Factor counts for Mersenne numbers that are completely factored (cofactor is at least SPRP to 10 bases) as of Fri May 9 20:28:23 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 600 600 528 528 100.000000 50 50 100.000000 1200 1200 592 592 100.000000 19 19 100.000000 2400 2400 414 414 100.000000 17 17 100.000000 4800 5200 153 153 100.000000 17 17 100.000000 10000 10000 109 109 100.000000 5 5 100.000000 20000 30000 106 106 100.000000 5 5 100.000000 50000 50000 59 59 100.000000 3 3 100.000000 100000 100000 9 9 100.000000 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 1 599 502 586 85.665529 96 96 100.000000 600 600 511 528 96.780303 50 50 100.000000 1200 1200 570 592 96.283784 19 19 100.000000 2400 2400 399 414 96.376812 17 17 100.000000 4800 5200 127 153 83.006536 17 17 100.000000 10000 10000 82 109 75.229358 5 5 100.000000 20000 30000 68 106 64.150943 5 5 100.000000 50000 50000 28 59 47.457627 3 3 100.000000 100000 100000 7 9 77.777778 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 1 599 336 586 57.337884 65 96 67.708333 600 600 426 528 80.681818 43 50 86.000000 1200 1200 504 592 85.135135 16 19 84.210526 2400 2400 344 414 83.091787 11 17 64.705882 4800 5200 93 153 60.784314 13 17 76.470588 10000 10000 39 109 35.779817 2 5 40.000000 20000 30000 25 106 23.584906 3 5 60.000000 50000 50000 11 59 18.644068 3 0.000000 100000 100000 9 0.000000 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 1 599 174 586 29.692833 41 96 42.708333 600 600 299 528 56.628788 32 50 64.000000 1200 1200 396 592 66.891892 10 19 52.631579 2400 2400 275 414 66.425121 7 17 41.176471 4800 5200 46 153 30.065359 8 17 47.058824 10000 10000 14 109 12.844037 1 5 20.000000 20000 30000 10 106 9.433962 1 5 20.000000 50000 50000 1 59 1.694915 3 0.000000 100000 100000 9 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 74 586 12.627986 23 96 23.958333 600 600 184 528 34.848485 17 50 34.000000 1200 1200 270 592 45.608108 7 19 36.842105 2400 2400 208 414 50.241546 5 17 29.411765 4800 5200 14 153 9.150327 2 17 11.764706 10000 10000 8 109 7.339450 1 5 20.000000 20000 30000 3 106 2.830189 1 5 20.000000 50000 50000 59 0.000000 3 0.000000 100000 100000 9 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 24 586 4.095563 9 96 9.375000 600 600 90 528 17.045455 9 50 18.000000 1200 1200 166 592 28.040541 4 19 21.052632 2400 2400 158 414 38.164251 4 17 23.529412 4800 5200 7 153 4.575163 1 17 5.882353 10000 10000 4 109 3.669725 5 0.000000 20000 30000 1 106 0.943396 5 0.000000 50000 50000 59 0.000000 3 0.000000 100000 100000 9 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 9 586 1.535836 3 96 3.125000 600 600 38 528 7.196970 4 50 8.000000 1200 1200 89 592 15.033784 1 19 5.263158 2400 2400 106 414 25.603865 1 17 5.882353 4800 5200 3 153 1.960784 1 17 5.882353 10000 10000 2 109 1.834862 5 0.000000 20000 30000 106 0.000000 5 0.000000 50000 50000 59 0.000000 3 0.000000 100000 100000 9 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 5 586 0.853242 2 96 2.083333 600 600 19 528 3.598485 1 50 2.000000 1200 1200 49 592 8.277027 19 0.000000 2400 2400 65 414 15.700483 17 0.000000 4800 5200 1 153 0.653595 17 0.000000 10000 10000 109 0.000000 5 0.000000 20000 30000 106 0.000000 5 0.000000 50000 50000 59 0.000000 3 0.000000 100000 100000 9 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 3 586 0.511945 1 96 1.041667 600 600 2 528 0.378788 50 0.000000 1200 1200 24 592 4.054054 19 0.000000 2400 2400 41 414 9.903382 17 0.000000 4800 5200 153 0.000000 17 0.000000 10000 10000 109 0.000000 5 0.000000 20000 30000 106 0.000000 5 0.000000 50000 50000 59 0.000000 3 0.000000 100000 100000 9 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 2 586 0.341297 96 0.000000 600 600 528 0.000000 50 0.000000 1200 1200 11 592 1.858108 19 0.000000 2400 2400 22 414 5.314010 17 0.000000 4800 5200 153 0.000000 17 0.000000 10000 10000 109 0.000000 5 0.000000 20000 30000 106 0.000000 5 0.000000 50000 50000 59 0.000000 3 0.000000 100000 100000 9 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 2 586 0.341297 96 0.000000 600 600 528 0.000000 50 0.000000 1200 1200 3 592 0.506757 19 0.000000 2400 2400 14 414 3.381643 17 0.000000 4800 5200 153 0.000000 17 0.000000 10000 10000 109 0.000000 5 0.000000 20000 30000 106 0.000000 5 0.000000 50000 50000 59 0.000000 3 0.000000 100000 100000 9 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 2 586 0.341297 96 0.000000 600 600 528 0.000000 50 0.000000 1200 1200 592 0.000000 19 0.000000 2400 2400 8 414 1.932367 17 0.000000 4800 5200 153 0.000000 17 0.000000 10000 10000 109 0.000000 5 0.000000 20000 30000 106 0.000000 5 0.000000 50000 50000 59 0.000000 3 0.000000 100000 100000 9 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 2 586 0.341297 96 0.000000 600 600 528 0.000000 50 0.000000 1200 1200 592 0.000000 19 0.000000 2400 2400 2 414 0.483092 17 0.000000 4800 5200 153 0.000000 17 0.000000 10000 10000 109 0.000000 5 0.000000 20000 30000 106 0.000000 5 0.000000 50000 50000 59 0.000000 3 0.000000 100000 100000 9 0.000000 4 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 2 586 0.341297 96 0.000000 600 600 528 0.000000 50 0.000000 1200 1200 592 0.000000 19 0.000000 2400 2400 414 0.000000 17 0.000000 4800 5200 153 0.000000 17 0.000000 10000 10000 109 0.000000 5 0.000000 20000 30000 106 0.000000 5 0.000000 50000 50000 59 0.000000 3 0.000000 100000 100000 9 0.000000 4 0.000000 Mersenne numbers with at least 15 known primitive factors within each exponent range Start Length 15 Count Percent 15 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 15 Factors w/ Data Expon.s 15 Factors 1 599 2 586 0.341297 96 0.000000 600 600 528 0.000000 50 0.000000 1200 1200 592 0.000000 19 0.000000 2400 2400 414 0.000000 17 0.000000 4800 5200 153 0.000000 17 0.000000 10000 10000 109 0.000000 5 0.000000 20000 30000 106 0.000000 5 0.000000 50000 50000 59 0.000000 3 0.000000 100000 100000 9 0.000000 4 0.000000 Mersenne numbers with at least 16 known primitive factors within each exponent range Start Length 16 Count Percent 16 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 16 Factors w/ Data Expon.s 16 Factors 1 599 1 586 0.170648 96 0.000000 600 600 528 0.000000 50 0.000000 1200 1200 592 0.000000 19 0.000000 2400 2400 414 0.000000 17 0.000000 4800 5200 153 0.000000 17 0.000000 10000 10000 109 0.000000 5 0.000000 20000 30000 106 0.000000 5 0.000000 50000 50000 59 0.000000 3 0.000000 100000 100000 9 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 $