Factor counts for Mersenne numbers that are completely factored (cofactor is at least SPRP to 10 bases) as of Tue Feb 16 04:16:56 PST 2010 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 1 599 586 586 100.000000 96 96 100.000000 600 600 549 549 100.000000 60 60 100.000000 1200 1200 622 622 100.000000 20 20 100.000000 2400 2400 451 451 100.000000 17 17 100.000000 4800 5200 181 181 100.000000 17 17 100.000000 10000 10000 127 127 100.000000 8 8 100.000000 20000 30000 112 112 100.000000 7 7 100.000000 50000 50000 71 71 100.000000 6 6 100.000000 100000 100000 33 33 100.000000 4 4 100.000000 200000 484128 5 5 100.000000 5 5 100.000000 684128 infinite (no data) Mersenne numbers with at least 2 known primitive 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 1 599 500 586 85.324232 96 96 100.000000 600 600 532 549 96.903461 60 60 100.000000 1200 1200 600 622 96.463023 20 20 100.000000 2400 2400 436 451 96.674058 17 17 100.000000 4800 5200 155 181 85.635359 17 17 100.000000 10000 10000 100 127 78.740157 8 8 100.000000 20000 30000 74 112 66.071429 7 7 100.000000 50000 50000 37 71 52.112676 6 6 100.000000 100000 100000 22 33 66.666667 4 4 100.000000 200000 484128 5 5 100.000000 5 5 100.000000 Mersenne numbers with at least 3 known primitive factors within each exponent range Start Length 3 Count Percent 3 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 3 Factors w/ Data Expon.s 3 Factors 1 599 330 586 56.313993 65 96 67.708333 600 600 447 549 81.420765 53 60 88.333333 1200 1200 531 622 85.369775 17 20 85.000000 2400 2400 381 451 84.478936 11 17 64.705882 4800 5200 115 181 63.535912 13 17 76.470588 10000 10000 53 127 41.732283 5 8 62.500000 20000 30000 29 112 25.892857 4 7 57.142857 50000 50000 16 71 22.535211 3 6 50.000000 100000 100000 9 33 27.272727 4 0.000000 200000 484128 5 0.000000 5 0.000000 Mersenne numbers with at least 4 known primitive factors within each exponent range Start Length 4 Count Percent 4 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 4 Factors w/ Data Expon.s 4 Factors 1 599 167 586 28.498294 40 96 41.666667 600 600 319 549 58.105647 41 60 68.333333 1200 1200 417 622 67.041801 10 20 50.000000 2400 2400 308 451 68.292683 7 17 41.176471 4800 5200 61 181 33.701657 8 17 47.058824 10000 10000 25 127 19.685039 2 8 25.000000 20000 30000 13 112 11.607143 1 7 14.285714 50000 50000 2 71 2.816901 1 6 16.666667 100000 100000 4 33 12.121212 4 0.000000 200000 484128 5 0.000000 5 0.000000 Mersenne numbers with at least 5 known primitive factors within each exponent range Start Length 5 Count Percent 5 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 5 Factors w/ Data Expon.s 5 Factors 1 599 68 586 11.604096 22 96 22.916667 600 600 197 549 35.883424 23 60 38.333333 1200 1200 282 622 45.337621 7 20 35.000000 2400 2400 233 451 51.662971 5 17 29.411765 4800 5200 22 181 12.154696 2 17 11.764706 10000 10000 16 127 12.598425 1 8 12.500000 20000 30000 4 112 3.571429 1 7 14.285714 50000 50000 1 71 1.408451 1 6 16.666667 100000 100000 2 33 6.060606 4 0.000000 200000 484128 5 0.000000 5 0.000000 Mersenne numbers with at least 6 known primitive factors within each exponent range Start Length 6 Count Percent 6 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 6 Factors w/ Data Expon.s 6 Factors 1 599 20 586 3.412969 8 96 8.333333 600 600 97 549 17.668488 12 60 20.000000 1200 1200 171 622 27.491961 4 20 20.000000 2400 2400 176 451 39.024390 4 17 23.529412 4800 5200 11 181 6.077348 1 17 5.882353 10000 10000 8 127 6.299213 8 0.000000 20000 30000 1 112 0.892857 7 0.000000 50000 50000 71 0.000000 6 0.000000 100000 100000 1 33 3.030303 4 0.000000 200000 484128 5 0.000000 5 0.000000 Mersenne numbers with at least 7 known primitive factors within each exponent range Start Length 7 Count Percent 7 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 7 Factors w/ Data Expon.s 7 Factors 1 599 7 586 1.194539 3 96 3.125000 600 600 39 549 7.103825 4 60 6.666667 1200 1200 92 622 14.790997 1 20 5.000000 2400 2400 122 451 27.050998 1 17 5.882353 4800 5200 5 181 2.762431 1 17 5.882353 10000 10000 3 127 2.362205 8 0.000000 20000 30000 112 0.000000 7 0.000000 50000 50000 71 0.000000 6 0.000000 100000 100000 33 0.000000 4 0.000000 200000 484128 5 0.000000 5 0.000000 Mersenne numbers with at least 8 known primitive factors within each exponent range Start Length 8 Count Percent 8 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 8 Factors w/ Data Expon.s 8 Factors 1 599 3 586 0.511945 2 96 2.083333 600 600 19 549 3.460838 1 60 1.666667 1200 1200 51 622 8.199357 20 0.000000 2400 2400 75 451 16.629712 17 0.000000 4800 5200 2 181 1.104972 17 0.000000 10000 10000 1 127 0.787402 8 0.000000 20000 30000 112 0.000000 7 0.000000 50000 50000 71 0.000000 6 0.000000 100000 100000 33 0.000000 4 0.000000 200000 484128 5 0.000000 5 0.000000 Mersenne numbers with at least 9 known primitive factors within each exponent range Start Length 9 Count Percent 9 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 9 Factors w/ Data Expon.s 9 Factors 1 599 1 586 0.170648 1 96 1.041667 600 600 2 549 0.364299 60 0.000000 1200 1200 25 622 4.019293 20 0.000000 2400 2400 51 451 11.308204 17 0.000000 4800 5200 1 181 0.552486 17 0.000000 10000 10000 1 127 0.787402 8 0.000000 20000 30000 112 0.000000 7 0.000000 50000 50000 71 0.000000 6 0.000000 100000 100000 33 0.000000 4 0.000000 200000 484128 5 0.000000 5 0.000000 Mersenne numbers with at least 10 known primitive factors within each exponent range Start Length 10 Count Percent 10 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 10 Factors w/ Data Expon.s 10 Factors 1 599 586 0.000000 96 0.000000 600 600 549 0.000000 60 0.000000 1200 1200 12 622 1.929260 20 0.000000 2400 2400 27 451 5.986696 17 0.000000 4800 5200 181 0.000000 17 0.000000 10000 10000 127 0.000000 8 0.000000 20000 30000 112 0.000000 7 0.000000 50000 50000 71 0.000000 6 0.000000 100000 100000 33 0.000000 4 0.000000 200000 484128 5 0.000000 5 0.000000 Mersenne numbers with at least 11 known primitive factors within each exponent range Start Length 11 Count Percent 11 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 11 Factors w/ Data Expon.s 11 Factors 1 599 586 0.000000 96 0.000000 600 600 549 0.000000 60 0.000000 1200 1200 4 622 0.643087 20 0.000000 2400 2400 17 451 3.769401 17 0.000000 4800 5200 181 0.000000 17 0.000000 10000 10000 127 0.000000 8 0.000000 20000 30000 112 0.000000 7 0.000000 50000 50000 71 0.000000 6 0.000000 100000 100000 33 0.000000 4 0.000000 200000 484128 5 0.000000 5 0.000000 Mersenne numbers with at least 12 known primitive factors within each exponent range Start Length 12 Count Percent 12 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 12 Factors w/ Data Expon.s 12 Factors 1 599 586 0.000000 96 0.000000 600 600 549 0.000000 60 0.000000 1200 1200 622 0.000000 20 0.000000 2400 2400 10 451 2.217295 17 0.000000 4800 5200 181 0.000000 17 0.000000 10000 10000 127 0.000000 8 0.000000 20000 30000 112 0.000000 7 0.000000 50000 50000 71 0.000000 6 0.000000 100000 100000 33 0.000000 4 0.000000 200000 484128 5 0.000000 5 0.000000 Mersenne numbers with at least 13 known primitive factors within each exponent range Start Length 13 Count Percent 13 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 13 Factors w/ Data Expon.s 13 Factors 1 599 586 0.000000 96 0.000000 600 600 549 0.000000 60 0.000000 1200 1200 622 0.000000 20 0.000000 2400 2400 4 451 0.886918 17 0.000000 4800 5200 181 0.000000 17 0.000000 10000 10000 127 0.000000 8 0.000000 20000 30000 112 0.000000 7 0.000000 50000 50000 71 0.000000 6 0.000000 100000 100000 33 0.000000 4 0.000000 200000 484128 5 0.000000 5 0.000000 Mersenne numbers with at least 14 known primitive factors within each exponent range Start Length 14 Count Percent 14 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 14 Factors w/ Data Expon.s 14 Factors 1 599 586 0.000000 96 0.000000 600 600 549 0.000000 60 0.000000 1200 1200 622 0.000000 20 0.000000 2400 2400 1 451 0.221729 17 0.000000 4800 5200 181 0.000000 17 0.000000 10000 10000 127 0.000000 8 0.000000 20000 30000 112 0.000000 7 0.000000 50000 50000 71 0.000000 6 0.000000 100000 100000 33 0.000000 4 0.000000 200000 484128 5 0.000000 5 0.000000 Will Edgington http://www.garlic.com/~wedgingt/mersenne.html $Id: cnt1stfactors,v 1.47 2008/04/27 02:12:07 wedgingt Exp $