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+278,4,4,233,233,233,100.0,tight +279,4,4,524287,524287,524287,100.0,tight +281,4,4,2147483647,2147483647,2147483647,100.0,tight +283,4,3,8191,8191,8191,100.0,tight +287,4,4,127,127,127,100.0,tight +288,4,4,233,233,233,100.0,tight +289,4,4,524287,524287,524287,100.0,tight +291,4,4,2147483647,2147483647,2147483647,100.0,tight +293,4,4,8191,8191,8191,100.0,tight +297,4,4,127,127,127,100.0,tight +298,4,4,233,233,233,100.0,tight +299,4,4,524287,524287,524287,100.0,tight diff --git a/docs/stats/divisor_trajectory_mu10_classes.csv b/docs/stats/divisor_trajectory_mu10_classes.csv new file mode 100644 index 0000000..47c8d5b --- /dev/null +++ b/docs/stats/divisor_trajectory_mu10_classes.csv @@ -0,0 +1,48 @@ +q , mu10 , support, class +127 , 0.2436974789915966 , 119 , A +233 , 0.2436974789915966 , 119 , A +524287 , 0.24786324786324787, 117 , A +3449 , 0.25 , 8 , A +2298041 , 0.3529411764705882 , 34 , A +2147483647 , 0.375 , 40 , A +2305843009213693696 , 0.38095238095238093, 21 , A +8191 , 0.38666666666666666, 75 , A +15193 , 0.4 , 15 , A +48544121 , 0.4193548387096774 , 31 , A +18121 , 0.43478260869565216, 23 , A +1433 , 0.4782608695652174 , 23 , A +2305843009213693952 , 0.5454545454545454 , 11 , A +1913 , 0.6470588235294118 , 17 , B +618970019642690068730085376, 0.6521739130434783 , 23 , B +22000409 , 0.6666666666666667 , 9 , B +43441 , 0.75 , 20 , B +54217 , 1.0 , 13 , B +11113 , 1.0 , 7 , B +1504073 , 1.0 , 11 , B +704161 , 1.0588235294117647 , 17 , B +730753 , 1.1176470588235294 , 17 , B +13822297 , 1.125 , 8 , B +10960009 , 1.1666666666666665 , 6 , B +1466449 , 1.25 , 12 , B +4513 , 1.3333333333333335 , 21 , B +6361 , 1.5294117647058825 , 17 , C +622577 , 1.5454545454545454 , 11 , C +1121297 , 1.625 , 8 , C +27409 , 2.0 , 4 , C +2806537 , 2.6 , 5 , C +26849 , 2.666666666666667 , 3 , C +12619129 , 3.0 , 2 , C +931921 , 3.5 , 4 , C +59233 , 3.5 , 4 , C +35897 , 3.75 , 4 , C +855857 , 3.75 , 4 , C +23209 , 4.0 , 2 , C +40841 , 4.5 , 2 , D +35081 , 4.5 , 2 , D +63577 , 6.0 , 2 , D +15854617 , 6.0 , 1 , D +33569 , 9.0 , 2 , D +53617 , 9.0 , 1 , D +554129 , 11.0 , 1 , D +3189281 , 12.0 , 1 , D +43721 , 15.0 , 1 , D diff --git a/docs/stats/divisors_only_original_by_p_int.csv b/docs/stats/divisors_only_original_by_p_int.csv new file mode 100644 index 0000000..3409bd2 --- /dev/null +++ b/docs/stats/divisors_only_original_by_p_int.csv @@ -0,0 +1,5 @@ +r, 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 , 88 , 89 , 90 , 91 , 92 , 93 , 94 , 95 , 96 , 97 , 98 , 99 , 100 , 101 , 102 , 103 , 104 , 105 , 106 , 107, 108, 109 , 110 , 111 , 112 , 113 , 114 , 115 , 116 , 117, 118, 119 , 120 , 121 , 122 , 123 , 124 , 125 , 126 , 127, 128, 129 , 130 , 131 , 132 , 133 , 134 , 135 , 136 , 137, 138, 139 , 140 , 141 , 142 , 143 , 144 , 145 , 146 , 147, 148, 149 , 150 , 151 , 152 , 153 , 154 , 155 , 156 , 157, 158, 159 , 160 , 161 , 162 , 163 , 164, 165, 166 , 167, 168, 169 , 170 , 171 , 172 , 173 , 174, 175, 176 , 177, 178, 179 , 180 , 181 , 182 , 183 , 184, 185, 186 , 187, 188, 189 , 190 , 191 , 192 , 193 , 194, 195, 196 , 197, 198, 199 , 200 , 201 , 202 , 203 , 204, 205, 206 , 207, 208, 209 , 210 , 211 , 212 , 213 , 214, 215, 216 , 217, 218, 219 , 220 , 221 , 222 , 223 , 224, 225, 226 , 227, 228, 229 , 230 , 231 , 232 , 233 , 234, 235, 236 , 237, 238, 239 , 240 , 241 , 242 , 243 , 244, 245, 246 , 247, 248, 249 , 250 , 251 , 252 , 253 , 254, 255, 256 , 257, 258, 259 , 260 , 261 , 262 , 263 , 264, 265, 266 , 267, 268, 269 , 270 , 271 , 272, 273 , 274, 275, 276 , 277, 278, 279 , 280 , 281 , 282, 283 , 284, 285, 286, 287, 288, 289 , 290 , 291 , 292, 293 , 294, 295, 296, 297, 298, 299 , 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1504073 , , 8191, , , 48544121, 127, 233, 524287, 618970019642690137449562112, 1504073 , , 8191, , , 48544121, 127, 233, 524287, 618970019642690137449562112, 1466449 , , 4513, , , 48544121, 127, 233, 524287, , 1466449 , , 8191, , , 48544121, 127, 233, 524287, , 1121297 , , 8191, , , 48544121, 127, 233, 524287, , 2147483647, , 8191, , , , 127, 233, 524287, , 2147483647, , 6361, , , , 127, 233, 524287, , 2147483647, , 8191, , , , 127, 233, 524287, , 2147483647, , 8191, , , , 127, 233, 524287, , 2147483647, , 6361, , , , 127, 233, 524287, , 2147483647, , 4513, , , , 127, 233, 524287, , 2147483647, , 8191, , , , 127, 233, 524287, , 2147483647, , 8191, , , , 127, 233, 524287, diff --git a/docs/stats/mersenne_divisors_ge_127_original.csv b/docs/stats/mersenne_divisors_ge_127_original.csv new file mode 100644 index 0000000..53659b0 --- /dev/null +++ b/docs/stats/mersenne_divisors_ge_127_original.csv @@ -0,0 +1,2392 @@ 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+offset,total,dominant_digit,dominant_share,strong_dominance,allowed_digits_min15pct,allowed_mask,dominant_bit,allowed_mask_hex,dominant_bit_hex,allowed_digits_from_mask +1,120,3,0.45,False,"3,7",6,2,0x6,0x2,"3,7" +2,56,1,0.6607142857142857,True,"1,9",9,1,0x9,0x1,"1,9" +3,120,1,0.7833333333333333,True,"1,3",3,1,0x3,0x1,"1,3" +4,51,3,0.4705882352941176,False,"3,7,9",14,2,0xE,0x2,"3,7,9" +5,49,1,0.5102040816326531,False,"1,9",9,1,0x9,0x1,"1,9" +6,96,1,0.6458333333333334,True,"1,7",5,1,0x5,0x1,"1,7" +7,120,7,1.0,True,7,4,4,0x4,0x4,7 +8,120,3,1.0,True,3,2,2,0x2,0x2,3 +9,120,7,0.9916666666666668,True,7,4,4,0x4,0x4,7 +10,64,1,0.359375,False,"1,3,7",7,1,0x7,0x1,"1,3,7" diff --git a/docs/stats/offset_last_digit_lookup_mask_class_B.csv b/docs/stats/offset_last_digit_lookup_mask_class_B.csv new file mode 100644 index 0000000..b99daff --- /dev/null +++ b/docs/stats/offset_last_digit_lookup_mask_class_B.csv @@ -0,0 +1,7 @@ +offset,total,dominant_digit,dominant_share,strong_dominance,allowed_digits_min15pct,allowed_mask,dominant_bit,allowed_mask_hex,dominant_bit_hex,allowed_digits_from_mask,min_total_required,usable +1,43,3,0.6976744186046512,True,"3,9",10,2,0xA,0x2,"3,9",10,True +3,22,3,1.0,True,3,2,2,0x2,0x2,3,10,True +4,24,7,0.375,False,"3,7,9",14,4,0xE,0x4,"3,7,9",10,True +5,10,9,1.0,True,9,8,8,0x8,0x8,9,10,True +6,35,1,0.6,True,"1,7",5,1,0x5,0x1,"1,7",10,True +10,36,1,0.5,False,"1,3",3,1,0x3,0x1,"1,3",10,True diff --git a/docs/stats/offset_last_digit_lookup_mask_class_C.csv b/docs/stats/offset_last_digit_lookup_mask_class_C.csv new file mode 100644 index 0000000..6ee61f5 --- /dev/null +++ b/docs/stats/offset_last_digit_lookup_mask_class_C.csv @@ -0,0 +1,8 @@ +offset,total,dominant_digit,dominant_share,strong_dominance,allowed_digits_min15pct,allowed_mask,dominant_bit,allowed_mask_hex,dominant_bit_hex,allowed_digits_from_mask,min_total_required,usable +1,9,7,1.0,True,7,4,4,0x4,0x4,7,10,False +2,6,7,1.0,True,7,4,4,0x4,0x4,7,10,False +3,18,1,1.0,True,1,1,1,0x1,0x1,1,10,True +4,3,9,1.0,True,9,8,8,0x8,0x8,9,10,False +5,12,9,1.0,True,9,8,8,0x8,0x8,9,10,True +6,10,3,0.5,False,"3,7",6,2,0x6,0x2,"3,7",10,True +10,22,7,0.7727272727272727,True,"1,7",5,4,0x5,0x4,"1,7",10,True diff --git a/docs/stats/offset_last_digit_lookup_mask_class_D.csv b/docs/stats/offset_last_digit_lookup_mask_class_D.csv new file mode 100644 index 0000000..4b97c8f --- /dev/null +++ b/docs/stats/offset_last_digit_lookup_mask_class_D.csv @@ -0,0 +1,5 @@ +offset,total,dominant_digit,dominant_share,strong_dominance,allowed_digits_min15pct,allowed_mask,dominant_bit,allowed_mask_hex,dominant_bit_hex,allowed_digits_from_mask,min_total_required,usable +2,2,1,1.0,True,1,1,1,0x1,0x1,1,5,False +4,2,7,1.0,True,7,4,4,0x4,0x4,7,5,False +6,16,1,0.5,False,"1,7,9",13,1,0xD,0x1,"1,7,9",5,True +10,2,9,1.0,True,9,8,8,0x8,0x8,9,5,False diff --git a/docs/stats/offset_last_digit_lookup_mask_classes_BCD.csv b/docs/stats/offset_last_digit_lookup_mask_classes_BCD.csv new file mode 100644 index 0000000..5cfe734 --- /dev/null +++ b/docs/stats/offset_last_digit_lookup_mask_classes_BCD.csv @@ -0,0 +1,18 @@ +offset,total,dominant_digit,dominant_share,strong_dominance,allowed_digits_min15pct,allowed_mask,dominant_bit,allowed_mask_hex,dominant_bit_hex,allowed_digits_from_mask,min_total_required,usable,class +1,43,3,0.6976744186046512,True,"3,9",10,2,0xA,0x2,"3,9",10,True,B +3,22,3,1.0,True,3,2,2,0x2,0x2,3,10,True,B +4,24,7,0.375,False,"3,7,9",14,4,0xE,0x4,"3,7,9",10,True,B +5,10,9,1.0,True,9,8,8,0x8,0x8,9,10,True,B +6,35,1,0.6,True,"1,7",5,1,0x5,0x1,"1,7",10,True,B +10,36,1,0.5,False,"1,3",3,1,0x3,0x1,"1,3",10,True,B +1,9,7,1.0,True,7,4,4,0x4,0x4,7,10,False,C +2,6,7,1.0,True,7,4,4,0x4,0x4,7,10,False,C +3,18,1,1.0,True,1,1,1,0x1,0x1,1,10,True,C +4,3,9,1.0,True,9,8,8,0x8,0x8,9,10,False,C +5,12,9,1.0,True,9,8,8,0x8,0x8,9,10,True,C +6,10,3,0.5,False,"3,7",6,2,0x6,0x2,"3,7",10,True,C +10,22,7,0.7727272727272727,True,"1,7",5,4,0x5,0x4,"1,7",10,True,C +2,2,1,1.0,True,1,1,1,0x1,0x1,1,5,False,D +4,2,7,1.0,True,7,4,4,0x4,0x4,7,5,False,D +6,16,1,0.5,False,"1,7,9",13,1,0xD,0x1,"1,7,9",5,True,D +10,2,9,1.0,True,9,8,8,0x8,0x8,9,5,False,D diff --git a/docs/stats/offset_last_digit_rules_all.csv b/docs/stats/offset_last_digit_rules_all.csv new file mode 100644 index 0000000..5ef6fba --- /dev/null +++ b/docs/stats/offset_last_digit_rules_all.csv @@ -0,0 +1,11 @@ +offset,total,dominant_digit,dominant_share,strong_dominance,allowed_digits_min15pct,p1,p3,p7,p9,entropy_bits +1,120,3,0.45,False,"3,7",0.0,0.45,0.44166666666666665,0.10833333333333334,1.3864787160709264 +2,56,1,0.6607142857142857,True,"1,9",0.6607142857142857,0.017857142857142856,0.14285714285714285,0.17857142857142858,1.343621788537162 +3,120,1,0.7833333333333333,True,"1,3",0.7833333333333333,0.19166666666666668,0.008333333333333333,0.016666666666666666,0.8887799535501084 +4,51,3,0.47058823529411764,False,"3,7,9",0.0,0.47058823529411764,0.27450980392156865,0.2549019607843137,1.5263903368352523 +5,49,1,0.5102040816326531,False,"1,9",0.5102040816326531,0.02040816326530612,0.02040816326530612,0.4489795918367347,1.2432016736174807 +6,96,1,0.6458333333333334,True,"1,7",0.6458333333333334,0.052083333333333336,0.25,0.052083333333333336,1.3514359151985766 +7,120,7,1.0,True,7,0.0,0.0,1.0,0.0,-0.0 +8,120,3,1.0,True,3,0.0,1.0,0.0,0.0,-0.0 +9,120,7,0.9916666666666667,True,7,0.008333333333333333,0.0,0.9916666666666667,0.0,0.06952964699480783 +10,64,1,0.359375,False,"1,3,7",0.359375,0.296875,0.3125,0.03125,1.7313889118361458 diff --git a/docs/stats/offset_last_digit_scoring_all.csv b/docs/stats/offset_last_digit_scoring_all.csv new file mode 100644 index 0000000..63c7b71 --- /dev/null +++ b/docs/stats/offset_last_digit_scoring_all.csv @@ -0,0 +1,41 @@ +offset, q_last_digit, p , score_neg_ln_p , total +1 , 1 , 0.0 , 27.631021115928547 , 120 +1 , 3 , 0.45 , 0.7985076962177716 , 120 +1 , 7 , 0.4416666666666666, 0.8171998292299243 , 120 +1 , 9 , 0.1083333333333333, 2.2225423853205095 , 120 +2 , 1 , 0.6607142857142857, 0.4144337780909248 , 56 +2 , 3 , 0.0178571428571428, 4.025351690735152 , 56 +2 , 7 , 0.1428571428571428, 1.9459101490553137 , 56 +2 , 9 , 0.1785714285714285, 1.722766597741104 , 56 +3 , 1 , 0.7833333333333333, 0.2441969605120421 , 120 +3 , 3 , 0.1916666666666666, 1.6519975268528966 , 120 +3 , 7 , 0.0083333333333333, 4.78749174278205 , 120 +3 , 9 , 0.0166666666666666, 4.094344562222105 , 120 +4 , 1 , 0.0 , 27.631021115928547 , 51 +4 , 3 , 0.4705882352941176, 0.7537718023763803 , 51 +4 , 7 , 0.2745098039215686, 1.2927683031090673 , 51 +4 , 9 , 0.2549019607843137, 1.3668762752627892 , 51 +5 , 1 , 0.5102040816326531, 0.6729444732424258 , 49 +5 , 3 , 0.0204081632653061, 3.891820298110628 , 49 +5 , 7 , 0.0204081632653061, 3.891820298110628 , 49 +5 , 9 , 0.4489795918367347, 0.8007778447523107 , 49 +6 , 1 , 0.6458333333333334, 0.4372138064227446 , 96 +6 , 3 , 0.0520833333333333, 2.9549102790337365 , 96 +6 , 7 , 0.25 , 1.3862943611198906 , 96 +6 , 9 , 0.0520833333333333, 2.9549102790337365 , 96 +7 , 1 , 0.0 , 27.631021115928547 , 120 +7 , 3 , 0.0 , 27.631021115928547 , 120 +7 , 7 , 1.0 , -0.0 , 120 +7 , 9 , 0.0 , 27.631021115928547 , 120 +8 , 1 , 0.0 , 27.631021115928547 , 120 +8 , 3 , 1.0 , -0.0 , 120 +8 , 7 , 0.0 , 27.631021115928547 , 120 +8 , 9 , 0.0 , 27.631021115928547 , 120 +9 , 1 , 0.0083333333333333, 4.78749174278205 , 120 +9 , 3 , 0.0 , 27.631021115928547 , 120 +9 , 7 , 0.9916666666666668, 0.008368249670516466, 120 +9 , 9 , 0.0 , 27.631021115928547 , 120 +10 , 1 , 0.359375 , 1.0233888674305223 , 64 +10 , 3 , 0.296875 , 1.2144441041932315 , 64 +10 , 7 , 0.3125 , 1.1631508098056809 , 64 +10 , 9 , 0.03125 , 3.4657359027997265 , 64 diff --git a/docs/stats/offset_last_digit_thresholds.csv b/docs/stats/offset_last_digit_thresholds.csv new file mode 100644 index 0000000..1201847 --- /dev/null +++ b/docs/stats/offset_last_digit_thresholds.csv @@ -0,0 +1,2 @@ +strong_dominance_threshold,allowed_digit_threshold,min_total_all,min_total_BC,min_total_D,score_function,p_source,digits_considered +0.6,0.15,20,10,5,"score = -ln(max(p, 1e-12))","offset_last_digit_rules_*.csv columns p1,p3,p7,p9","1,3,7,9"