Factor counts for Mersenne numbers that are completely factored (cofactor is at least SPRP to 10 bases) as of Sat May 26 16:09:53 PDT 2012 Will Edgington http://www.garlic.com/~wedgingt/mersenne.html $Id: cnt1stfactors,v 1.48 2010/03/19 17:18:14 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 w/ Data 1 Factors 1 599 586 586 100.000000 96 96 100.000000 600 600 571 571 100.000000 68 68 100.000000 1200 1200 642 642 100.000000 22 22 100.000000 2400 2400 475 475 100.000000 18 18 100.000000 4800 5200 182 182 100.000000 17 17 100.000000 10000 10000 130 130 100.000000 10 10 100.000000 20000 30000 114 114 100.000000 8 8 100.000000 50000 50000 72 72 100.000000 7 7 100.000000 100000 100000 41 41 100.000000 4 4 100.000000 200000 300000 10 10 100.000000 4 4 100.000000 500000 500000 5 5 100.000000 1 1 100.000000 1000000 1000000 1 1 100.000000 1 0.000000 2000000 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 w/ Data 2 Factors 1 599 500 586 85.324232 96 96 100.000000 600 600 554 571 97.022767 68 68 100.000000 1200 1200 620 642 96.573209 22 22 100.000000 2400 2400 460 475 96.842105 18 18 100.000000 4800 5200 156 182 85.714286 17 17 100.000000 10000 10000 103 130 79.230769 10 10 100.000000 20000 30000 76 114 66.666667 8 8 100.000000 50000 50000 38 72 52.777778 7 7 100.000000 100000 100000 27 41 65.853659 4 4 100.000000 200000 300000 5 10 50.000000 4 4 100.000000 500000 500000 2 5 40.000000 1 1 100.000000 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 w/ Data 3 Factors 1 599 330 586 56.313993 65 96 67.708333 600 600 467 571 81.786340 61 68 89.705882 1200 1200 550 642 85.669782 18 22 81.818182 2400 2400 405 475 85.263158 12 18 66.666667 4800 5200 116 182 63.736264 13 17 76.470588 10000 10000 56 130 43.076923 7 10 70.000000 20000 30000 30 114 26.315789 5 8 62.500000 50000 50000 17 72 23.611111 4 7 57.142857 100000 100000 11 41 26.829268 4 0.000000 200000 300000 10 0.000000 4 0.000000 500000 500000 5 0.000000 1 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 w/ Data 4 Factors 1 599 167 586 28.498294 40 96 41.666667 600 600 333 571 58.318739 48 68 70.588235 1200 1200 432 642 67.289720 11 22 50.000000 2400 2400 332 475 69.894737 8 18 44.444444 4800 5200 62 182 34.065934 8 17 47.058824 10000 10000 26 130 20.000000 3 10 30.000000 20000 30000 14 114 12.280702 2 8 25.000000 50000 50000 2 72 2.777778 1 7 14.285714 100000 100000 6 41 14.634146 4 0.000000 200000 300000 10 0.000000 4 0.000000 500000 500000 5 0.000000 1 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 w/ Data 5 Factors 1 599 68 586 11.604096 22 96 22.916667 600 600 206 571 36.077058 28 68 41.176471 1200 1200 293 642 45.638629 8 22 36.363636 2400 2400 256 475 53.894737 6 18 33.333333 4800 5200 23 182 12.637363 2 17 11.764706 10000 10000 16 130 12.307692 1 10 10.000000 20000 30000 4 114 3.508772 1 8 12.500000 50000 50000 1 72 1.388889 1 7 14.285714 100000 100000 3 41 7.317073 4 0.000000 200000 300000 10 0.000000 4 0.000000 500000 500000 5 0.000000 1 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 w/ Data 6 Factors 1 599 20 586 3.412969 8 96 8.333333 600 600 99 571 17.338004 14 68 20.588235 1200 1200 176 642 27.414330 4 22 18.181818 2400 2400 196 475 41.263158 4 18 22.222222 4800 5200 12 182 6.593407 1 17 5.882353 10000 10000 8 130 6.153846 10 0.000000 20000 30000 1 114 0.877193 8 0.000000 50000 50000 72 0.000000 7 0.000000 100000 100000 2 41 4.878049 4 0.000000 200000 300000 10 0.000000 4 0.000000 500000 500000 5 0.000000 1 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 w/ Data 7 Factors 1 599 7 586 1.194539 3 96 3.125000 600 600 40 571 7.005254 5 68 7.352941 1200 1200 96 642 14.953271 1 22 4.545455 2400 2400 141 475 29.684211 1 18 5.555556 4800 5200 5 182 2.747253 1 17 5.882353 10000 10000 3 130 2.307692 10 0.000000 20000 30000 114 0.000000 8 0.000000 50000 50000 72 0.000000 7 0.000000 100000 100000 41 0.000000 4 0.000000 200000 300000 10 0.000000 4 0.000000 500000 500000 5 0.000000 1 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 w/ Data 8 Factors 1 599 3 586 0.511945 2 96 2.083333 600 600 20 571 3.502627 2 68 2.941176 1200 1200 53 642 8.255452 22 0.000000 2400 2400 90 475 18.947368 18 0.000000 4800 5200 2 182 1.098901 17 0.000000 10000 10000 1 130 0.769231 10 0.000000 20000 30000 114 0.000000 8 0.000000 50000 50000 72 0.000000 7 0.000000 100000 100000 41 0.000000 4 0.000000 200000 300000 10 0.000000 4 0.000000 500000 500000 5 0.000000 1 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 w/ Data 9 Factors 1 599 1 586 0.170648 1 96 1.041667 600 600 2 571 0.350263 68 0.000000 1200 1200 25 642 3.894081 22 0.000000 2400 2400 57 475 12.000000 18 0.000000 4800 5200 1 182 0.549451 17 0.000000 10000 10000 1 130 0.769231 10 0.000000 20000 30000 114 0.000000 8 0.000000 50000 50000 72 0.000000 7 0.000000 100000 100000 41 0.000000 4 0.000000 200000 300000 10 0.000000 4 0.000000 500000 500000 5 0.000000 1 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 w/ Data 10 Factors 1 599 586 0.000000 96 0.000000 600 600 571 0.000000 68 0.000000 1200 1200 12 642 1.869159 22 0.000000 2400 2400 34 475 7.157895 18 0.000000 4800 5200 182 0.000000 17 0.000000 10000 10000 130 0.000000 10 0.000000 20000 30000 114 0.000000 8 0.000000 50000 50000 72 0.000000 7 0.000000 100000 100000 41 0.000000 4 0.000000 200000 300000 10 0.000000 4 0.000000 500000 500000 5 0.000000 1 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 w/ Data 11 Factors 1 599 586 0.000000 96 0.000000 600 600 571 0.000000 68 0.000000 1200 1200 4 642 0.623053 22 0.000000 2400 2400 21 475 4.421053 18 0.000000 4800 5200 182 0.000000 17 0.000000 10000 10000 130 0.000000 10 0.000000 20000 30000 114 0.000000 8 0.000000 50000 50000 72 0.000000 7 0.000000 100000 100000 41 0.000000 4 0.000000 200000 300000 10 0.000000 4 0.000000 500000 500000 5 0.000000 1 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 w/ Data 12 Factors 1 599 586 0.000000 96 0.000000 600 600 571 0.000000 68 0.000000 1200 1200 642 0.000000 22 0.000000 2400 2400 12 475 2.526316 18 0.000000 4800 5200 182 0.000000 17 0.000000 10000 10000 130 0.000000 10 0.000000 20000 30000 114 0.000000 8 0.000000 50000 50000 72 0.000000 7 0.000000 100000 100000 41 0.000000 4 0.000000 200000 300000 10 0.000000 4 0.000000 500000 500000 5 0.000000 1 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 w/ Data 13 Factors 1 599 586 0.000000 96 0.000000 600 600 571 0.000000 68 0.000000 1200 1200 642 0.000000 22 0.000000 2400 2400 4 475 0.842105 18 0.000000 4800 5200 182 0.000000 17 0.000000 10000 10000 130 0.000000 10 0.000000 20000 30000 114 0.000000 8 0.000000 50000 50000 72 0.000000 7 0.000000 100000 100000 41 0.000000 4 0.000000 200000 300000 10 0.000000 4 0.000000 500000 500000 5 0.000000 1 0.000000 Will Edgington http://www.garlic.com/~wedgingt/mersenne.html $Id: cnt1stfactors,v 1.48 2010/03/19 17:18:14 wedgingt Exp $