Factor counts for Mersenne numbers with cofactors that are composite or of unknown primality as of Tue Sep 30 06:15:13 PDT 2008 Will Edgington http://www.garlic.com/~wedgingt/mersenne.html $Id: cnt1stfactors,v 1.47 2008/04/27 02:12:07 wedgingt Exp $ Mersenne numbers with at least 1 known primitive factors within each exponent range Start Length 1 Count Percent 1 Count Precent of of Factors of All of All Factors of Prime of Prime Range Range All Expon.s Exp.s w/ Prime Expon.s Exp.s w/ Expon.s w/ Data 1 Factors w/ Data Expon.s 1 Factors 600 600 65 69 94.202899 34 35 97.142857 1200 1200 554 601 92.179700 127 139 91.366906 2400 2400 1738 1976 87.955466 243 269 90.334572 4800 5200 4196 5039 83.270490 523 564 92.730496 10000 10000 7372 9887 74.562557 904 1025 88.195122 20000 30000 20071 29890 67.149548 2418 2863 84.456863 50000 50000 29732 48730 61.013749 3654 4455 82.020202 100000 100000 66701 73579 90.652224 6335 8386 75.542571 200000 300000 187696 194384 96.559388 16865 23553 71.604467 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factors within each exponent range Start Length 2 Count Percent 2 Count Precent of of Factors of All of All Factors of Prime of Prime Range Range All Expon.s Exp.s w/ Prime Expon.s Exp.s w/ Expon.s w/ Data 2 Factors w/ Data Expon.s 2 Factors 600 600 51 69 73.913043 26 35 74.285714 1200 1200 410 601 68.219634 99 139 71.223022 2400 2400 1226 1976 62.044534 171 269 63.568773 4800 5200 2850 5039 56.558841 375 564 66.489362 10000 10000 4330 9887 43.794882 526 1025 51.317073 20000 30000 10296 29890 34.446303 1113 2863 38.875306 50000 50000 13877 48730 28.477324 1509 4455 33.872054 100000 100000 31165 73579 42.355835 2541 8386 30.300501 200000 300000 77315 194384 39.774364 5072 23553 21.534412 500000 500000 112731 306681 36.758391 6996 36958 18.929596 1000000 1000000 108429 452576 23.958186 11954 70433 16.972158 2000000 1000000 94142 429413 21.923416 8835 67882 13.015232 3000000 1000000 85000 413953 20.533732 7063 66329 10.648434 4000000 1000000 81071 402519 20.140913 7433 65367 11.371181 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38000000 1000000 45715 306395 14.920283 8668 57436 15.091580 39000000 1000000 45384 304686 14.895335 8613 57252 15.044016 40000000 1000000 43783 304079 14.398561 7315 57102 12.810409 41000000 1000000 41092 302670 13.576502 4878 56864 8.578362 42000000 1000000 40545 301819 13.433548 4986 56915 8.760432 43000000 1000000 40352 300473 13.429493 4946 56848 8.700394 44000000 1000000 39934 299394 13.338277 5016 56776 8.834719 45000000 1000000 39652 299253 13.250327 4978 56893 8.749758 46000000 1000000 39265 296848 13.227308 4886 56640 8.626412 47000000 1000000 39030 296379 13.168949 4916 56451 8.708437 48000000 1000000 38501 294896 13.055789 4829 56387 8.564031 49000000 1000000 38643 294668 13.114081 4980 56603 8.798120 50000000 1000000 39734 294018 13.514139 6279 56360 11.140880 51000000 1000000 39568 292617 13.522113 6413 56349 11.380859 52000000 1000000 37802 291741 12.957383 4913 56209 8.740593 53000000 1000000 37781 290925 12.986509 5045 56151 8.984702 54000000 1000000 37165 289958 12.817374 4863 55997 8.684394 55000000 1000000 37037 289298 12.802370 4954 56130 8.825940 56000000 1000000 36538 289295 12.630014 4835 56105 8.617770 57000000 1000000 36187 287198 12.600018 4803 55901 8.591975 58000000 1000000 36327 287200 12.648677 4755 55978 8.494409 59000000 1000000 35955 286303 12.558373 4752 55801 8.515976 60000000 1000000 36742 285608 12.864486 5810 55930 10.387985 61000000 1000000 36704 284572 12.897966 5876 55555 10.576906 62000000 1000000 36749 284332 12.924680 6169 55706 11.074211 63000000 1000000 36218 283242 12.786945 5864 55780 10.512729 64000000 1000000 36043 281676 12.795907 5986 55468 10.791808 65000000 1000000 35974 281349 12.786255 5916 55569 10.646224 66000000 1000000 35451 280724 12.628418 5718 55644 10.276041 67000000 1000000 35832 280486 12.774969 5865 55575 10.553306 68000000 1000000 35019 280024 12.505714 5700 55332 10.301453 69000000 1000000 34965 278728 12.544488 5845 55390 10.552446 70000000 1000000 35683 278135 12.829381 6530 55309 11.806397 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