存在等差k生素数公差d最小值使它中的素数之和遍历偶数

白新岭 · 发表于 2019-6-24 13:04

等差4生素数(30)的数量大概是最密4生素数数量的8倍，如果最小合成系数与最密4生素数一样的话，有望在38亿/64之内结束偶数不能有等差4生素数(30)合成的情况，验证范围明显缩小。

白新岭 · 发表于 2019-6-24 19:32

虽然验证范围缩小，但是不代表计算量缩小，原来210周期内只计算5个偶数，可现在却要计算105个偶数，是前者的21倍，还有一个要命的问题，原先只在很少4生素数中查找，现在，因为等差4生素数是前者的8倍，在加上一组中的4个素数都参与，8*4=32倍的数据量，这些都拖慢了程序运行。如果不考虑其它因素21*32=672，范围缩小64倍，扔就是672/64=10.5倍的计算量。

白新岭 · 发表于 2019-6-25 15:57

等差4生素数(30)，即(P,P+30,P+60,P+90)其系数为(15/4)^3*∏((1-4/P)/(1-1/P)^4)，（P≥7），其值（即连乘积的极限值）=33.2094285863553。
它是最密4生素数(P,P+2,P+6,P+8),即（0,2,4,2）的系数8倍，因为主项一致，所以数量也是它的8倍。

白新岭 · 发表于 2019-6-26 10:16

余数类统计
90 0
120 2
60 3
150 4
174 5
204 5
48 6
78 6
144 6
0 7
6 7
30 7
180 7
36 8
108 8
162 8
66 9
186 9
24 10
132 11
18 13
192 15
54 20
84 20
114 20
96 21
126 21
156 21
50 25
102 26
138 31
168 31
198 31
20 37
190 38
160 43
12 45
42 45
72 45
80 45
10 55
130 65
200 69
146 81
76 84
104 85
106 85
176 85
134 91
118 96
40 99
70 99
100 99
148 102
34 105
110 105
140 105
170 105
64 108
202 116
22 122
206 122
188 124
116 127
8 133
136 134
94 137
74 138
46 140
164 149
4 151
178 160
88 164
172 167
52 178
62 181
158 186
92 189
38 190
56 227
86 228
26 229
196 229
166 231
16 232
14 235
44 236
194 240
154 243
32 244
124 246
184 246
122 254
28 271
208 271
58 272
82 286
112 286
142 288
98 303
68 304
128 304
182 388
2 391
152 393
210类 12529
这是等差4生素数(30)不能合成的偶数统计结果，模210余90的偶数竟然无一反例，而且似乎比三生素数不能合成的偶数结束的还早，最大的一个偶数为11767394，直到18900000为止还没有出现第二个反例，说明后边已经没有反例了，同样的最密4生素数的结束范围在38亿左右，相差悬殊。

白新岭 · 发表于 2019-6-26 16:31

14#数据有点失误，因为程序把正好是素数的2倍偶数给检测到是不能合成的偶数（不是所有这样的偶数，只是一部分，因为其他偶数除是素数的2倍外，还可以有其他两个不同素数的和组成）。
所以不能合成偶数总量小于12529个。

白新岭 · 发表于 2019-6-26 16:31

14#数据有点失误，因为程序把正好是素数的2倍偶数给检测到是不能合成的偶数（不是所有这样的偶数，只是一部分，因为其他偶数除是素数的2倍外，还可以有其他两个不同素数的和组成）。
所以不能合成偶数总量小于12529个。

白新岭 · 发表于 2019-6-26 16:45

范围统计每段占比
21000 1062 1062 0.898857143
42000 1782 720 0.931428571
63000 2487 705 0.932857143
84000 3076 589 0.943904762
105000 3624 548 0.947809524
126000 4203 579 0.944857143
147000 4623 420 0.96
168000 5130 507 0.951714286
189000 5477 347 0.966952381
210000 5797 320 0.96952381
231000 6190 393 0.962571429
252000 6487 297 0.971714286
273000 6702 215 0.97952381
294000 6964 262 0.975047619
315000 7210 246 0.976571429
336000 7361 151 0.985619048
357000 7594 233 0.977809524
378000 7752 158 0.984952381
399000 7919 167 0.984095238
420000 8096 177 0.983142857
441000 8317 221 0.978952381
462000 8450 133 0.987333333
483000 8581 131 0.98752381
504000 8745 164 0.984380952
525000 8878 133 0.987333333
546000 9010 132 0.987428571
567000 9204 194 0.98152381
588000 9352 148 0.985904762
609000 9487 135 0.987142857
630000 9639 152 0.98552381
651000 9769 130 0.987619048
672000 9872 103 0.990190476
693000 9975 103 0.990190476
714000 10062 87 0.991714286
735000 10127 65 0.993809524
756000 10240 113 0.989238095
777000 10327 87 0.991714286
798000 10416 89 0.99152381
819000 10474 58 0.99447619
840000 10520 46 0.995619048
861000 10584 64 0.993904762
882000 10644 60 0.994285714
903000 10705 61 0.994190476
924000 10730 25 0.997619048
945000 10793 63 0.994
966000 10851 58 0.99447619
987000 10898 47 0.99552381
1008000 10950 52 0.995047619
1029000 11010 60 0.994285714
1050000 11058 48 0.995428571
1071000 11100 42 0.996
1092000 11147 47 0.99552381
1113000 11173 26 0.99752381
1134000 11193 20 0.998095238
1155000 11224 31 0.997047619
1176000 11272 48 0.995428571
1197000 11291 19 0.998190476
1218000 11327 36 0.996571429
1239000 11352 25 0.997619048
1260000 11382 30 0.997142857
1281000 11421 39 0.996285714
1302000 11441 20 0.998095238
1323000 11459 18 0.998285714
1344000 11476 17 0.998380952
1365000 11492 16 0.99847619
1386000 11515 23 0.997809524
1407000 11549 34 0.996761905
1428000 11583 34 0.996761905
1449000 11598 15 0.998571429
1470000 11621 23 0.997809524
1491000 11657 36 0.996571429
1512000 11687 30 0.997142857
1533000 11719 32 0.996952381
1554000 11737 18 0.998285714
1575000 11760 23 0.997809524
1596000 11788 28 0.997333333
1617000 11808 20 0.998095238
1638000 11821 13 0.998761905
1659000 11837 16 0.99847619
1680000 11869 32 0.996952381
1701000 11900 31 0.997047619
1722000 11908 8 0.999238095
1743000 11913 5 0.99952381
1764000 11942 29 0.997238095
1785000 11952 10 0.999047619
1806000 11963 11 0.998952381
1827000 11977 14 0.998666667
1848000 11998 21 0.998
1869000 12012 14 0.998666667
1890000 12036 24 0.997714286
1911000 12052 16 0.99847619
1932000 12074 22 0.997904762
1953000 12094 20 0.998095238
1974000 12125 31 0.997047619
1995000 12141 16 0.99847619
2016000 12155 14 0.998666667
2037000 12161 6 0.999428571
2058000 12183 22 0.997904762
2079000 12187 4 0.999619048
2100000 12194 7 0.999333333
2121000 12203 9 0.999142857
2142000 12207 4 0.999619048
2163000 12212 5 0.99952381
2184000 12213 1 0.999904762
2205000 12213 0 1
2226000 12217 4 0.999619048
2247000 12217 0 1
2268000 12220 3 0.999714286
2289000 12223 3 0.999714286
2310000 12233 10 0.999047619
2331000 12233 0 1
2352000 12237 4 0.999619048
2373000 12245 8 0.999238095
2394000 12247 2 0.999809524
2415000 12256 9 0.999142857
2436000 12260 4 0.999619048
2457000 12260 0 1
2478000 12267 7 0.999333333
2499000 12280 13 0.998761905
2520000 12280 0 1
2541000 12300 20 0.998095238
2562000 12306 6 0.999428571
2583000 12311 5 0.99952381
2604000 12321 10 0.999047619
2625000 12321 0 1
2646000 12324 3 0.999714286
2667000 12338 14 0.998666667
2688000 12341 3 0.999714286
2709000 12345 4 0.999619048
2730000 12345 0 1
2751000 12352 7 0.999333333
2772000 12359 7 0.999333333
2793000 12363 4 0.999619048
2814000 12368 5 0.99952381
2835000 12375 7 0.999333333
2856000 12376 1 0.999904762
2877000 12379 3 0.999714286
2898000 12386 7 0.999333333
2919000 12387 1 0.999904762
2940000 12391 4 0.999619048
2961000 12402 11 0.998952381
2982000 12406 4 0.999619048
3003000 12409 3 0.999714286
3024000 12418 9 0.999142857
3045000 12424 6 0.999428571
3066000 12424 0 1
3087000 12428 4 0.999619048
3108000 12435 7 0.999333333
3129000 12435 0 1
3150000 12442 7 0.999333333
3171000 12443 1 0.999904762
3192000 12443 0 1
3213000 12445 2 0.999809524
3234000 12451 6 0.999428571
3255000 12457 6 0.999428571
3276000 12457 0 1
3297000 12460 3 0.999714286
3318000 12463 3 0.999714286
3339000 12464 1 0.999904762
3360000 12469 5 0.99952381
3381000 12469 0 1
3402000 12474 5 0.99952381
3423000 12477 3 0.999714286
3444000 12480 3 0.999714286
3465000 12480 0 1
3486000 12484 4 0.999619048
3507000 12484 0 1
3528000 12485 1 0.999904762
3549000 12485 0 1
3570000 12488 3 0.999714286
3591000 12489 1 0.999904762
3612000 12492 3 0.999714286
3633000 12492 0 1
3654000 12492 0 1
3675000 12492 0 1
3696000 12492 0 1
3717000 12492 0 1
3738000 12495 3 0.999714286
3759000 12496 1 0.999904762
3780000 12502 6 0.999428571
3801000 12508 6 0.999428571
3822000 12508 0 1
3843000 12508 0 1
3864000 12508 0 1
3885000 12508 0 1
3906000 12511 3 0.999714286
3927000 12511 0 1
3948000 12514 3 0.999714286
3969000 12514 0 1
3990000 12518 4 0.999619048
4011000 12521 3 0.999714286
4032000 12522 1 0.999904762
4053000 12522 0 1
4074000 12522 0 1
4095000 12528 6 0.999428571
4116000 12534 6 0.999428571
4137000 12534 0 1
4158000 12534 0 1
4179000 12537 3 0.999714286
4200000 12537 0 1
4221000 12537 0 1
4242000 12538 1 0.999904762
4263000 12538 0 1
4284000 12538 0 1
4305000 12538 0 1
4326000 12541 3 0.999714286
4347000 12544 3 0.999714286
4368000 12544 0 1
4389000 12547 3 0.999714286
4410000 12551 4 0.999619048
4431000 12555 4 0.999619048
4452000 12555 0 1
4473000 12558 3 0.999714286
4494000 12558 0 1
4515000 12558 0 1
4536000 12558 0 1
4557000 12558 0 1
4578000 12565 7 0.999333333
4599000 12565 0 1
4620000 12565 0 1
4641000 12568 3 0.999714286
4662000 12568 0 1
4683000 12572 4 0.999619048
4704000 12572 0 1
4725000 12575 3 0.999714286
4746000 12575 0 1
4767000 12575 0 1
4788000 12575 0 1
4809000 12578 3 0.999714286
4830000 12578 0 1
4851000 12578 0 1
4872000 12579 1 0.999904762
4893000 12579 0 1
4914000 12579 0 1
4935000 12579 0 1
4956000 12579 0 1
4977000 12579 0 1
4998000 12579 0 1
5019000 12579 0 1
5040000 12579 0 1
5061000 12580 1 0.999904762
5082000 12583 3 0.999714286
5103000 12586 3 0.999714286
5124000 12586 0 1
5145000 12586 0 1
5166000 12586 0 1
5187000 12592 6 0.999428571
5208000 12592 0 1
5229000 12593 1 0.999904762
5250000 12593 0 1
5271000 12593 0 1
5292000 12596 3 0.999714286
5313000 12596 0 1
5334000 12596 0 1
5355000 12596 0 1
5376000 12596 0 1
5397000 12600 4 0.999619048
5418000 12600 0 1
5439000 12600 0 1
5460000 12600 0 1
5481000 12603 3 0.999714286
5502000 12603 0 1
5523000 12603 0 1
5544000 12603 0 1
5565000 12603 0 1
5586000 12603 0 1
5607000 12603 0 1
5628000 12603 0 1
5649000 12606 3 0.999714286
5670000 12606 0 1
5691000 12606 0 1
5712000 12606 0 1
5733000 12609 3 0.999714286
5754000 12609 0 1
5775000 12609 0 1
5796000 12609 0 1
5817000 12609 0 1
5838000 12609 0 1
5859000 12609 0 1
5880000 12612 3 0.999714286
5901000 12612 0 1
5922000 12612 0 1
5943000 12612 0 1
5964000 12612 0 1
5985000 12612 0 1
6006000 12612 0 1
6027000 12615 3 0.999714286
6048000 12615 0 1
6069000 12615 0 1
6090000 12615 0 1
6111000 12616 1 0.999904762
6132000 12616 0 1
6153000 12616 0 1
6174000 12616 0 1
6195000 12624 8 0.999238095
6216000 12624 0 1
6237000 12628 4 0.999619048
6258000 12628 0 1
6279000 12628 0 1
6300000 12628 0 1
6321000 12628 0 1
6342000 12628 0 1
6363000 12628 0 1
6384000 12628 0 1
6405000 12628 0 1
6426000 12628 0 1
6447000 12628 0 1
6468000 12628 0 1
6489000 12631 3 0.999714286
6510000 12631 0 1
6531000 12633 2 0.999809524
6552000 12633 0 1
6573000 12633 0 1
6594000 12633 0 1
6615000 12633 0 1
6636000 12633 0 1
6657000 12633 0 1
6678000 12636 3 0.999714286
6699000 12636 0 1
6720000 12636 0 1
6741000 12636 0 1
6762000 12636 0 1
6783000 12639 3 0.999714286
6804000 12639 0 1
6825000 12639 0 1
6846000 12639 0 1
6867000 12639 0 1
6888000 12640 1 0.999904762
6909000 12640 0 1
6930000 12640 0 1
6951000 12640 0 1
6972000 12640 0 1
6993000 12640 0 1
7014000 12640 0 1
7035000 12640 0 1
7056000 12640 0 1
7077000 12640 0 1
7098000 12640 0 1
7119000 12640 0 1
7140000 12640 0 1
7161000 12640 0 1
7182000 12640 0 1
7203000 12640 0 1
7224000 12643 3 0.999714286
7245000 12643 0 1
7266000 12643 0 1
7287000 12643 0 1
7308000 12643 0 1
7329000 12643 0 1
7350000 12643 0 1
7371000 12643 0 1
7392000 12643 0 1
7413000 12646 3 0.999714286
7434000 12646 0 1
7455000 12646 0 1
7476000 12646 0 1
7497000 12646 0 1
7518000 12646 0 1
7539000 12646 0 1
7560000 12646 0 1
7581000 12646 0 1
7602000 12646 0 1
7623000 12646 0 1
7644000 12646 0 1
7665000 12646 0 1
7686000 12646 0 1
7707000 12646 0 1
7728000 12646 0 1
7749000 12646 0 1
7770000 12646 0 1
7791000 12647 1 0.999904762
7812000 12647 0 1
7833000 12647 0 1
7854000 12647 0 1
7875000 12647 0 1
7896000 12647 0 1
7917000 12647 0 1
7938000 12647 0 1
7959000 12647 0 1
7980000 12647 0 1
8001000 12647 0 1
8022000 12647 0 1
8043000 12647 0 1
8064000 12647 0 1
8085000 12647 0 1
8106000 12647 0 1
8127000 12647 0 1
8148000 12647 0 1
8169000 12647 0 1
8190000 12647 0 1
8211000 12650 3 0.999714286
8232000 12650 0 1
8253000 12650 0 1
8274000 12650 0 1
8295000 12650 0 1
8316000 12650 0 1
8337000 12650 0 1
8358000 12650 0 1
8379000 12650 0 1
8400000 12650 0 1
8421000 12650 0 1
8442000 12650 0 1
8463000 12650 0 1
8484000 12650 0 1
8505000 12650 0 1
8526000 12650 0 1
8547000 12650 0 1
8568000 12650 0 1
8589000 12650 0 1
8610000 12650 0 1
8631000 12650 0 1
8652000 12650 0 1
8673000 12650 0 1
8694000 12650 0 1
8715000 12650 0 1
8736000 12650 0 1
8757000 12650 0 1
8778000 12650 0 1
8799000 12650 0 1
8820000 12650 0 1
8841000 12653 3 0.999714286
8862000 12653 0 1
8883000 12653 0 1
8904000 12653 0 1
8925000 12653 0 1
8946000 12653 0 1
8967000 12653 0 1
8988000 12653 0 1
9009000 12653 0 1
9030000 12653 0 1
9051000 12653 0 1
9072000 12653 0 1
9093000 12653 0 1
9114000 12653 0 1
9135000 12653 0 1
9156000 12653 0 1
9177000 12653 0 1
9198000 12653 0 1
9219000 12653 0 1
9240000 12656 3 0.999714286
9261000 12656 0 1
9282000 12656 0 1
9303000 12656 0 1
9324000 12656 0 1
9345000 12656 0 1
9366000 12656 0 1
9387000 12656 0 1
9408000 12656 0 1
9429000 12656 0 1
9450000 12656 0 1
9471000 12656 0 1
9492000 12656 0 1
9513000 12656 0 1
9534000 12656 0 1
9555000 12656 0 1
9576000 12656 0 1
9597000 12656 0 1
9618000 12656 0 1
9639000 12656 0 1
9660000 12656 0 1
9681000 12656 0 1
9702000 12656 0 1
9723000 12656 0 1
9744000 12656 0 1
9765000 12656 0 1
9786000 12656 0 1
9807000 12659 3 0.999714286
9828000 12659 0 1
9849000 12659 0 1
9870000 12659 0 1
9891000 12659 0 1
9912000 12659 0 1
9933000 12659 0 1
9954000 12659 0 1
9975000 12659 0 1
9996000 12659 0 1
10017000 12659 0 1
10038000 12659 0 1
10059000 12659 0 1
10080000 12659 0 1
10101000 12659 0 1
10122000 12659 0 1
10143000 12659 0 1
10164000 12659 0 1
10185000 12659 0 1
10206000 12661 2 0.999809524
10227000 12662 1 0.999904762
10248000 12662 0 1
10269000 12662 0 1
10290000 12662 0 1
10311000 12662 0 1
10332000 12662 0 1
10353000 12662 0 1
10374000 12662 0 1
10395000 12662 0 1
10416000 12662 0 1
10437000 12662 0 1
10458000 12662 0 1
10479000 12662 0 1
10500000 12662 0 1
10521000 12662 0 1
10542000 12662 0 1
10563000 12662 0 1
10584000 12662 0 1
10605000 12662 0 1
10626000 12662 0 1
10647000 12662 0 1
10668000 12662 0 1
10689000 12662 0 1
10710000 12662 0 1
10731000 12662 0 1
10752000 12662 0 1
10773000 12662 0 1
10794000 12662 0 1
10815000 12662 0 1
10836000 12663 1 0.999904762
10857000 12663 0 1
10878000 12663 0 1
10899000 12663 0 1
10920000 12663 0 1
10941000 12663 0 1
10962000 12663 0 1
10983000 12663 0 1
11004000 12663 0 1
11025000 12663 0 1
11046000 12663 0 1
11067000 12663 0 1
11088000 12663 0 1
11109000 12663 0 1
11130000 12663 0 1
11151000 12663 0 1
11172000 12663 0 1
11193000 12663 0 1
11214000 12663 0 1
11235000 12663 0 1
11256000 12663 0 1
11277000 12663 0 1
11298000 12663 0 1
11319000 12663 0 1
11340000 12663 0 1
11361000 12663 0 1
11382000 12663 0 1
11403000 12663 0 1
11424000 12663 0 1
11445000 12663 0 1
11466000 12663 0 1
11487000 12663 0 1
11508000 12663 0 1
11529000 12663 0 1
11550000 12663 0 1
11571000 12663 0 1
11592000 12663 0 1
11613000 12663 0 1
11634000 12663 0 1
11655000 12663 0 1
11676000 12663 0 1
11697000 12663 0 1
11718000 12663 0 1
11739000 12663 0 1
11760000 12663 0 1
11781000 12669 6 0.999428571
这是等差4生素数(30)不能合成偶数的变换情况，比最密4生素数的区间缩小了10倍，在最密4生素数合成偶数的变化中，区间是21万，这里只是2.1万。
下楼将把第一个区间划分成100份，再看一看其变化趋势。

白新岭 · 发表于 2019-6-26 16:45

范围统计每段占比
21000 1062 1062 0.898857143
42000 1782 720 0.931428571
63000 2487 705 0.932857143
84000 3076 589 0.943904762
105000 3624 548 0.947809524
126000 4203 579 0.944857143
147000 4623 420 0.96
168000 5130 507 0.951714286
189000 5477 347 0.966952381
210000 5797 320 0.96952381
231000 6190 393 0.962571429
252000 6487 297 0.971714286
273000 6702 215 0.97952381
294000 6964 262 0.975047619
315000 7210 246 0.976571429
336000 7361 151 0.985619048
357000 7594 233 0.977809524
378000 7752 158 0.984952381
399000 7919 167 0.984095238
420000 8096 177 0.983142857
441000 8317 221 0.978952381
462000 8450 133 0.987333333
483000 8581 131 0.98752381
504000 8745 164 0.984380952
525000 8878 133 0.987333333
546000 9010 132 0.987428571
567000 9204 194 0.98152381
588000 9352 148 0.985904762
609000 9487 135 0.987142857
630000 9639 152 0.98552381
651000 9769 130 0.987619048
672000 9872 103 0.990190476
693000 9975 103 0.990190476
714000 10062 87 0.991714286
735000 10127 65 0.993809524
756000 10240 113 0.989238095
777000 10327 87 0.991714286
798000 10416 89 0.99152381
819000 10474 58 0.99447619
840000 10520 46 0.995619048
861000 10584 64 0.993904762
882000 10644 60 0.994285714
903000 10705 61 0.994190476
924000 10730 25 0.997619048
945000 10793 63 0.994
966000 10851 58 0.99447619
987000 10898 47 0.99552381
1008000 10950 52 0.995047619
1029000 11010 60 0.994285714
1050000 11058 48 0.995428571
1071000 11100 42 0.996
1092000 11147 47 0.99552381
1113000 11173 26 0.99752381
1134000 11193 20 0.998095238
1155000 11224 31 0.997047619
1176000 11272 48 0.995428571
1197000 11291 19 0.998190476
1218000 11327 36 0.996571429
1239000 11352 25 0.997619048
1260000 11382 30 0.997142857
1281000 11421 39 0.996285714
1302000 11441 20 0.998095238
1323000 11459 18 0.998285714
1344000 11476 17 0.998380952
1365000 11492 16 0.99847619
1386000 11515 23 0.997809524
1407000 11549 34 0.996761905
1428000 11583 34 0.996761905
1449000 11598 15 0.998571429
1470000 11621 23 0.997809524
1491000 11657 36 0.996571429
1512000 11687 30 0.997142857
1533000 11719 32 0.996952381
1554000 11737 18 0.998285714
1575000 11760 23 0.997809524
1596000 11788 28 0.997333333
1617000 11808 20 0.998095238
1638000 11821 13 0.998761905
1659000 11837 16 0.99847619
1680000 11869 32 0.996952381
1701000 11900 31 0.997047619
1722000 11908 8 0.999238095
1743000 11913 5 0.99952381
1764000 11942 29 0.997238095
1785000 11952 10 0.999047619
1806000 11963 11 0.998952381
1827000 11977 14 0.998666667
1848000 11998 21 0.998
1869000 12012 14 0.998666667
1890000 12036 24 0.997714286
1911000 12052 16 0.99847619
1932000 12074 22 0.997904762
1953000 12094 20 0.998095238
1974000 12125 31 0.997047619
1995000 12141 16 0.99847619
2016000 12155 14 0.998666667
2037000 12161 6 0.999428571
2058000 12183 22 0.997904762
2079000 12187 4 0.999619048
2100000 12194 7 0.999333333
2121000 12203 9 0.999142857
2142000 12207 4 0.999619048
2163000 12212 5 0.99952381
2184000 12213 1 0.999904762
2205000 12213 0 1
2226000 12217 4 0.999619048
2247000 12217 0 1
2268000 12220 3 0.999714286
2289000 12223 3 0.999714286
2310000 12233 10 0.999047619
2331000 12233 0 1
2352000 12237 4 0.999619048
2373000 12245 8 0.999238095
2394000 12247 2 0.999809524
2415000 12256 9 0.999142857
2436000 12260 4 0.999619048
2457000 12260 0 1
2478000 12267 7 0.999333333
2499000 12280 13 0.998761905
2520000 12280 0 1
2541000 12300 20 0.998095238
2562000 12306 6 0.999428571
2583000 12311 5 0.99952381
2604000 12321 10 0.999047619
2625000 12321 0 1
2646000 12324 3 0.999714286
2667000 12338 14 0.998666667
2688000 12341 3 0.999714286
2709000 12345 4 0.999619048
2730000 12345 0 1
2751000 12352 7 0.999333333
2772000 12359 7 0.999333333
2793000 12363 4 0.999619048
2814000 12368 5 0.99952381
2835000 12375 7 0.999333333
2856000 12376 1 0.999904762
2877000 12379 3 0.999714286
2898000 12386 7 0.999333333
2919000 12387 1 0.999904762
2940000 12391 4 0.999619048
2961000 12402 11 0.998952381
2982000 12406 4 0.999619048
3003000 12409 3 0.999714286
3024000 12418 9 0.999142857
3045000 12424 6 0.999428571
3066000 12424 0 1
3087000 12428 4 0.999619048
3108000 12435 7 0.999333333
3129000 12435 0 1
3150000 12442 7 0.999333333
3171000 12443 1 0.999904762
3192000 12443 0 1
3213000 12445 2 0.999809524
3234000 12451 6 0.999428571
3255000 12457 6 0.999428571
3276000 12457 0 1
3297000 12460 3 0.999714286
3318000 12463 3 0.999714286
3339000 12464 1 0.999904762
3360000 12469 5 0.99952381
3381000 12469 0 1
3402000 12474 5 0.99952381
3423000 12477 3 0.999714286
3444000 12480 3 0.999714286
3465000 12480 0 1
3486000 12484 4 0.999619048
3507000 12484 0 1
3528000 12485 1 0.999904762
3549000 12485 0 1
3570000 12488 3 0.999714286
3591000 12489 1 0.999904762
3612000 12492 3 0.999714286
3633000 12492 0 1
3654000 12492 0 1
3675000 12492 0 1
3696000 12492 0 1
3717000 12492 0 1
3738000 12495 3 0.999714286
3759000 12496 1 0.999904762
3780000 12502 6 0.999428571
3801000 12508 6 0.999428571
3822000 12508 0 1
3843000 12508 0 1
3864000 12508 0 1
3885000 12508 0 1
3906000 12511 3 0.999714286
3927000 12511 0 1
3948000 12514 3 0.999714286
3969000 12514 0 1
3990000 12518 4 0.999619048
4011000 12521 3 0.999714286
4032000 12522 1 0.999904762
4053000 12522 0 1
4074000 12522 0 1
4095000 12528 6 0.999428571
4116000 12534 6 0.999428571
4137000 12534 0 1
4158000 12534 0 1
4179000 12537 3 0.999714286
4200000 12537 0 1
4221000 12537 0 1
4242000 12538 1 0.999904762
4263000 12538 0 1
4284000 12538 0 1
4305000 12538 0 1
4326000 12541 3 0.999714286
4347000 12544 3 0.999714286
4368000 12544 0 1
4389000 12547 3 0.999714286
4410000 12551 4 0.999619048
4431000 12555 4 0.999619048
4452000 12555 0 1
4473000 12558 3 0.999714286
4494000 12558 0 1
4515000 12558 0 1
4536000 12558 0 1
4557000 12558 0 1
4578000 12565 7 0.999333333
4599000 12565 0 1
4620000 12565 0 1
4641000 12568 3 0.999714286
4662000 12568 0 1
4683000 12572 4 0.999619048
4704000 12572 0 1
4725000 12575 3 0.999714286
4746000 12575 0 1
4767000 12575 0 1
4788000 12575 0 1
4809000 12578 3 0.999714286
4830000 12578 0 1
4851000 12578 0 1
4872000 12579 1 0.999904762
4893000 12579 0 1
4914000 12579 0 1
4935000 12579 0 1
4956000 12579 0 1
4977000 12579 0 1
4998000 12579 0 1
5019000 12579 0 1
5040000 12579 0 1
5061000 12580 1 0.999904762
5082000 12583 3 0.999714286
5103000 12586 3 0.999714286
5124000 12586 0 1
5145000 12586 0 1
5166000 12586 0 1
5187000 12592 6 0.999428571
5208000 12592 0 1
5229000 12593 1 0.999904762
5250000 12593 0 1
5271000 12593 0 1
5292000 12596 3 0.999714286
5313000 12596 0 1
5334000 12596 0 1
5355000 12596 0 1
5376000 12596 0 1
5397000 12600 4 0.999619048
5418000 12600 0 1
5439000 12600 0 1
5460000 12600 0 1
5481000 12603 3 0.999714286
5502000 12603 0 1
5523000 12603 0 1
5544000 12603 0 1
5565000 12603 0 1
5586000 12603 0 1
5607000 12603 0 1
5628000 12603 0 1
5649000 12606 3 0.999714286
5670000 12606 0 1
5691000 12606 0 1
5712000 12606 0 1
5733000 12609 3 0.999714286
5754000 12609 0 1
5775000 12609 0 1
5796000 12609 0 1
5817000 12609 0 1
5838000 12609 0 1
5859000 12609 0 1
5880000 12612 3 0.999714286
5901000 12612 0 1
5922000 12612 0 1
5943000 12612 0 1
5964000 12612 0 1
5985000 12612 0 1
6006000 12612 0 1
6027000 12615 3 0.999714286
6048000 12615 0 1
6069000 12615 0 1
6090000 12615 0 1
6111000 12616 1 0.999904762
6132000 12616 0 1
6153000 12616 0 1
6174000 12616 0 1
6195000 12624 8 0.999238095
6216000 12624 0 1
6237000 12628 4 0.999619048
6258000 12628 0 1
6279000 12628 0 1
6300000 12628 0 1
6321000 12628 0 1
6342000 12628 0 1
6363000 12628 0 1
6384000 12628 0 1
6405000 12628 0 1
6426000 12628 0 1
6447000 12628 0 1
6468000 12628 0 1
6489000 12631 3 0.999714286
6510000 12631 0 1
6531000 12633 2 0.999809524
6552000 12633 0 1
6573000 12633 0 1
6594000 12633 0 1
6615000 12633 0 1
6636000 12633 0 1
6657000 12633 0 1
6678000 12636 3 0.999714286
6699000 12636 0 1
6720000 12636 0 1
6741000 12636 0 1
6762000 12636 0 1
6783000 12639 3 0.999714286
6804000 12639 0 1
6825000 12639 0 1
6846000 12639 0 1
6867000 12639 0 1
6888000 12640 1 0.999904762
6909000 12640 0 1
6930000 12640 0 1
6951000 12640 0 1
6972000 12640 0 1
6993000 12640 0 1
7014000 12640 0 1
7035000 12640 0 1
7056000 12640 0 1
7077000 12640 0 1
7098000 12640 0 1
7119000 12640 0 1
7140000 12640 0 1
7161000 12640 0 1
7182000 12640 0 1
7203000 12640 0 1
7224000 12643 3 0.999714286
7245000 12643 0 1
7266000 12643 0 1
7287000 12643 0 1
7308000 12643 0 1
7329000 12643 0 1
7350000 12643 0 1
7371000 12643 0 1
7392000 12643 0 1
7413000 12646 3 0.999714286
7434000 12646 0 1
7455000 12646 0 1
7476000 12646 0 1
7497000 12646 0 1
7518000 12646 0 1
7539000 12646 0 1
7560000 12646 0 1
7581000 12646 0 1
7602000 12646 0 1
7623000 12646 0 1
7644000 12646 0 1
7665000 12646 0 1
7686000 12646 0 1
7707000 12646 0 1
7728000 12646 0 1
7749000 12646 0 1
7770000 12646 0 1
7791000 12647 1 0.999904762
7812000 12647 0 1
7833000 12647 0 1
7854000 12647 0 1
7875000 12647 0 1
7896000 12647 0 1
7917000 12647 0 1
7938000 12647 0 1
7959000 12647 0 1
7980000 12647 0 1
8001000 12647 0 1
8022000 12647 0 1
8043000 12647 0 1
8064000 12647 0 1
8085000 12647 0 1
8106000 12647 0 1
8127000 12647 0 1
8148000 12647 0 1
8169000 12647 0 1
8190000 12647 0 1
8211000 12650 3 0.999714286
8232000 12650 0 1
8253000 12650 0 1
8274000 12650 0 1
8295000 12650 0 1
8316000 12650 0 1
8337000 12650 0 1
8358000 12650 0 1
8379000 12650 0 1
8400000 12650 0 1
8421000 12650 0 1
8442000 12650 0 1
8463000 12650 0 1
8484000 12650 0 1
8505000 12650 0 1
8526000 12650 0 1
8547000 12650 0 1
8568000 12650 0 1
8589000 12650 0 1
8610000 12650 0 1
8631000 12650 0 1
8652000 12650 0 1
8673000 12650 0 1
8694000 12650 0 1
8715000 12650 0 1
8736000 12650 0 1
8757000 12650 0 1
8778000 12650 0 1
8799000 12650 0 1
8820000 12650 0 1
8841000 12653 3 0.999714286
8862000 12653 0 1
8883000 12653 0 1
8904000 12653 0 1
8925000 12653 0 1
8946000 12653 0 1
8967000 12653 0 1
8988000 12653 0 1
9009000 12653 0 1
9030000 12653 0 1
9051000 12653 0 1
9072000 12653 0 1
9093000 12653 0 1
9114000 12653 0 1
9135000 12653 0 1
9156000 12653 0 1
9177000 12653 0 1
9198000 12653 0 1
9219000 12653 0 1
9240000 12656 3 0.999714286
9261000 12656 0 1
9282000 12656 0 1
9303000 12656 0 1
9324000 12656 0 1
9345000 12656 0 1
9366000 12656 0 1
9387000 12656 0 1
9408000 12656 0 1
9429000 12656 0 1
9450000 12656 0 1
9471000 12656 0 1
9492000 12656 0 1
9513000 12656 0 1
9534000 12656 0 1
9555000 12656 0 1
9576000 12656 0 1
9597000 12656 0 1
9618000 12656 0 1
9639000 12656 0 1
9660000 12656 0 1
9681000 12656 0 1
9702000 12656 0 1
9723000 12656 0 1
9744000 12656 0 1
9765000 12656 0 1
9786000 12656 0 1
9807000 12659 3 0.999714286
9828000 12659 0 1
9849000 12659 0 1
9870000 12659 0 1
9891000 12659 0 1
9912000 12659 0 1
9933000 12659 0 1
9954000 12659 0 1
9975000 12659 0 1
9996000 12659 0 1
10017000 12659 0 1
10038000 12659 0 1
10059000 12659 0 1
10080000 12659 0 1
10101000 12659 0 1
10122000 12659 0 1
10143000 12659 0 1
10164000 12659 0 1
10185000 12659 0 1
10206000 12661 2 0.999809524
10227000 12662 1 0.999904762
10248000 12662 0 1
10269000 12662 0 1
10290000 12662 0 1
10311000 12662 0 1
10332000 12662 0 1
10353000 12662 0 1
10374000 12662 0 1
10395000 12662 0 1
10416000 12662 0 1
10437000 12662 0 1
10458000 12662 0 1
10479000 12662 0 1
10500000 12662 0 1
10521000 12662 0 1
10542000 12662 0 1
10563000 12662 0 1
10584000 12662 0 1
10605000 12662 0 1
10626000 12662 0 1
10647000 12662 0 1
10668000 12662 0 1
10689000 12662 0 1
10710000 12662 0 1
10731000 12662 0 1
10752000 12662 0 1
10773000 12662 0 1
10794000 12662 0 1
10815000 12662 0 1
10836000 12663 1 0.999904762
10857000 12663 0 1
10878000 12663 0 1
10899000 12663 0 1
10920000 12663 0 1
10941000 12663 0 1
10962000 12663 0 1
10983000 12663 0 1
11004000 12663 0 1
11025000 12663 0 1
11046000 12663 0 1
11067000 12663 0 1
11088000 12663 0 1
11109000 12663 0 1
11130000 12663 0 1
11151000 12663 0 1
11172000 12663 0 1
11193000 12663 0 1
11214000 12663 0 1
11235000 12663 0 1
11256000 12663 0 1
11277000 12663 0 1
11298000 12663 0 1
11319000 12663 0 1
11340000 12663 0 1
11361000 12663 0 1
11382000 12663 0 1
11403000 12663 0 1
11424000 12663 0 1
11445000 12663 0 1
11466000 12663 0 1
11487000 12663 0 1
11508000 12663 0 1
11529000 12663 0 1
11550000 12663 0 1
11571000 12663 0 1
11592000 12663 0 1
11613000 12663 0 1
11634000 12663 0 1
11655000 12663 0 1
11676000 12663 0 1
11697000 12663 0 1
11718000 12663 0 1
11739000 12663 0 1
11760000 12663 0 1
11781000 12669 6 0.999428571
这是等差4生素数(30)不能合成偶数的变换情况，比最密4生素数的区间缩小了10倍，在最密4生素数合成偶数的变化中，区间是21万，这里只是2.1万。
下楼将把第一个区间划分成100份，再看一看其变化趋势。

白新岭 · 发表于 2019-6-26 16:50

范围统计每段占比
210 33 33 0.685714286
420 56 23 0.780952381
630 61 5 0.952380952
840 74 13 0.876190476
1050 90 16 0.847619048
1260 101 11 0.895238095
1470 110 9 0.914285714
1680 124 14 0.866666667
1890 140 16 0.847619048
2100 159 19 0.819047619
2310 168 9 0.914285714
2520 176 8 0.923809524
2730 191 15 0.857142857
2940 194 3 0.971428571
3150 196 2 0.980952381
3360 204 8 0.923809524
3570 219 15 0.857142857
3780 229 10 0.904761905
3990 231 2 0.980952381
4200 235 4 0.961904762
4410 243 8 0.923809524
4620 244 1 0.99047619
4830 254 10 0.904761905
5040 271 17 0.838095238
5250 281 10 0.904761905
5460 297 16 0.847619048
5670 312 15 0.857142857
5880 332 20 0.80952381
6090 352 20 0.80952381
6300 368 16 0.847619048
6510 388 20 0.80952381
6720 398 10 0.904761905
6930 407 9 0.914285714
7140 410 3 0.971428571
7350 426 16 0.847619048
7560 449 23 0.780952381
7770 464 15 0.857142857
7980 480 16 0.847619048
8190 493 13 0.876190476
8400 515 22 0.79047619
8610 541 26 0.752380952
8820 555 14 0.866666667
9030 574 19 0.819047619
9240 586 12 0.885714286
9450 592 6 0.942857143
9660 603 11 0.895238095
9870 614 11 0.895238095
10080 630 16 0.847619048
10290 639 9 0.914285714
10500 642 3 0.971428571
10710 651 9 0.914285714
10920 657 6 0.942857143
11130 663 6 0.942857143
11340 674 11 0.895238095
11550 686 12 0.885714286
11760 686 0 1
11970 695 9 0.914285714
12180 711 16 0.847619048
12390 716 5 0.952380952
12600 728 12 0.885714286
12810 745 17 0.838095238
13020 751 6 0.942857143
13230 761 10 0.904761905
13440 771 10 0.904761905
13650 779 8 0.923809524
13860 780 1 0.99047619
14070 781 1 0.99047619
14280 785 4 0.961904762
14490 800 15 0.857142857
14700 809 9 0.914285714
14910 821 12 0.885714286
15120 823 2 0.980952381
15330 827 4 0.961904762
15540 834 7 0.933333333
15750 845 11 0.895238095
15960 857 12 0.885714286
16170 867 10 0.904761905
16380 883 16 0.847619048
16590 892 9 0.914285714
16800 899 7 0.933333333
17010 905 6 0.942857143
17220 920 15 0.857142857
17430 940 20 0.80952381
17640 945 5 0.952380952
17850 956 11 0.895238095
18060 973 17 0.838095238
18270 980 7 0.933333333
18480 988 8 0.923809524
18690 990 2 0.980952381
18900 1000 10 0.904761905
19110 1005 5 0.952380952
19320 1014 9 0.914285714
19530 1022 8 0.923809524
19740 1026 4 0.961904762
19950 1035 9 0.914285714
20160 1036 1 0.99047619
20370 1036 0 1
20580 1048 12 0.885714286
20790 1060 12 0.885714286
21000 1062 2 0.980952381
这是细分后的变化情况，起步能合成的偶数就占到68%以上。

白新岭 · 发表于 2019-6-27 20:00

因式分解 n = (10^140-1)/9:
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 = 11 × 29 × 41 × 71 × 101 × 239 × 271 × 281 × 421 × 3541 × 4649 × 9091 × 27961 × 123551 × 909091 × 3471301 × 4147571 × 13489841 × 121499449 × 60368344121 × 102598800232111471 × 265212793249617641 × 848654483879497562821
这是WIMS上的一个因式分解，它含有等差4生素数的因子11,41,71,101（公差30）.

		自动登录	找回密码
密码			注册

存在等差k生素数公差d最小值使它中的素数之和遍历偶数

浏览过的版块