[原创]三个奇素数和的分布

白新岭

奇数→→有序3元素数组→→组数比值
9→→1→→
11→→3→→3
13→→6→→2
15→→7→→1.166666667
17→→9→→1.285714286
19→→12→→1.333333333
21→→16→→1.333333333
23→→18→→1.125
25→→21→→1.166666667
27→→27→→1.285714286
29→→30→→1.111111111
31→→30→→1
33→→34→→1.133333333
35→→36→→1.058823529
37→→42→→1.166666667
39→→46→→1.095238095
41→→48→→1.043478261
43→→48→→1
45→→51→→1.0625
47→→63→→1.235294118
49→→60→→0.952380952
51→→64→→1.066666667
53→→81→→1.265625
55→→75→→0.925925926
57→→76→→1.013333333
59→→87→→1.144736842
61→→87→→1
63→→90→→1.034482759
65→→102→→1.133333333
67→→105→→1.029411765
69→→97→→0.923809524
71→→117→→1.206185567
73→→114→→0.974358974
75→→105→→0.921052632
77→→144→→1.371428571
79→→129→→0.895833333
81→→126→→0.976744186
83→→159→→1.261904762
85→→141→→0.886792453
87→→145→→1.028368794
89→→177→→1.220689655
91→→162→→0.915254237
93→→160→→0.987654321
95→→195→→1.21875
97→→186→→0.953846154
99→→153→→0.822580645
101→→207→→1.352941176
103→→201→→0.971014493
105→→171→→0.850746269
107→→237→→1.385964912
109→→210→→0.886075949
111→→187→→0.89047619
113→→255→→1.363636364
115→→234→→0.917647059
117→→222→→0.948717949
119→→279→→1.256756757
121→→261→→0.935483871
123→→247→→0.946360153
125→→294→→1.190283401
127→→282→→0.959183673
129→→238→→0.843971631
131→→321→→1.348739496
133→→306→→0.953271028
135→→240→→0.784313725
137→→348→→1.45
139→→303→→0.870689655
141→→250→→0.825082508
143→→369→→1.476
145→→327→→0.886178862
147→→294→→0.899082569
149→→384→→1.306122449
151→→348→→0.90625
153→→315→→0.905172414
155→→387→→1.228571429
157→→390→→1.007751938
159→→313→→0.802564103
161→→429→→1.370607029
163→→411→→0.958041958
165→→312→→0.759124088
167→→450→→1.442307692
169→→390→→0.866666667
171→→348→→0.892307692
173→→507→→1.456896552
175→→423→→0.834319527
177→→367→→0.867612293
179→→495→→1.348773842
181→→462→→0.933333333
183→→403→→0.872294372
185→→513→→1.272952854
187→→516→→1.005847953
189→→396→→0.76744186
191→→552→→1.393939394
193→→525→→0.951086957
195→→387→→0.737142857
197→→579→→1.496124031
199→→537→→0.92746114
201→→442→→0.823091248
203→→612→→1.384615385
205→→537→→0.87745098
207→→468→→0.87150838
209→→630→→1.346153846
211→→576→→0.914285714
213→→520→→0.902777778
215→→666→→1.280769231
217→→636→→0.954954955
219→→478→→0.751572327
221→→699→→1.462343096
223→→666→→0.9527897
225→→477→→0.716216216
227→→729→→1.528301887
229→→657→→0.901234568
231→→507→→0.771689498
233→→741→→1.461538462
235→→636→→0.858299595
237→→550→→0.864779874
239→→762→→1.385454545
241→→723→→0.948818898
243→→606→→0.838174274
245→→756→→1.247524752
247→→777→→1.027777778
249→→595→→0.765765766
251→→831→→1.396638655
253→→795→→0.9566787
255→→588→→0.739622642
257→→891→→1.515306122
259→→789→→0.885521886
261→→612→→0.775665399
263→→900→→1.470588235
265→→798→→0.886666667
267→→661→→0.828320802
269→→912→→1.379727685
271→→870→→0.953947368
273→→693→→0.796551724
275→→909→→1.311688312
277→→927→→1.01980198
279→→684→→0.737864078
281→→987→→1.442982456
283→→969→→0.981762918
285→→693→→0.715170279
287→→1020→→1.471861472
289→→939→→0.920588235
291→→748→→0.796592119
293→→1086→→1.451871658
295→→921→→0.848066298
297→→792→→0.859934853
299→→1095→→1.382575758
301→→996→→0.909589041
303→→820→→0.823293173
305→→1098→→1.33902439
307→→1086→→0.989071038
309→→802→→0.738489871
311→→1161→→1.447630923
313→→1110→→0.956072351
315→→792→→0.713513514
317→→1215→→1.534090909
319→→1086→→0.89382716
321→→841→→0.774401473
323→→1230→→1.46254459
325→→1077→→0.875609756
327→→913→→0.847725162
329→→1206→→1.320920044
331→→1146→→0.950248756
333→→942→→0.821989529
335→→1242→→1.318471338
337→→1206→→0.971014493
339→→910→→0.754560531
341→→1362→→1.496703297
343→→1260→→0.925110132
345→→894→→0.70952381
347→→1401→→1.567114094
349→→1239→→0.884368308
351→→951→→0.767554479
353→→1425→→1.498422713
355→→1221→→0.856842105
357→→999→→0.818181818
359→→1404→→1.405405405
361→→1323→→0.942307692
363→→1020→→0.770975057
365→→1380→→1.352941176
367→→1401→→1.015217391
369→→1032→→0.736616702
371→→1482→→1.436046512
373→→1407→→0.949392713
375→→1008→→0.71641791
377→→1557→→1.544642857
379→→1356→→0.870905588
381→→1111→→0.819321534
383→→1635→→1.471647165
385→→1350→→0.825688073
387→→1131→→0.837777778
389→→1569→→1.387267905
391→→1494→→0.952198853
393→→1174→→0.785809906
395→→1587→→1.351788756
397→→1584→→0.998109641
399→→1122→→0.708333333
401→→1674→→1.49197861
403→→1599→→0.955197133
405→→1086→→0.679174484
407→→1725→→1.58839779
409→→1587→→0.92
411→→1216→→0.766225583
413→→1755→→1.443256579
415→→1512→→0.861538462
417→→1264→→0.835978836
419→→1746→→1.381329114
421→→1641→→0.939862543
423→→1320→→0.804387569
425→→1767→→1.338636364
427→→1743→→0.986417657
429→→1245→→0.714285714
431→→1872→→1.503614458
433→→1794→→0.958333333
435→→1221→→0.680602007
437→→1977→→1.619164619
439→→1758→→0.8892261
441→→1299→→0.73890785
443→→1971→→1.517321016
445→→1692→→0.858447489
447→→1399→→0.826832151
449→→1944→→1.389563974
451→→1869→→0.961419753
453→→1462→→0.78223649
455→→1869→→1.278385773
457→→1926→→1.030497592
459→→1404→→0.728971963
461→→2070→→1.474358974
463→→1965→→0.949275362
465→→1401→→0.712977099
467→→2172→→1.550321199
469→→1929→→0.888121547
471→→1471→→0.76257128
473→→2193→→1.49082257
475→→1929→→0.879616963
477→→1524→→0.790046656
479→→2229→→1.462598425
481→→2073→→0.930013459
483→→1560→→0.752532562
485→→2118→→1.357692308
487→→2160→→1.019830028
489→→1531→→0.708796296
491→→2277→→1.487263227
493→→2232→→0.980237154
495→→1500→→0.672043011
497→→2313→→1.542
499→→2136→→0.923476005
501→→1615→→0.756086142
503→→2409→→1.491640867
505→→2079→→0.863013699
507→→1686→→0.810966811
509→→2427→→1.439501779
511→→2205→→0.908529048
513→→1776→→0.805442177
515→→2352→→1.324324324
517→→2367→→1.006377551
519→→1681→→0.710181665
521→→2538→→1.509815586
523→→2427→→0.956264775
525→→1614→→0.665018541
527→→2598→→1.609665428
529→→2346→→0.903002309
531→→1773→→0.755754476
533→→2604→→1.468697124
535→→2322→→0.891705069
537→→1828→→0.787252369
539→→2556→→1.398249453
541→→2433→→0.951877934
543→→1909→→0.784628031
545→→2535→→1.327920377
547→→2514→→0.991715976
549→→1875→→0.745823389
551→→2754→→1.4688
553→→2571→→0.933551198
555→→1779→→0.691948658
557→→2802→→1.575042159
559→→2529→→0.902569593
561→→1866→→0.737841044
563→→2865→→1.535369775
565→→2481→→0.865968586
567→→1926→→0.776299879
569→→2850→→1.479750779
571→→2613→→0.916842105
573→→2032→→0.77765021
575→→2712→→1.334645669
577→→2748→→1.013274336
579→→1993→→0.725254731
581→→2871→→1.440541897
583→→2781→→0.968652038
585→→1896→→0.681769148
587→→2994→→1.579113924
589→→2724→→0.909819639
591→→2068→→0.75917768
593→→3084→→1.491295938
595→→2589→→0.839494163
597→→2101→→0.811510236
599→→3045→→1.449309852
601→→2835→→0.931034483
603→→2172→→0.766137566
605→→2958→→1.361878453
607→→2964→→1.002028398
609→→2073→→0.699392713
611→→3174→→1.531114327
613→→2997→→0.944234405
615→→2049→→0.683683684
617→→3231→→1.576866764
619→→3018→→0.934076137
621→→2226→→0.737574553
623→→3222→→1.447439353
625→→2850→→0.884543762
627→→2271→→0.796842105
629→→3285→→1.446499339
631→→3042→→0.926027397
633→→2401→→0.789283366
635→→3240→→1.349437734
637→→3123→→0.963888889
639→→2268→→0.726224784
641→→3441→→1.517195767
643→→3231→→0.938971229
645→→2187→→0.676880223
647→→3534→→1.615912209
649→→3204→→0.906621392
651→→2328→→0.72659176
653→→3567→→1.532216495
655→→3075→→0.862068966
657→→2454→→0.79804878
659→→3534→→1.4400978
661→→3348→→0.947368421
663→→2538→→0.758064516
665→→3354→→1.321513002
667→→3459→→1.031305903
669→→2461→→0.711477306
671→→3654→→1.484762292
673→→3480→→0.952380952
675→→2397→→0.688793103
677→→3819→→1.593241552
679→→3369→→0.882168107
681→→2551→→0.757197982
683→→3852→→1.50999608
685→→3312→→0.859813084
687→→2641→→0.797403382
689→→3852→→1.458538432
691→→3591→→0.932242991
693→→2625→→0.730994152
695→→3681→→1.402285714
697→→3714→→1.008964955
699→→2629→→0.707862143
701→→3948→→1.501711677
703→→3810→→0.965045593
705→→2532→→0.664566929
707→→3993→→1.577014218
709→→3684→→0.922614576
711→→2715→→0.736970684
713→→4095→→1.508287293
715→→3432→→0.838095238
717→→2899→→0.84469697
719→→4113→→1.418765091
721→→3726→→0.905908096
723→→2878→→0.772410091
725→→3945→→1.370743572
727→→3936→→0.997718631
729→→2778→→0.705792683
731→→4224→→1.520518359
733→→4044→→0.957386364
735→→2616→→0.646884273
737→→4293→→1.641055046
739→→3918→→0.912648498
741→→2871→→0.732771822
743→→4386→→1.5276907
745→→3774→→0.860465116
747→→2997→→0.794117647
749→→4245→→1.416416416
751→→4023→→0.94770318
753→→3043→→0.756400696
755→→4176→→1.372329938
757→→4158→→0.995689655
759→→3036→→0.73015873
761→→4488→→1.47826087
763→→4173→→0.929812834
765→→2865→→0.686556434
767→→4554→→1.589528796
769→→4158→→0.913043478
771→→3028→→0.728234728
773→→4725→→1.560435931
775→→4026→→0.852063492
777→→3150→→0.782414307
779→→4602→→1.460952381
781→→4224→→0.917861799
783→→3240→→0.767045455
785→→4401→→1.358333333
787→→4518→→1.026584867
789→→3184→→0.704736609
791→→4605→→1.44629397
793→→4488→→0.974592834
795→→3009→→0.670454545
797→→4797→→1.594217348
799→→4398→→0.916823014
801→→3291→→0.748294679
803→→4935→→1.499544211
805→→4149→→0.840729483
807→→3334→→0.803567125
809→→4872→→1.461307738
811→→4575→→0.939039409
813→→3352→→0.732677596
815→→4659→→1.389916468
817→→4752→→1.019961365
819→→3255→→0.684974747
821→→5007→→1.538248848
823→→4749→→0.948472139
825→→3120→→0.656980417
827→→5037→→1.614423077
829→→4725→→0.938058368
831→→3424→→0.724656085
833→→5046→→1.473714953
835→→4497→→0.891200951
837→→3498→→0.777851901
839→→5130→→1.466552316
841→→4803→→0.93625731
843→→3691→→0.768478035
845→→4950→→1.341099973
847→→4875→→0.984848485
849→→3511→→0.720205128
851→→5283→→1.504699516
853→→5097→→0.964792731
855→→3357→→0.658622719
857→→5397→→1.607685433
859→→4998→→0.926070039
861→→3585→→0.717286915
863→→5451→→1.520502092
865→→4698→→0.861860209
867→→3642→→0.775223499
869→→5394→→1.481054366
871→→5127→→0.950500556
873→→3828→→0.746635459
875→→5055→→1.320532915
877→→5298→→1.048071217
879→→3715→→0.701208003
881→→5538→→1.490713324
883→→5283→→0.953954496
885→→3606→→0.682566723
887→→5748→→1.594009983
889→→5118→→0.89039666
891→→3777→→0.737983587
893→→5760→→1.525019857
895→→5085→→0.8828125
897→→3864→→0.759882006
899→→5784→→1.49689441
901→→5433→→0.939315353
903→→3918→→0.721148537
905→→5460→→1.393568147
907→→5517→→1.01043956
909→→3849→→0.697661773
911→→5871→→1.525331255
913→→5613→→0.956055187
915→→3738→→0.665954035
917→→5847→→1.564205457
919→→5478→→0.936890713
921→→4006→→0.731288792
923→→5988→→1.494757863
925→→5253→→0.877254509
927→→4185→→0.796687607
929→→6132→→1.465232975
931→→5577→→0.909491194
933→→4159→→0.745741438
935→→5670→→1.363308488
937→→5871→→1.035449735
939→→4072→→0.693578607
941→→6207→→1.524312377
943→→5946→→0.957950701
945→→3816→→0.641775984
947→→6267→→1.642295597
949→→5679→→0.906175203
951→→4180→→0.736045078
953→→6294→→1.505741627
955→→5598→→0.889418494
957→→4293→→0.766881029
959→→6126→→1.426974144
961→→5928→→0.967678746
963→→4410→→0.743927126
965→→5985→→1.357142857
967→→6102→→1.019548872
969→→4332→→0.70993117
971→→6513→→1.503462604
973→→6033→→0.926301244
975→→4041→→0.669816012
977→→6561→→1.623608018
979→→5988→→0.912665752
981→→4413→→0.736973948
983→→6627→→1.501699524
985→→5775→→0.871435038
987→→4389→→0.76
989→→6576→→1.498291183
991→→6156→→0.936131387
993→→4609→→0.748700455
995→→6258→→1.35777826
997→→6507→→1.03978907
999→→4497→→0.69110189
以上给出了1000以内的奇数的3元有序素数组。从结果看，开始并非显示素数的多组性质，按3元素数合成概率，应该是素数奇数的3元有序数组最多，合奇数的数组较少，越是小的因子的合数越明显，可是开始并未出现此种分布，当大些时候才显现出来，这是因为能整除的个体对局部，小范围的影响，随着奇数的增大，个体的整除性影响变小，类别的比例显现出来。另外除了开始的比值不符合理论值外，以后的能与理论值吻合。理论计算值，连续的3个奇数拥有的3元有序数组比例最大值小于根号π，大概值为1.74。

白新岭

无论整数分拆，m个自然数和的分布，限定定义域方程的正整数解（限定方法为不能整除P1,P2,P3,....),还是歌猜问题都是一类问题，它们的正整数解的组数公式也是同次多项代数表达式。例如把一个整数拆分成3个整数的数目，ax+by+cz=n的正整数解的组数，不能整除2，3，5，7，11的x,y,z,能使x+y+z=n成立的正整数解的组数，都是一族2次代数式多项式。物理相通，一脉相承。规律一致，都有周期可言。

白新岭

有没有人对超过2元的素数和分布感兴趣。如果感兴趣就发表一些自己的看法。

白新岭

之所以提出三元素数和的分布问题，是想印证无论2元的，还是多元的，无论是无限个条件，还是有限个条件，都是一类问题，都离不开基本元的合成，在周期上的方法是没有区别的，只有一周内的方法是不均匀的，有区分的。

白新岭

重在参与，重在实践。要想从理论上对歌猜有清晰的认识，就需要研究特殊定义域方程解的组数与条件的关系。先看一看奇数域中方程x+y=n的正整数解的组数（实际就是x,y不能整除2时，方程正整数解的组数），然后再求不能被2，3整除时，方程x+y=n的正整数解的组数；接下来探讨一下不能被2，3，5整除时，方程x+y=n的正整数解的组数；一直把条件增加下去，会发现什么呢？进了门就有出路。预祝有兴趣的数学爱好者心想事成。

申一言

[这个贴子最后由申一言在 2009/05/25 05:29pm 第 1 次编辑]


    证明式: Y(Nn)≥1.5(Nn-3),  Nn＞3
    计算式:
                  [Nn+12(√Nn-1)]^2
           Y(Nn)=------------------
                    (2logNn+3)^3
                  ((算                                                                                                                                                                                                                                                                                            

熊一兵

我以为白新岭解决哥猜的思路是对的,也许再结合<概率素数论>就能成功,后一工作我希望你来做,前提是你要先搞懂这一理论,我现在在争取这一理论获得学术认可,不知何时有机会来做这一工作

wangyangke

http://www.mathchina.com/cgi-bin/topic.cgi?forum=12&topic=856&show=0

白新岭

[这个贴子最后由白新岭在 2009/06/14 00:23pm 第 1 次编辑]

多谢熊一兵的支持与厚望。

白新岭

谢谢wangyangke对本帖的浏览与回复。