Factor counts for Mersenne numbers that are completely factored (cofactor is at least SPRP to 10 bases) as of Tue Sep 30 06:15:11 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 1 599 586 586 100.000000 96 96 100.000000 600 600 530 530 100.000000 51 51 100.000000 1200 1200 596 596 100.000000 19 19 100.000000 2400 2400 421 421 100.000000 17 17 100.000000 4800 5200 159 159 100.000000 17 17 100.000000 10000 10000 111 111 100.000000 6 6 100.000000 20000 30000 107 107 100.000000 5 5 100.000000 50000 50000 67 67 100.000000 3 3 100.000000 100000 100000 21 21 100.000000 4 4 100.000000 200000 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 1 599 501 586 85.494881 96 96 100.000000 600 600 513 530 96.792453 51 51 100.000000 1200 1200 574 596 96.308725 19 19 100.000000 2400 2400 406 421 96.437055 17 17 100.000000 4800 5200 133 159 83.647799 17 17 100.000000 10000 10000 84 111 75.675676 6 6 100.000000 20000 30000 69 107 64.485981 5 5 100.000000 50000 50000 33 67 49.253731 3 3 100.000000 100000 100000 14 21 66.666667 4 4 100.000000 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 1 599 331 586 56.484642 65 96 67.708333 600 600 428 530 80.754717 44 51 86.274510 1200 1200 507 596 85.067114 16 19 84.210526 2400 2400 351 421 83.372922 11 17 64.705882 4800 5200 98 159 61.635220 13 17 76.470588 10000 10000 41 111 36.936937 3 6 50.000000 20000 30000 26 107 24.299065 3 5 60.000000 50000 50000 13 67 19.402985 3 0.000000 100000 100000 2 21 9.523810 4 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 600 600 301 530 56.792453 33 51 64.705882 1200 1200 398 596 66.778523 10 19 52.631579 2400 2400 281 421 66.745843 7 17 41.176471 4800 5200 51 159 32.075472 8 17 47.058824 10000 10000 16 111 14.414414 2 6 33.333333 20000 30000 11 107 10.280374 1 5 20.000000 50000 50000 1 67 1.492537 3 0.000000 100000 100000 21 0.000000 4 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 600 600 185 530 34.905660 18 51 35.294118 1200 1200 271 596 45.469799 7 19 36.842105 2400 2400 209 421 49.643705 5 17 29.411765 4800 5200 18 159 11.320755 2 17 11.764706 10000 10000 8 111 7.207207 1 6 16.666667 20000 30000 3 107 2.803738 1 5 20.000000 50000 50000 67 0.000000 3 0.000000 100000 100000 21 0.000000 4 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 90 530 16.981132 9 51 17.647059 1200 1200 167 596 28.020134 4 19 21.052632 2400 2400 158 421 37.529691 4 17 23.529412 4800 5200 10 159 6.289308 1 17 5.882353 10000 10000 4 111 3.603604 6 0.000000 20000 30000 1 107 0.934579 5 0.000000 50000 50000 67 0.000000 3 0.000000 100000 100000 21 0.000000 4 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 38 530 7.169811 4 51 7.843137 1200 1200 89 596 14.932886 1 19 5.263158 2400 2400 106 421 25.178147 1 17 5.882353 4800 5200 5 159 3.144654 1 17 5.882353 10000 10000 2 111 1.801802 6 0.000000 20000 30000 107 0.000000 5 0.000000 50000 50000 67 0.000000 3 0.000000 100000 100000 21 0.000000 4 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 19 530 3.584906 1 51 1.960784 1200 1200 49 596 8.221477 19 0.000000 2400 2400 65 421 15.439430 17 0.000000 4800 5200 2 159 1.257862 17 0.000000 10000 10000 111 0.000000 6 0.000000 20000 30000 107 0.000000 5 0.000000 50000 50000 67 0.000000 3 0.000000 100000 100000 21 0.000000 4 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 2 530 0.377358 51 0.000000 1200 1200 24 596 4.026846 19 0.000000 2400 2400 41 421 9.738717 17 0.000000 4800 5200 1 159 0.628931 17 0.000000 10000 10000 111 0.000000 6 0.000000 20000 30000 107 0.000000 5 0.000000 50000 50000 67 0.000000 3 0.000000 100000 100000 21 0.000000 4 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 600 600 530 0.000000 51 0.000000 1200 1200 11 596 1.845638 19 0.000000 2400 2400 22 421 5.225653 17 0.000000 4800 5200 159 0.000000 17 0.000000 10000 10000 111 0.000000 6 0.000000 20000 30000 107 0.000000 5 0.000000 50000 50000 67 0.000000 3 0.000000 100000 100000 21 0.000000 4 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 600 600 530 0.000000 51 0.000000 1200 1200 3 596 0.503356 19 0.000000 2400 2400 14 421 3.325416 17 0.000000 4800 5200 159 0.000000 17 0.000000 10000 10000 111 0.000000 6 0.000000 20000 30000 107 0.000000 5 0.000000 50000 50000 67 0.000000 3 0.000000 100000 100000 21 0.000000 4 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 600 600 530 0.000000 51 0.000000 1200 1200 596 0.000000 19 0.000000 2400 2400 8 421 1.900238 17 0.000000 4800 5200 159 0.000000 17 0.000000 10000 10000 111 0.000000 6 0.000000 20000 30000 107 0.000000 5 0.000000 50000 50000 67 0.000000 3 0.000000 100000 100000 21 0.000000 4 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 600 600 530 0.000000 51 0.000000 1200 1200 596 0.000000 19 0.000000 2400 2400 2 421 0.475059 17 0.000000 4800 5200 159 0.000000 17 0.000000 10000 10000 111 0.000000 6 0.000000 20000 30000 107 0.000000 5 0.000000 50000 50000 67 0.000000 3 0.000000 100000 100000 21 0.000000 4 0.000000 Will Edgington http://www.garlic.com/~wedgingt/mersenne.html $Id: cnt1stfactors,v 1.47 2008/04/27 02:12:07 wedgingt Exp $