ゴールドバッハの予想１０
ゴールドバッハの予想で面白い規則を発見した
g1=p-n(n-1)
g2=n(n+1)-p
となる、p,g1,g2が素数の組み合わせが必ず存在する
ただし、pは0と1を含む
g1+g2=2n
p=g1+n(n-1)=n(n+1)-g2
ゴールドバッハの予想の任意の偶数の分割点で素数が作れる対が1つ以上存在するということだ
pが素数ということに何か関係があるのか？
調査した結果は、以下の通り
p=0を含まない場合は
n<2000
で
n=1,2,3,31
だけが例外となる
n,g1,g2,p
1
2
3
4,5,3,17
5,3,7,23
6,7,5,37
7,11,3,53
8,3,13,59
9,7,11,79
10,7,13,97
11,3,19,113
12,5,19,137
13,7,19,163
14,11,17,193
15,13,17,223
16,29,3,269
17,5,29,277
18,5,31,311
19,7,31,349
20,3,37,383
21,11,31,431
22,37,7,499
23,3,43,509
24,5,43,557
25,7,43,607
26,11,41,661
27,7,47,709
28,13,43,769
29,11,47,823
30,7,53,877
31
32,5,59,997
33,5,61,1061
34,7,61,1129
35,3,67,1193
36,19,53,1279
37,67,7,1399
38,3,73,1409
39,5,73,1487
40,7,73,1567
41,23,59,1663
42,11,73,1733
43,67,19,1873
44,41,47,1933
45,7,83,1987
46,13,79,2083
47,41,53,2203
48,13,83,2269
49,19,79,2371
50,17,83,2467
51,29,73,2579
52,7,97,2659
53,47,59,2803
54,41,67,2903
55,31,79,3001
56,3,109,3083
57,11,103,3203
58,7,109,3313
59,11,107,3433
60,7,113,3547
61,13,109,3673
62,11,113,3793
63,13,113,3919
64,19,109,4051
65,17,113,4177
66,59,73,4349
67,61,73,4483
68,5,131,4561
69,11,127,4703
70,31,109,4861
71,3,139,4973
72,7,137,5119
73,67,79,5323
74,11,137,5413
75,13,137,5563
76,43,109,5743
77,5,149,5857
78,5,151,6011
79,139,19,6301
80,3,157,6323
81,11,151,6491
82,37,127,6679
83,17,149,6823
84,5,163,6977
85,19,151,7159
86,23,149,7333
87,7,167,7489
88,13,163,7669
89,41,137,7873
90,7,173,8017
91,19,163,8209
92,5,179,8377
93,7,179,8563
94,37,151,8779
95,11,179,8941
96,13,179,9133
97,31,163,9343
98,5,191,9511
99,17,181,9719
100,7,193,9907
101,3,199,10103
102,11,193,10313
103,7,199,10513
104,11,197,10723
105,17,193,10937
106,19,193,11149
107,41,173,11383
108,23,193,11579
109,7,211,11779
110,47,173,12037
111,29,193,12239
112,151,73,12583
113,3,223,12659
114,17,211,12899
115,37,193,13147
116,41,191,13381
117,5,229,13577
118,73,163,13879
119,41,197,14083
120,13,227,14293
121,13,229,14533
122,5,239,14767
123,7,239,15013
124,7,241,15259
125,11,239,15511
126,11,241,15761
127,31,223,16033
128,17,239,16273
129,7,251,16519
130,61,199,16831
131,11,251,17041
132,7,257,17299
133,43,223,17599
134,5,263,17827
135,7,263,18097
136,73,199,18433
137,5,269,18637
138,5,271,18911
139,37,241,19219
140,3,277,19463
141,11,271,19751
142,7,277,20029
143,17,269,20323
144,7,281,20599
145,7,283,20887
146,23,269,21193
147,31,263,21493
148,103,193,21859
149,41,257,22093
150,17,283,22367
151,19,283,22669
152,11,293,22963
153,13,293,23269
154,31,277,23593
155,3,307,23873
156,43,269,24223
157,7,307,24499
158,3,313,24809
159,5,313,25127
160,7,313,25447
161,11,311,25771
162,17,307,26099
163,43,283,26449
164,89,239,26821
165,13,317,27073
166,19,313,27409
167,17,317,27739
168,43,293,28099
169,157,181,28549
170,23,317,28753
171,31,311,29101
172,31,313,29443
173,107,239,29863
174,11,337,30113
175,19,331,30469
176,3,349,30803
177,7,347,31159
178,7,349,31513
179,11,347,31873
180,13,347,32233
181,31,331,32611
182,71,293,33013
183,53,313,33359
184,31,337,33703
185,17,353,34057
186,19,353,34429
187,37,337,34819
188,3,373,35159
189,5,373,35537
190,13,367,35923
191,3,379,36293
192,5,379,36677
193,103,283,37159
194,5,383,37447
195,17,373,37847
196,19,373,38239
197,41,353,38653
198,13,383,39019
199,331,67,39733
200,41,359,39841
201,13,389,40213
202,7,397,40609
203,5,401,41011
204,41,367,41453
205,31,379,41851
206,53,359,42283
207,41,373,42683
208,7,409,43063
209,71,347,43543
210,23,397,43913
211,73,349,44383
212,41,383,44773
213,5,421,45161
214,7,421,45589
215,11,419,46021
216,11,421,46451
217,61,373,46933
218,3,433,47309
219,37,401,47779
220,7,433,48187
221,3,439,48623
222,47,397,49109
223,97,349,49603
224,5,443,49957
225,11,439,50411
226,43,409,50893
227,5,449,51307
228,13,443,51769
229,37,421,52249
230,3,457,52673
231,19,443,53149
232,31,433,53623
233,3,463,54059
234,19,449,54541
235,31,439,55021
236,41,431,55501
237,17,457,55949
238,37,439,56443
239,11,467,56893
240,13,467,57373
241,19,463,57859
242,41,443,58363
243,103,383,58909
244,67,421,59359
245,11,479,59791
246,61,431,60331
247,31,463,60793
248,5,491,61261
249,67,431,61819
250,61,439,62311
251,3,499,62753
252,47,457,63299
253,43,463,63799
254,17,491,64279
255,11,499,64781
256,13,499,65293
257,47,467,65839
258,37,479,66343
259,19,499,66841
260,29,491,67369
261,23,499,67883
262,61,463,68443
263,3,523,68909
264,7,521,69439
265,31,499,69991
266,11,521,70501
267,47,487,71069
268,13,523,71569
269,17,521,72109
270,17,523,72647
271,19,523,73189
272,227,317,73939
273,23,523,74279
274,127,421,74929
275,3,547,75353
276,31,521,75931
277,67,487,76519
278,263,293,77269
279,11,547,77573
280,19,541,78139
281,41,521,78721
282,17,547,79259
283,67,499,79873
284,101,467,80473
285,13,557,80953
286,109,463,81619
287,71,503,82153
288,67,509,82723
289,37,541,83269
290,3,577,83813
291,11,571,84401
292,7,577,84979
293,83,503,85639
294,19,569,86161
295,13,577,86743
296,83,509,87403
297,31,563,87943
298,157,439,88663
299,5,593,89107
300,53,547,89753
301,79,523,90379
302,5,599,90907
303,7,599,91513
304,7,601,92119
305,3,607,92723
306,41,571,93371
307,7,607,93949
308,3,613,94559
309,5,613,95177
310,13,607,95803
311,59,563,96469
312,7,617,97039
313,193,433,97849
314,41,587,98323
315,17,613,98927
316,19,613,99559
317,17,617,100189
318,5,631,100811
319,7,631,101449
320,23,617,102103
321,41,601,102761
322,31,613,103393
323,3,643,104009
324,7,641,104659
325,19,631,105319
326,83,569,106033
327,47,607,106649
328,13,643,107269
329,11,647,107923
330,17,643,108587
331,223,439,109453
332,5,659,109897
333,7,659,110563
334,7,661,111229
335,23,647,111913
336,11,661,112571
337,97,577,113329
338,3,673,113909
339,17,661,114599
340,19,661,115279
341,23,659,115963
342,41,643,116663
343,13,673,117319
344,41,647,118033
345,7,683,118687
346,19,673,119389
347,17,677,120079
348,23,673,120779
349,79,619,121531
350,17,683,122167
351,11,691,122861
352,31,673,123583
353,47,659,124303
354,17,691,124979
355,37,673,125707
356,53,659,126433
357,31,683,127123
358,43,673,127849
359,41,677,128563
360,37,683,129277
361,61,661,130021
362,5,719,130687
363,7,719,131413
364,19,709,132151
365,3,727,132863
366,41,691,133631
367,271,463,134593
368,3,733,135059
369,37,701,135829
370,7,733,136537
371,3,739,137273
372,67,677,138079
373,7,739,138763
374,89,659,139591
375,31,719,140281
376,61,691,141061
377,101,653,141853
378,23,733,142529
379,19,739,143281
380,17,743,144037
381,11,751,144791
382,7,757,145549
383,83,683,146389
384,11,757,147083
385,13,757,147853
386,29,743,148639
387,17,757,149399
388,37,739,150193
389,59,719,150991
390,7,773,151717
391,43,739,152533
392,41,743,153313
393,17,769,154073
394,31,757,154873
395,89,701,155719
396,73,719,156493
397,7,787,157219
398,23,773,158029
399,41,757,158843
400,31,769,159631
401,41,761,160441
402,31,773,161233
403,73,733,162079
404,11,797,162823
405,13,797,163633
406,73,739,164503
407,5,809,165247
408,7,809,166063
409,199,619,167071
410,173,647,167863
411,13,809,168523
412,37,787,169369
413,83,743,170239
414,41,787,171023
415,79,751,171889
416,3,829,172643
417,11,823,173483
418,163,673,174469
419,191,647,175333
420,11,829,175991
421,103,739,176923
422,17,827,177679
423,7,839,178513
424,109,739,179461
425,11,839,180211
426,13,839,181063
427,127,727,182029
428,17,839,182773
429,71,787,183683
430,7,853,184477
431,41,821,185371
432,37,827,186229
433,13,853,187069
434,5,863,187927
435,11,859,188801
436,139,733,189799
437,11,863,190543
438,47,829,191453
439,109,769,192391
440,3,877,193163
441,29,853,194069
442,127,757,195049
443,3,883,195809
444,7,881,196699
445,61,829,197641
446,83,809,198553
447,11,883,199373
448,37,859,200293
449,11,887,201163
450,13,887,202063
451,73,829,203023
452,17,887,203869
453,47,859,204803
454,97,811,205759
455,23,887,206593
456,29,883,207509
457,127,787,208519
458,5,911,209311
459,7,911,210229
460,13,907,211153
461,101,821,212161
462,5,919,212987
463,43,883,213949
464,17,911,214849
465,11,919,215771
466,13,919,216703
467,347,587,217969
468,73,863,218629
469,31,907,219523
470,83,857,220513
471,23,919,221393
472,37,907,222349
473,17,929,223273
474,7,941,224209
475,13,937,225163
476,23,929,226123
477,101,853,227153
478,97,859,228103
479,131,827,229093
480,19,941,229939
481,79,883,230959
482,17,947,231859
483,13,953,232819
484,109,859,233881
485,3,967,234743
486,311,661,236021
487,67,907,236749
488,317,659,237973
489,7,971,238639
490,13,967,239623
491,41,941,240631
492,17,967,241589
493,103,883,242659
494,11,977,243553
495,23,967,244553
496,73,919,245593
497,11,983,246523
498,13,983,247519
499,7,991,248509
500,3,997,249503
501,83,919,250583
502,37,967,251539
503,53,953,252559
504,31,977,253543
505,73,937,254593
506,41,971,255571
507,37,977,256579
508,157,859,257713
509,41,977,258613
510,29,991,259619
511,103,919,260713
512,5,1019,261637
513,163,863,262819
514,199,829,263881
515,47,983,264757
516,41,991,265781
517,67,967,266839
518,5,1031,267811
519,19,1019,268861
520,7,1033,269887
521,3,1039,270923
522,5,1039,271967
523,37,1009,273043
524,17,1031,274069
525,29,1021,275129
526,31,1021,276181
527,71,983,277273
528,5,1051,278261
529,139,919,279451
530,41,1019,280411
531,79,983,281509
532,67,997,282559
533,17,1049,283573
534,29,1039,284651
535,7,1063,285697
536,3,1069,286763
537,41,1033,287873
538,7,1069,288913
539,17,1061,289999
540,17,1063,291077
541,43,1039,292183
542,107,977,293329
543,47,1039,294353
544,19,1069,295411
545,29,1061,296509
546,31,1061,297601
547,31,1063,298693
548,353,743,300109
549,5,1093,300857
550,103,997,302053
551,41,1061,303091
552,11,1093,304163
553,73,1033,305329
554,5,1103,306367
555,41,1069,307511
556,61,1051,308641
557,131,983,309823
558,13,1103,310819
559,109,1009,312031
560,89,1031,313129
561,13,1109,314173
562,31,1093,315313
563,17,1109,316423
564,31,1097,317563
565,163,967,318823
566,29,1103,319819
567,5,1129,320927
568,283,853,322339
569,41,1097,323233
570,11,1129,324341
571,73,1069,325543
572,47,1097,326659
573,23,1123,327779
574,19,1129,328921
575,47,1103,330097
576,59,1093,331259
577,157,997,332509
578,173,983,333679
579,5,1153,334667
580,37,1123,335857
581,59,1103,337039
582,11,1153,338153
583,127,1039,339433
584,5,1163,340477
585,7,1163,341647
586,79,1093,342889
587,71,1103,344053
588,73,1103,345229
589,61,1117,346393
590,29,1151,347539
591,19,1163,348709
592,31,1153,349903
593,5,1181,351061
594,7,1181,352249
595,97,1093,353527
596,41,1151,354661
597,7,1187,355819
598,67,1129,357073
599,11,1187,358213
600,7,1193,359407
601,181,1021,360781
602,41,1163,361843
603,13,1193,363019
604,79,1129,364291
605,47,1163,365467
606,83,1129,366713
607,307,907,368149
608,23,1193,369079
609,101,1117,370373
610,19,1201,371509
611,29,1193,372739
612,11,1213,373943
613,13,1213,375169
614,11,1217,376393
615,7,1223,377617
616,61,1171,378901
617,131,1103,380203
618,13,1223,381319
619,7,1231,382549
620,11,1229,383791
621,19,1223,385039
622,151,1093,386413
623,23,1223,387529
624,61,1187,388813
625,97,1153,390097
626,23,1229,391273
627,17,1237,392519
628,103,1153,393859
629,107,1151,395119
630,23,1237,396293
631,13,1249,397543
632,41,1223,398833
633,37,1229,400093
634,19,1249,401341
635,11,1259,402601
636,41,1231,403901
637,211,1063,405343
638,17,1259,406423
639,41,1237,407723
640,67,1213,409027
641,3,1279,410243
642,5,1279,411527
643,457,829,413263
644,5,1283,414097
645,11,1279,415391
646,163,1129,416833
647,107,1187,418069
648,5,1291,419261
649,19,1279,420571
650,41,1259,421891
651,23,1279,423173
652,67,1237,424519
653,23,1283,425779
654,5,1303,427067
655,31,1279,428401
656,53,1259,429733
657,7,1307,430999
658,37,1279,432343
659,11,1307,433633
660,17,1303,434957
661,19,1303,436279
662,5,1319,437587
663,7,1319,438913
664,7,1321,440239
665,3,1327,441563
666,13,1319,442903
667,31,1303,444253
668,17,1319,445573
669,17,1321,446909
670,19,1321,448249
671,59,1283,449629
672,17,1327,450929
673,277,1069,452533
674,29,1319,453631
675,23,1327,454973
676,103,1249,456403
677,137,1217,457789
678,107,1249,459113
679,31,1327,460393
680,83,1277,461803
681,139,1223,463219
682,37,1327,464479
683,263,1103,466069
684,41,1327,467213
685,73,1297,468613
686,83,1289,469993
687,71,1303,471353
688,283,1093,472939
689,5,1373,474037
690,7,1373,475417
691,61,1321,476851
692,17,1367,478189
693,5,1381,479561
694,61,1327,481003
695,17,1373,482347
696,31,1361,483751
697,97,1297,485209
698,137,1259,486643
699,31,1367,487933
700,109,1291,489409
701,41,1361,490741
702,191,1213,492293
703,367,1039,493873
704,47,1361,494959
705,107,1303,496427
706,109,1303,497839
707,41,1373,499183
708,137,1279,500693
709,349,1069,502321
710,233,1187,503623
711,41,1381,504851
712,97,1327,506329
713,17,1409,507673
714,5,1423,509087
715,103,1327,510613
716,23,1409,511963
717,67,1367,513439
718,13,1423,514819
719,5,1433,516247
720,31,1409,517711
721,163,1279,519283
722,5,1439,520567
723,73,1373,522079
724,67,1381,523519
725,41,1409,524941
726,23,1429,526373
727,7,1447,527809
728,3,1453,529259
729,19,1439,530731
730,13,1447,532183
731,3,1459,533633
732,11,1453,535103
733,7,1459,536563
734,29,1439,538051
735,11,1459,539501
736,181,1291,541141
737,101,1373,542533
738,5,1471,543911
739,151,1327,545533
740,107,1373,546967
741,11,1471,548351
742,61,1423,549883
743,5,1481,551311
744,17,1471,552809
745,19,1471,554299
746,53,1439,555823
747,7,1487,557269
748,13,1483,558769
749,47,1451,560299
750,11,1489,561761
751,13,1489,563263
752,227,1277,564979
753,17,1489,566273
754,79,1429,567841
755,149,1361,569419
756,41,1471,570821
757,31,1483,572323
758,23,1493,573829
759,37,1481,575359
760,193,1327,577033
761,11,1511,578371
762,101,1423,579983
763,37,1489,581443
764,5,1523,582937
765,71,1459,584531
766,61,1471,586051
767,11,1523,587533
768,53,1483,589109
769,7,1531,590599
770,89,1451,592219
771,19,1523,593689
772,241,1303,595453
773,23,1523,596779
774,5,1543,598307
775,7,1543,599857
776,191,1361,601591
777,31,1523,602983
778,73,1483,604579
779,59,1499,606121
780,7,1553,607627
781,19,1543,609199
782,41,1523,610783
783,13,1553,612319
784,97,1471,613969
785,137,1433,615577
786,29,1543,617039
787,7,1567,618589
788,5,1571,620161
789,7,1571,621739
790,31,1549,623341
791,71,1511,624961
792,5,1579,626477
793,7,1579,628063
794,101,1487,629743
795,19,1571,631249
796,61,1531,632881
797,71,1523,634483
798,17,1579,636023
799,67,1531,637669
800,107,1493,639307
801,53,1549,640853
802,367,1237,642769
803,23,1583,644029
804,29,1579,645641
805,43,1567,647263
806,11,1601,648841
807,7,1607,650449
808,7,1609,652063
809,257,1361,653929
810,11,1609,655301
811,13,1609,656923
812,17,1607,658549
813,43,1583,660199
814,97,1531,661879
815,107,1523,663517
816,11,1621,665051
817,151,1483,666823
818,227,1409,668533
819,29,1609,669971
820,211,1429,671791
821,71,1571,673291
822,17,1627,674879
823,67,1579,676573
824,47,1601,678199
825,23,1627,679823
826,31,1621,681481
827,17,1637,683119
828,37,1619,684793
829,37,1621,686449
830,3,1657,688073
831,41,1621,689771
832,7,1657,691399
833,47,1619,693103
834,41,1627,694763
835,13,1657,696403
836,179,1493,698239
837,61,1613,699793
838,7,1669,701413
839,41,1637,703123
840,11,1669,704771
841,193,1489,706633
842,17,1667,708139
843,17,1669,709823
844,31,1657,711523
845,53,1637,713233
846,23,1669,714893
847,67,1627,716629
848,3,1693,718259
849,29,1669,719981
850,37,1663,721687
851,3,1699,723353
852,5,1699,725057
853,97,1609,726853
854,89,1619,728551
855,17,1693,730187
856,13,1699,731893
857,47,1667,733639
858,53,1663,735359
859,19,1699,737041
860,107,1613,738847
861,13,1709,740473
862,31,1693,742213
863,17,1709,743923
864,101,1627,745733
865,31,1699,747391
866,233,1499,749323
867,41,1693,750863
868,13,1723,752569
869,5,1733,754297
870,71,1669,756101
871,271,1471,758041
872,11,1733,759523
873,5,1741,761261
874,139,1609,763141
875,137,1613,764887
876,11,1741,766511
877,7,1747,768259
878,47,1709,770053
879,101,1657,771863
880,13,1747,773533
881,29,1733,775309
882,67,1697,777109
883,13,1753,778819
884,59,1709,780631
885,47,1723,782387
886,19,1753,784129
887,41,1733,785923
888,113,1663,787769
889,79,1699,789511
890,47,1733,791257
891,113,1669,793103
892,7,1777,794779
893,263,1523,796819
894,41,1747,798383
895,13,1777,800143
896,239,1553,802159
897,5,1789,803717
898,127,1669,805633
899,101,1697,807403
900,41,1759,809141
901,13,1789,810913
902,167,1637,812869
903,53,1753,814559
904,139,1669,816451
905,23,1787,818143
906,59,1753,819989
907,61,1753,821803
908,107,1709,823663
909,17,1801,825389
910,37,1783,827227
911,101,1721,829111
912,41,1783,830873
913,37,1789,832693
914,5,1823,834487
915,7,1823,836317
916,31,1801,838171
917,137,1697,840109
918,53,1783,841859
919,7,1831,843649
920,173,1667,845653
921,19,1823,847339
922,61,1783,849223
923,233,1613,851239
924,37,1811,852889
925,181,1669,854881
926,239,1613,856789
927,31,1823,858433
928,67,1789,860323
929,11,1847,862123
930,13,1847,863983
931,103,1759,865933
932,41,1823,867733
933,43,1823,869599
934,37,1831,871459
935,3,1867,873293
936,41,1831,875201
937,181,1693,877213
938,263,1613,879169
939,11,1867,880793
940,223,1657,882883
941,263,1619,884803
942,5,1879,886427
943,7,1879,888313
944,179,1709,890371
945,11,1879,892091
946,19,1873,893989
947,17,1877,895879
948,23,1873,897779
949,19,1879,899671
950,167,1733,901717
951,29,1873,903479
952,277,1627,905629
953,293,1613,907549
954,41,1867,909203
955,31,1879,911101
956,11,1901,912991
957,137,1777,915029
958,127,1789,916933
959,11,1907,918733
960,13,1907,920653
961,139,1783,922699
962,11,1913,924493
963,227,1699,926633
964,67,1861,928399
965,17,1913,930277
966,19,1913,932209
967,271,1663,934393
968,227,1709,936283
969,31,1907,938023
970,67,1873,939997
971,41,1901,941911
972,31,1913,943843
973,67,1879,945823
974,17,1931,947719
975,17,1933,949667
976,229,1723,951829
977,41,1913,953593
978,5,1951,955511
979,181,1777,957643
980,29,1931,959449
981,13,1949,961393
982,367,1597,963709
983,353,1613,965659
984,17,1951,967289
985,19,1951,969259
986,41,1931,971251
987,97,1877,973279
988,43,1933,975199
989,71,1907,977203
990,7,1973,979117
991,109,1873,981199
992,11,1973,983083
993,7,1979,985063
994,37,1951,987079
995,41,1949,989071
996,43,1949,991063
997,241,1753,993253
998,3,1993,995009
999,11,1987,997013
1000,7,1993,999007
1001,3,1999,1001003
1002,17,1987,1003019
1003,7,1999,1005013
1004,11,1997,1007023
1005,17,1993,1009037
1006,61,1951,1011091
1007,11,2003,1013053
1008,5,2011,1015061
1009,67,1951,1017139
1010,3,2017,1019093
1011,19,2003,1021129
1012,31,1993,1023163
1013,47,1979,1025203
1014,17,2011,1027199
1015,37,1993,1029247
1016,59,1973,1031299
1017,17,2017,1033289
1018,7,2029,1035313
1019,59,1979,1037401
1020,41,1999,1039421
1021,31,2011,1041451
1022,5,2039,1043467
1023,17,2029,1045523
1024,37,2011,1047589
1025,11,2039,1049611
1026,13,2039,1051663
1027,37,2017,1053739
1028,53,2003,1055809
1029,19,2039,1057831
1030,61,1999,1059931
1031,83,1979,1062013
1032,37,2027,1064029
1033,277,1789,1066333
1034,137,1931,1068259
1035,7,2063,1070197
1036,79,1993,1072339
1037,11,2063,1074343
1038,23,2053,1076429
1039,199,1879,1078681
1040,53,2027,1080613
1041,19,2063,1082659
1042,331,1753,1085053
1043,3,2083,1086809
1044,61,2027,1088953
1045,37,2053,1091017
1046,89,2003,1093159
1047,7,2087,1095169
1048,67,2029,1097323
1049,11,2087,1099363
1050,17,2083,1101467
1051,229,1873,1103779
1052,17,2087,1105669
1053,7,2099,1107763
1054,19,2089,1109881
1055,41,2069,1112011
1056,31,2081,1114111
1057,31,2083,1116223
1058,3,2113,1118309
1059,7,2111,1120429
1060,31,2089,1122571
1061,59,2063,1124719
1062,41,2083,1126823
1063,37,2089,1128943
1064,17,2111,1131049
1065,17,2113,1133177
1066,43,2089,1135333
1067,5,2129,1137427
1068,67,2069,1139623
1069,109,2029,1141801
1070,113,2027,1143943
1071,13,2129,1145983
1072,151,1993,1148263
1073,107,2039,1150363
1074,17,2131,1152419
1075,13,2137,1154563
1076,11,2141,1156711
1077,11,2143,1158863
1078,157,1999,1161163
1079,5,2153,1163167
1080,29,2131,1165349
1081,79,2083,1167559
1082,167,1997,1169809
1083,5,2161,1171811
1084,7,2161,1173979
1085,83,2087,1176223
1086,59,2113,1178369
1087,37,2137,1180519
1088,23,2153,1182679
1089,181,1997,1185013
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1091,3,2179,1189193
1092,157,2027,1191529
1093,97,2089,1193653
1094,59,2129,1195801
1095,11,2179,1197941
1096,193,1999,1200313
1097,317,1877,1202629
1098,107,2089,1204613
1099,19,2179,1206721
1100,173,2027,1209073
1101,41,2161,1211141
1102,271,1933,1213573
1103,3,2203,1215509
1104,47,2161,1217759
1105,31,2179,1219951
1106,101,2111,1222231
1107,61,2153,1224403
1108,37,2179,1226593
1109,11,2207,1228783
1110,7,2213,1230997
1111,109,2113,1233319
1112,17,2207,1235449
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1114,139,2089,1240021
1115,251,1979,1242361
1116,19,2213,1244359
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1120,97,2143,1253377
1121,29,2213,1255549
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1123,157,2089,1260163
1124,41,2207,1262293
1125,37,2213,1264537
1126,13,2239,1266763
1127,11,2243,1269013
1128,43,2213,1271299
1129,37,2221,1273549
1130,47,2213,1275817
1131,83,2179,1278113
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1135,19,2251,1287109
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1177,67,2287,1384219
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1190,3,2377,1414913
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1194,41,2347,1424483
1195,97,2293,1426927
1196,11,2381,1429231
1197,37,2357,1431649
1198,13,2383,1434019
1199,41,2357,1436443
1200,17,2383,1438817
1201,109,2293,1441309
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1203,13,2393,1446019
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1205,29,2381,1450849
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1234,127,2341,1521649
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1256,443,2069,1576723
1257,11,2503,1578803
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1297,307,2287,1681219
1298,17,2579,1683523
1299,7,2591,1686109
1300,223,2377,1688923
1301,59,2543,1691359
1302,127,2477,1694029
1303,103,2503,1696609
1304,17,2591,1699129
1305,89,2521,1701809
1306,229,2383,1704559
1307,461,2153,1707403
1308,37,2579,1709593
1309,181,2437,1712353
1310,3,2617,1714793
1311,29,2593,1717439
1312,7,2617,1720039
1313,83,2543,1722739
1314,19,2609,1725301
1315,13,2617,1727923
1316,11,2621,1730551
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1318,43,2593,1735849
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1320,19,2621,1741099
1321,103,2539,1743823
1322,101,2543,1746463
1323,67,2579,1749073
1324,31,2617,1751683
1325,3,2647,1754303
1326,19,2633,1756969
1327,61,2593,1759663
1328,23,2633,1762279
1329,37,2621,1764949
1330,109,2551,1767679
1331,3,2659,1770233
1332,31,2633,1772923
1333,7,2659,1775563
1334,251,2417,1778473
1335,11,2659,1780901
1336,151,2521,1783711
1337,131,2543,1786363
1338,5,2671,1788911
1339,127,2551,1791709
1340,17,2663,1794277
1341,19,2663,1796959
1342,181,2503,1799803
1343,293,2393,1802599
1344,5,2683,1804997
1345,13,2677,1807693
1346,233,2459,1810603
1347,11,2683,1813073
1348,103,2593,1815859
1349,5,2693,1818457
1350,17,2683,1821167
1351,13,2689,1823863
1352,5,2699,1826557
1353,43,2663,1829299
1354,31,2677,1831993
1355,47,2663,1834717
1356,13,2699,1837393
1357,31,2683,1840123
1358,3,2713,1842809
1359,19,2699,1845541
1360,7,2713,1848247
1361,59,2663,1851019
1362,31,2693,1853713
1363,13,2713,1856419
1364,41,2687,1859173
1365,19,2711,1861879
1366,193,2539,1864783
1367,101,2633,1867423
1368,23,2713,1870079
1369,7,2731,1872799
1370,11,2729,1875541
1371,11,2731,1878281
1372,67,2677,1881079
1373,17,2729,1883773
1374,7,2741,1886509
1375,37,2713,1889287
1376,89,2663,1892089
1377,5,2749,1894757
1378,67,2689,1897573
1379,5,2753,1900267
1380,41,2719,1903061
1381,373,2389,1906153
1382,857,1907,1909399
1383,13,2753,1911319
1384,397,2371,1914469
1385,17,2753,1916857
1386,23,2749,1919633
1387,181,2593,1922563
1388,23,2753,1925179
1389,37,2741,1927969
1390,73,2707,1930783
1391,173,2609,1933663
1392,17,2767,1936289
1393,67,2719,1939123
1394,47,2741,1941889
1395,37,2753,1944667
1396,73,2719,1947493
1397,41,2753,1950253
1398,7,2789,1953013
1399,7,2791,1955809
1400,3,2797,1958603
1401,11,2791,1961411
1402,367,2437,1964569
1403,5,2801,1967011
1404,7,2801,1969819
1405,7,2803,1972627
1406,113,2699,1975543
1407,47,2767,1978289
1408,97,2719,1981153
1409,17,2801,1983889
1410,23,2797,1986713
1411,73,2749,1989583
1412,5,2819,1992337
1413,107,2719,1995263
1414,37,2791,1998019
1415,53,2777,2000863
1416,13,2819,2003653
1417,31,2803,2006503
1418,563,2273,2009869
1419,5,2833,2012147
1420,109,2731,2015089
1421,23,2819,2017843
1422,67,2777,2020729
1423,97,2749,2023603
1424,317,2531,2026669
1425,7,2843,2029207
1426,61,2791,2032111
1427,11,2843,2034913
1428,37,2819,2037793
1429,67,2791,2040679
1430,17,2843,2043487
1431,19,2843,2046349
1432,157,2707,2049349
1433,653,2213,2052709
1434,11,2857,2054933
1435,67,2803,2057857
1436,11,2861,2060671
1437,17,2857,2063549
1438,157,2719,2066563
1439,59,2819,2069341
1440,19,2861,2072179
1441,223,2659,2075263
1442,47,2837,2077969
1443,43,2843,2080849
1444,157,2731,2083849
1445,101,2789,2086681
1446,41,2851,2089511
1447,7,2887,2092369
1448,53,2843,2095309
1449,19,2879,2098171
1450,43,2857,2101093
1451,23,2879,2103973
1452,67,2837,2106919
1453,193,2713,2109949
1454,89,2819,2112751
1455,59,2851,2115629
1456,61,2851,2118541
1457,11,2903,2121403
1458,13,2903,2124319
1459,67,2851,2127289
1460,101,2819,2130241
1461,61,2861,2133121
1462,37,2887,2136019
1463,83,2843,2138989
1464,31,2897,2141863
1465,139,2791,2144899
1466,179,2753,2147869
1467,17,2917,2150639
1468,223,2713,2153779
1469,29,2909,2156521
1470,23,2917,2159453
1471,139,2803,2162509
1472,101,2843,2165413
1473,7,2939,2168263
1474,181,2767,2171383
1475,47,2903,2174197
1476,13,2939,2177113
1477,37,2917,2180089
1478,347,2609,2183353
1479,41,2917,2186003
1480,73,2887,2188993
1481,173,2789,2192053
1482,37,2927,2194879
1483,463,2503,2198269
1484,5,2963,2200777
1485,31,2939,2203771
1486,283,2689,2206993
1487,5,2969,2209687
1488,7,2969,2212663
1489,7,2971,2215639
1490,11,2969,2218621
1491,43,2939,2221633
1492,97,2887,2224669
1493,83,2903,2227639
1494,19,2969,2230561
1495,193,2797,2233723
1496,53,2939,2236573
1497,137,2857,2239649
1498,43,2953,2242549
1499,41,2957,2245543
1500,29,2971,2248529
1501,271,2731,2251771
1502,5,2999,2254507
1503,5,3001,2257511
1504,7,3001,2260519
1505,11,2999,2263531
1506,41,2971,2266571
1507,97,2917,2269639
1508,47,2969,2272603
1509,19,2999,2275591
1510,103,2917,2278693
1511,53,2969,2281663
1512,5,3019,2284637
1513,307,2719,2287963
1514,149,2879,2290831
1515,19,3011,2293729
1516,199,2833,2296939
1517,11,3023,2299783
1518,73,2963,2302879
1519,67,2971,2305909
1520,3,3037,2308883
1521,73,2969,2311993
1522,7,3037,2314969
1523,83,2963,2318089
1524,37,3011,2321089
1525,367,2683,2324467
1526,3,3049,2327153
1527,101,2953,2330303
1528,37,3019,2333293
1529,47,3011,2336359
1530,59,3001,2339429
1531,13,3049,2342443
1532,41,3023,2345533
1533,17,3049,2348573
1534,19,3049,2351641
1535,107,2963,2354797
1536,31,3041,2357791
1537,271,2803,2361103
1538,107,2969,2364013
1539,11,3067,2366993
1540,13,3067,2370073
1541,71,3011,2373211
1542,17,3067,2376239
1543,283,2803,2379589
1544,89,2999,2382481
1545,173,2917,2385653
1546,13,3079,2388583
1547,71,3023,2391733
1548,157,2939,2394913
1549,79,3019,2397931
1550,257,2843,2401207
1551,19,3083,2404069
1552,37,3067,2407189
1553,17,3089,2410273
1554,59,3049,2413421
1555,31,3079,2416501
1556,3,3109,2419583
1557,5,3109,2422697
1558,313,2803,2426119
1559,107,3011,2429029
1560,37,3083,2432077
1561,43,3079,2435203
1562,101,3023,2438383
1563,43,3083,2441449
1564,241,2887,2444773
1565,173,2957,2447833
1566,23,3109,2450813
1567,331,2803,2454253
1568,17,3119,2457073
1569,89,3049,2460281
1570,337,2803,2463667
1571,23,3119,2466493
1572,61,3083,2469673
1573,67,3079,2472823
1574,59,3089,2475961
1575,67,3083,2479117
1576,43,3109,2482243
1577,227,2927,2485579
1578,47,3109,2488553
1579,97,3061,2491759
1580,251,2909,2495071
1581,41,3121,2498021
1582,127,3037,2501269
1583,167,2999,2504473
1584,157,3011,2507629
1585,61,3109,2510701
1586,83,3089,2513893
1587,11,3163,2516993
1588,13,3163,2520169
1589,11,3167,2523343
1590,11,3169,2526521
1591,349,2833,2530039
1592,47,3137,2532919
1593,67,3119,2536123
1594,19,3169,2539261
1595,23,3167,2542453
1596,71,3121,2545691
1597,127,3067,2548939
1598,107,3089,2552113
1599,11,3187,2555213
1600,19,3181,2558419
1601,83,3119,2561683
1602,17,3187,2564819
1603,613,2593,2568619
1604,197,3011,2571409
1605,29,3181,2574449
1606,31,3181,2577661
1607,5,3209,2580847
1608,193,3023,2584249
1609,139,3079,2587411
1610,3,3217,2590493
1611,19,3203,2593729
1612,37,3187,2596969
1613,5,3221,2600161
1614,7,3221,2603389
1615,67,3163,2606677
1616,113,3119,2609953
1617,5,3229,2613077
1618,73,3163,2616379
1619,17,3221,2619559
1620,19,3221,2622799
1621,271,2971,2626291
1622,107,3137,2629369
1623,17,3229,2632523
1624,31,3217,2635783
1625,41,3209,2639041
1626,83,3169,2642333
1627,67,3187,2645569
1628,5,3251,2648761
1629,89,3169,2652101
1630,43,3217,2655313
1631,53,3209,2658583
1632,5,3259,2661797
1633,7,3259,2665063
1634,11,3257,2668333
1635,17,3253,2671607
1636,19,3253,2674879
1637,17,3257,2678149
1638,17,3259,2681423
1639,19,3259,2684701
1640,23,3257,2687983
1641,11,3271,2691251
1642,727,2557,2695249
1643,167,3119,2697973
1644,17,3271,2701109
1645,37,3253,2704417
1646,41,3251,2707711
1647,127,3167,2711089
1648,37,3259,2714293
1649,41,3257,2717593
1650,41,3259,2720891
1651,31,3271,2724181
1652,281,3023,2727733
1653,47,3259,2730803
1654,37,3271,2734099
1655,107,3203,2737477
1656,41,3271,2740721
1657,457,2857,2744449
1658,3,3313,2747309
1659,19,3299,2750641
1660,61,3259,2754001
1661,101,3221,2757361
1662,5,3319,2760587
1663,307,3019,2764213
1664,191,3137,2767423
1665,11,3319,2770571
1666,31,3301,2773921
1667,11,3323,2777233
1668,127,3209,2780683
1669,31,3307,2783923
1670,41,3299,2787271
1671,83,3259,2790653
1672,31,3313,2793943
1673,3,3343,2797259
1674,5,3343,2800607
1675,79,3271,2804029
1676,23,3329,2807323
1677,11,3343,2810663
1678,97,3259,2814103
1679,59,3299,2817421
1680,13,3347,2820733
1681,43,3319,2824123
1682,107,3257,2827549
1683,7,3359,2830813
1684,7,3361,2834179
1685,11,3359,2837551
1686,29,3343,2840939
1687,31,3343,2844313
1688,5,3371,2847661
1689,17,3361,2851049
1690,37,3343,2854447
1691,11,3371,2857801
1692,41,3343,2861213
1693,13,3373,2864569
1694,17,3371,2867959
1695,17,3373,2871347
1696,331,3061,2875051
1697,191,3203,2878303
1698,7,3389,2881513
1699,37,3361,2884939
1700,11,3389,2888311
1701,29,3373,2891729
1702,337,3067,2895439
1703,107,3299,2898613
1704,19,3389,2901931
1705,19,3391,2905339
1706,23,3389,2908753
1707,71,3343,2912213
1708,43,3373,2915599
1709,5,3413,2918977
1710,107,3313,2922497
1711,31,3391,2925841
1712,11,3413,2929243
1713,173,3253,2932829
1714,97,3331,2936179
1715,23,3407,2939533
1716,19,3413,2942959
1717,601,2833,2946973
1718,107,3329,2949913
1719,131,3307,2953373
1720,67,3373,2956747
1721,53,3389,2960173
1722,37,3407,2963599
1723,103,3343,2967109
1724,149,3299,2970601
1725,17,3433,2973917
1726,19,3433,2977369
1727,41,3413,2980843
1728,7,3449,2984263
1729,127,3331,2987839
1730,47,3413,2991217
1731,13,3449,2994643
1732,151,3313,2998243
1733,383,3083,3001939
1734,5,3463,3005027
1735,79,3391,3008569
1736,3,3469,3011963
1737,5,3469,3015437
1738,13,3463,3018919
1739,89,3389,3022471
1740,11,3469,3025871
1741,19,3463,3029359
1742,17,3467,3032839
1743,37,3449,3036343
1744,19,3469,3039811
1745,23,3467,3043303
1746,59,3433,3046829
1747,691,2803,3050953
1748,653,2843,3054409
1749,29,3469,3057281
1750,43,3457,3060793
1751,41,3461,3064291
1752,37,3467,3067789
1753,1117,2389,3072373
1754,17,3491,3074779
1755,97,3413,3078367
1756,43,3469,3081823
1757,311,3203,3085603
1758,17,3499,3088823
1759,409,3109,3092731
1760,53,3467,3095893
1761,31,3491,3099391
1762,7,3517,3102889
1763,443,3083,3106849
1764,37,3491,3109969
1765,61,3469,3113521
1766,41,3491,3117031
1767,5,3529,3120527
1768,7,3529,3124063
1769,89,3449,3127681
1770,7,3533,3131137
1771,13,3529,3134683
1772,587,2957,3138799
1773,7,3539,3141763
1774,37,3511,3145339
1775,17,3533,3148867
1776,41,3511,3152441
1777,7,3547,3155959
1778,227,3329,3159733
1779,41,3517,3163103
1780,31,3529,3166651
1781,3,3559,3170183
1782,157,3407,3173899
1783,67,3499,3177373
1784,107,3461,3180979
1785,29,3541,3184469
1786,73,3499,3188083
1787,41,3533,3191623
1788,5,3571,3195161
1789,7,3571,3198739
1790,23,3557,3202333
1791,83,3499,3205973
1792,37,3547,3209509
1793,3,3583,3213059
1794,7,3581,3216649
1795,79,3511,3220309
1796,53,3539,3223873
1797,11,3583,3227423
1798,97,3499,3231103
1799,17,3581,3234619
1800,19,3581,3238219
1801,421,3181,3242221
1802,257,3347,3245659
1803,47,3559,3249053
1804,67,3541,3252679
1805,29,3581,3256249
1806,79,3533,3259909
1807,67,3547,3263509
1808,83,3533,3267139
1809,47,3571,3270719
1810,73,3547,3274363
1811,41,3581,3277951
1812,11,3613,3281543
1813,13,3613,3285169
1814,5,3623,3288787
1815,23,3607,3292433
1816,103,3529,3296143
1817,17,3617,3299689
1818,13,3623,3303319
1819,277,3361,3307219
1820,59,3581,3310639
1821,19,3623,3314239
1822,7,3637,3317869
1823,23,3623,3321529
1824,67,3581,3325219
1825,7,3643,3328807
1826,263,3389,3332713
1827,107,3547,3336209
1828,157,3499,3339913
1829,41,3617,3343453
1830,17,3643,3347087
1831,103,3559,3350833
1832,5,3659,3354397
1833,7,3659,3358063
1834,31,3637,3361753
1835,47,3623,3365437
1836,13,3659,3369073
1837,31,3643,3372763
1838,3,3673,3376409
1839,7,3671,3380089
1840,139,3541,3383899
1841,11,3671,3387451
1842,11,3673,3391133
1843,13,3673,3394819
1844,107,3581,3398599
1845,31,3659,3402211
1846,19,3673,3405889
1847,17,3677,3409579
1848,23,3673,3413279
1849,61,3637,3417013
1850,3,3697,3420653
1851,31,3671,3424381
1852,7,3697,3428059
1853,317,3389,3432073
1854,7,3701,3435469
1855,37,3673,3439207
1856,3,3709,3442883
1857,17,3697,3446609
1858,7,3709,3450313
1859,59,3659,3454081
1860,23,3697,3457763
1861,139,3583,3461599
1862,101,3623,3465283
1863,113,3613,3469019
1864,199,3529,3472831
1865,53,3677,3476413
1866,41,3691,3480131
1867,97,3637,3483919
1868,197,3539,3487753
1869,19,3719,3491311
1870,13,3727,3495043
1871,3,3739,3498773
1872,17,3727,3502529
1873,73,3673,3506329
1874,809,2939,3510811
1875,11,3739,3513761
1876,43,3709,3517543
1877,137,3617,3521389
1878,23,3733,3525029
1879,19,3739,3528781
1880,41,3719,3532561
1881,23,3739,3536303
1882,67,3697,3540109
1883,5,3761,3543811
1884,41,3727,3547613
1885,127,3643,3551467
1886,3,3769,3555113
1887,97,3677,3558979
1888,193,3583,3562849
1889,11,3767,3566443
1890,13,3767,3570223
1891,151,3631,3574141
1892,191,3593,3577963
1893,53,3733,3581609
1894,61,3727,3585403
1895,11,3779,3589141
1896,53,3739,3592973
1897,61,3733,3596773
1898,17,3779,3600523
1899,71,3727,3604373
1900,61,3739,3608161
1901,41,3761,3611941
1902,7,3797,3615709
1903,67,3739,3619573
1904,41,3767,3623353
1905,83,3727,3627203
1906,43,3769,3630973
1907,47,3767,3634789
1908,83,3733,3638639
1909,79,3739,3642451
1910,41,3779,3646231
1911,53,3769,3650063
1912,31,3793,3653863
1913,23,3803,3657679
1914,61,3767,3661543
1915,7,3823,3665317
1916,443,3389,3669583
1917,37,3797,3673009
1918,13,3823,3676819
1919,5,3833,3680647
1920,7,3833,3684487
1921,73,3769,3688393
1922,47,3797,3692209
1923,13,3833,3696019
1924,109,3739,3699961
1925,3,3847,3703703
1926,83,3769,3707633
1927,127,3727,3711529
1928,557,3299,3715813
1929,7,3851,3719119
1930,151,3709,3723121
1931,11,3851,3726841
1932,11,3853,3730703
1933,13,3853,3734569
1934,107,3761,3738529
1935,47,3823,3742337
1936,19,3853,3746179
1937,347,3527,3750379
1938,23,3853,3753929
1939,109,3769,3757891
1940,47,3833,3761707
1941,29,3853,3765569
1942,31,3853,3769453
1943,53,3833,3773359
1944,37,3851,3777229
1945,37,3853,3781117
1946,3,3889,3784973
1947,41,3853,3788903
1948,127,3769,3792883
1949,101,3797,3796753
1950,67,3833,3800617
1951,163,3739,3804613
1952,227,3677,3808579
1953,53,3853,3812309
1954,337,3571,3816499
1955,59,3851,3820129
1956,89,3823,3824069
1957,7,3907,3827899
1958,5,3911,3831811
1959,29,3889,3835751
1960,43,3877,3839683
1961,11,3911,3843571
1962,7,3917,3847489
1963,7,3919,3851413
1964,461,3467,3855793
1965,19,3911,3859279
1966,13,3919,3863203
1967,11,3923,3867133
1968,17,3919,3871073
1969,331,3607,3875323
1970,17,3923,3878947
1971,11,3931,3882881
1972,271,3673,3887083
1973,3,3943,3890759
1974,5,3943,3894707
1975,97,3853,3898747
1976,41,3911,3902641
1977,7,3947,3906559
1978,13,3943,3910519
1979,41,3917,3914503
1980,71,3889,3918491
1981,43,3919,3922423
1982,197,3767,3926539
1983,307,3659,3930613
1984,37,3931,3934309
1985,41,3929,3938281
1986,83,3889,3942293
1987,31,3943,3946213
1988,47,3929,3950203
1989,67,3911,3954199
1990,37,3943,3958147
1991,53,3929,3962143
1992,17,3967,3966089
1993,523,3463,3970579
1994,311,3677,3974353
1995,23,3967,3978053
1996,103,3889,3982123
1997,197,3797,3986209
1998,67,3929,3990073
1999,67,3931,3994069
