 1736), (5, 286), (6, 30)] ... 420 0.7878 251981 [(0, 114035), (1, 91121), (2, 35464), (3, 9322), (4, 1740), (5, 257), (6, 35)] ... 430 0.7860 251480 [(0, 114127), (1, 90705), (2, 35357), (3, 9246), (4, 1744), (5, 265), (6, 35)] ... 440 0.7886 250948 [(0, 113305), (1, 90876), (2, 35657), (3, 9081), (4, 1727), (5, 272), (6, 25)] ... 450 0.7833 250884 [(0, 114310), (1, 90016), (2, 35483), (3, 9105), (4, 1666), (5, 269), (6, 30)] ... 460 0.7850 250741 [(0, 113786), (1, 90385), (2, 35502), (3, 9130), (4, 1670), (5, 228), (6, 36)] ... 470 0.7859 250378 [(0, 113431), (1, 90518), (2, 35371), (3, 9054), (4, 1722), (5, 248), (6, 28)] ... 480 0.7840 250046 [(0, 113693), (1, 90189), (2, 35010), (3, 9123), (4, 1735), (5, 256), (6, 35)] ... 490 0.7805 249908 [(0, 114093), (1, 89754), (2, 35212), (3, 8878), (4, 1663), (5, 273), (6, 33)] ... 500 0.7780 248972 [(0, 113746), (1, 89757), (2, 34794), (3, 8669), (4, 1719), (5, 250), (6, 33)] ... 510 0.7807 249155 [(0, 113471), (1, 89926), (2, 34988), (3, 8796), (4, 1685), (5, 257), (6, 30)] ... 520 0.7807 248946 [(0, 113511), (1, 89641), (2, 34994), (3, 8803), (4, 1705), (5, 250), (6, 39)] ... 530 0.7809 248786 [(0, 113356), (1, 89812), (2, 34694), (3, 8941), (4, 1708), (5, 239), (6, 33)] ... 540 0.7802 248395 [(0, 113242), (1, 89602), (2, 34796), (3, 8741), (4, 1724), (5, 256), (6, 34)] ... 550 0.7760 248453 [(0, 113772), (1, 89384), (2, 34631), (3, 8807), (4, 1596), (5, 230), (6, 30)] ... 560 0.7750 248174 [(0, 114019), (1, 88844), (2, 34659), (3, 8743), (4, 1639), (5, 234), (6, 34)] ... 570 0.7771 247573 [(0, 113510), (1, 88878), (2, 34374), (3, 8809), (4, 1725), (5, 240), (6, 30)] ... 580 0.7742 247706 [(0, 113790), (1, 88896), (2, 34377), (3, 8754), (4, 1617), (5, 243), (6, 27)] ... 590 0.7721 247554 [(0, 113884), (1, 88884), (2, 34297), (3, 8597), (4, 1624), (5, 237), (6, 28)] ... 600 0.7710 247492 [(0, 113981), (1, 88804), (2, 34276), (3, 8583), (4, 1578), (5, 229), (6, 39)] ... 610 0.7677 247219 [(0, 114203), (1, 88858), (2, 33702), (3, 8610), (4, 1575), (5, 235), (6, 32)] ... 620 0.7692 246968 [(0, 114115), (1, 88482), (2, 33917), (3, 8487), (4, 1680), (5, 245), (6, 39)] ... 630 0.7708 246612 [(0, 113680), (1, 88584), (2, 33843), (3, 8546), (4, 1654), (5, 266), (6, 33)] ... 640 0.7701 246337 [(0, 113386), (1, 88777), (2, 33823), (3, 8473), (4, 1581), (5, 259), (6, 32)] ... 650 0.7698 246737 [(0, 113918), (1, 88333), (2, 34017), (3, 8636), (4, 1551), (5, 247), (6, 33)] ... 660 0.7680 246030 [(0, 113540), (1, 88430), (2, 33837), (3, 8360), (4, 1582), (5, 242), (6, 32)] ... 670 0.7644 245757 [(0, 113845), (1, 88263), (2, 33465), (3, 8366), (4, 1566), (5, 215), (6, 33)] ... 680 0.7658 245787 [(0, 113641), (1, 88437), (2, 33441), (3, 8462), (4, 1537), (5, 239), (6, 27)] ... 690 0.7659 245703 [(0, 113569), (1, 88242), (2, 33771), (3, 8354), (4, 1523), (5, 211), (6, 32)] ... 700 0.7668 245352 [(0, 113608), (1, 87804), (2, 33641), (3, 8463), (4, 1558), (5, 244), (6, 33)] ... 710 0.7648 244972 [(0, 113539), (1, 87890), (2, 33273), (3, 8471), (4, 1523), (5, 243), (6, 28)] ... 720 0.7644 245184 [(0, 113935), (1, 87545), (2, 33427), (3, 8391), (4, 1618), (5, 236), (6, 26)] ... 730 0.7652 245079 [(0, 113582), (1, 87783), (2, 33523), (3, 8356), (4, 1563), (5, 244), (6, 25)] ... 740 0.7565 244798 [(0, 114355), (1, 87580), (2, 33040), (3, 8055), (4, 1526), (5, 205), (6, 35)] ... 750 0.7607 244333 [(0, 113545), (1, 87550), (2, 33408), (3, 8103), (4, 1469), (5, 226), (6, 32)] ... 760 0.7621 243953 [(0, 113427), (1, 87239), (2, 33288), (3, 8177), (4, 1579), (5, 205), (6, 36)] ... 770 0.7614 244365 [(0, 113732), (1, 87427), (2, 33099), (3, 8319), (4, 1497), (5, 258), (6, 28)] ... 780 0.7616 244317 [(0, 113703), (1, 87408), (2, 33075), (3, 8308), (4, 1553), (5, 240), (6, 26)] ... 790 0.7614 243951 [(0, 113478), (1, 87447), (2, 32958), (3, 8201), (4, 1591), (5, 234), (6, 38)] ... 800 0.7595 243911 [(0, 113618), (1, 87250), (2, 33117), (3, 8186), (4, 1513), (5, 199), (6, 26)] ... 810 0.7567 243779 [(0, 113769), (1, 87468), (2, 32679), (3, 8089), (4, 1529), (5, 221), (6, 23)] ... 820 0.7601 243246 [(0, 113284), (1, 87023), (2, 33068), (3, 8061), (4, 1534), (5, 242), (6, 31)] ... 830 0.7560 243520 [(0, 114059), (1, 86643), (2, 33054), (3, 8007), (4, 1484), (5, 239), (6, 29)] ... 840 0.7572 243475 [(0, 113841), (1, 86807), (2, 32902), (3, 8217), (4, 1474), (5, 202), (6, 30)] ... 850 0.7553 242837 [(0, 113625), (1, 86590), (2, 32979), (3, 7972), (4, 1441), (5, 203), (6, 25)] ... 860 0.7542 243266 [(0, 114015), (1, 86811), (2, 32620), (3, 8112), (4, 1473), (5, 212), (6, 22)] ... 870 0.7531 242535 [(0, 113753), (1, 86502), (2, 32615), (3, 7998), (4, 1424), (5, 220), (6, 22)] ... 880 0.7557 242701 [(0, 113370), (1, 86996), (2, 32567), (3, 8038), (4, 1500), (5, 209), (6, 18)] ... 890 0.7521 242267 [(0, 113823), (1, 86265), (2, 32508), (3, 8001), (4, 1452), (5, 194), (6, 20)] ... 900 0.7540 242432 [(0, 113677), (1, 86539), (2, 32395), (3, 8107), (4, 1453), (5, 240), (6, 18)] ... 910 0.7505 242402 [(0, 113748), (1, 86906), (2, 32115), (3, 8001), (4, 1399), (5, 208), (6, 23)] ... 920 0.7513 242037 [(0, 113677), (1, 86408), (2, 32334), (3, 7965), (4, 1424), (5, 204), (6, 23)] ... 930 0.7501 241756 [(0, 113649), (1, 86297), (2, 32266), (3, 7914), (4, 1400), (5, 209), (6, 19)] ... 940 0.7503 241870 [(0, 113824), (1, 86370), (2, 31927), (3, 8035), (4, 1463), (5, 225), (6, 25)] ... 950 0.7485 242143 [(0, 114015), (1, 86590), (2, 31914), (3, 7900), (4, 1512), (5, 191), (6, 21)] ... 960 0.7504 241632 [(0, 113855), (1, 85777), (2, 32432), (3, 7876), (4, 1450), (5, 211), (6, 29)] ... 970 0.7469 241411 [(0, 113839), (1, 86280), (2, 31752), (3, 7857), (4, 1476), (5, 192), (6, 15)] ... 980 0.7477 241568 [(0, 113837), (1, 86216), (2, 32081), (3, 7779), (4, 1404), (5, 221), (6, 27)] ... 990 0.7475 241536 [(0, 113812), (1, 86173), (2, 32188), (3, 7734), (4, 1395), (5, 191), (6, 36)] ...