数论问题巅峰对决

蔡家雄

定义：若 15k±2 和 15k±4 是 四生素数，则称 15k 为 双中数。

奇数双中比猜想：一奇数均可表为两个双中数之比。

3 = 83226465 /27742155,

5 = 335769525 /67153905,

7 = 12812415 /1830345,
7 = 198328725 /28332675,
7 = 232772925 /33253275,
7 = 639984345 /91426335,

9 = 163690065 /18187785,

等式右边（分数）的分母，就是双中数 15k 的值，，，，

ysr

3000与10000之间的k*105有32组4生素数对: (用时3.125秒）
/334421/334423/334427/334429k=3185
/340931/340933/340937/340939k=3247
/346391/346393/346397/346399k=3299
/419051/419053/419057/419059k=3991
/427241/427243/427247/427249k=4069
/442571/442573/442577/442579k=4215
/470081/470083/470087/470089k=4477
/477011/477013/477017/477019k=4543
/510611/510613/510617/510619k=4863
/518801/518803/518807/518809k=4941
/536441/536443/536447/536449k=5109
/570041/570043/570047/570049k=5429
/594821/594823/594827/594829k=5665
/633461/633463/633467/633469k=6033
/666431/666433/666437/666439k=6347
/680291/680293/680297/680299k=6479
/715151/715153/715157/715159k=6811
/734471/734473/734477/734479k=6995
/736361/736363/736367/736369k=7013
/795791/795793/795797/795799k=7579
/814061/814063/814067/814069k=7753
/823721/823723/823727/823729k=7845
/845981/845983/845987/845989k=8057
/857951/857953/857957/857959k=8171
/876011/876013/876017/876019k=8343
/881471/881473/881477/881479k=8395
/889871/889873/889877/889879k=8475
/954971/954973/954977/954979k=9095
/958541/958543/958547/958549k=9129
/978071/978073/978077/978079k=9315
/1022381/1022383/1022387/1022389k=9737
/1043591/1043593/1043597/1043599k=9939
3000与10000之间的k*825有10组4生素数对: (用时6.171875秒）
/2696921/2696923/2696927/2696929k=3269
/3366821/3366823/3366827/3366829k=4081
/4596071/4596073/4596077/4596079k=5571
/4734671/4734673/4734677/4734679k=5739
/5025071/5025073/5025077/5025079k=6091
/5930921/5930923/5930927/5930929k=7189
/6156971/6156973/6156977/6156979k=7463
/6843371/6843373/6843377/6843379k=8295
/7305371/7305373/7305377/7305379k=8855
/7882871/7882873/7882877/7882879k=9555

ysr

10000与40000之间的k*825有37组4生素数对: (用时45.58594秒）
/8513171/8513173/8513177/8513179k=10319
/8557721/8557723/8557727/8557729k=10373
/9511421/9511423/9511427/9511429k=11529
/10187921/10187923/10187927/10187929k=12349
/12636521/12636523/12636527/12636529k=15317
/13940021/13940023/13940027/13940029k=16897
/14623121/14623123/14623127/14623129k=17725
/14812871/14812873/14812877/14812879k=17955
/14928371/14928373/14928377/14928379k=18095
/14974571/14974573/14974577/14974579k=18151
/16712021/16712023/16712027/16712029k=20257
/16815971/16815973/16815977/16815979k=20383
/18578171/18578173/18578177/18578179k=22519
/18873521/18873523/18873527/18873529k=22877
/18918071/18918073/18918077/18918079k=22931
/19046771/19046773/19046777/19046779k=23087
/19160621/19160623/19160627/19160629k=23225
/19497221/19497223/19497227/19497229k=23633
/20049971/20049973/20049977/20049979k=24303
/22678421/22678423/22678427/22678429k=27489
/22788971/22788973/22788977/22788979k=27623
/23417621/23417623/23417627/23417629k=28385
/23463821/23463823/23463827/23463829k=28441
/24001721/24001723/24001727/24001729k=29093
/24462071/24462073/24462077/24462079k=29651
/24572621/24572623/24572627/24572629k=29785
/25074221/25074223/25074227/25074229k=30393
/26074121/26074123/26074127/26074129k=31605
/27875921/27875923/27875927/27875929k=33789
/27979871/27979873/27979877/27979879k=33915
/28194371/28194373/28194377/28194379k=34175
/28841171/28841173/28841177/28841179k=34959
/28920371/28920373/28920377/28920379k=35055
/29395571/29395573/29395577/29395579k=35631
/29763521/29763523/29763527/29763529k=36077
/29920271/29920273/29920277/29920279k=36267
/32710421/32710423/32710427/32710429k=39649

ysr

10000与40000之间的k*105有107组4生素数对: (用时22.55859秒）
/1063961/1063963/1063967/1063969k=10133
/1065011/1065013/1065017/1065019k=10143
/1091261/1091263/1091267/1091269k=10393
/1093991/1093993/1093997/1093999k=10419
/1122131/1122133/1122137/1122139k=10687
/1137881/1137883/1137887/1137889k=10837
/1157831/1157833/1157837/1157839k=11027
/1163711/1163713/1163717/1163719k=11083
/1167701/1167703/1167707/1167709k=11121
/1172531/1172533/1172537/1172539k=11167
/1173581/1173583/1173587/1173589k=11177
/1228391/1228393/1228397/1228399k=11699
/1233431/1233433/1233437/1233439k=11747
/1246241/1246243/1246247/1246249k=11869
/1272281/1272283/1272287/1272289k=12117
/1285511/1285513/1285517/1285519k=12243
/1298111/1298113/1298117/1298119k=12363
/1324571/1324573/1324577/1324579k=12615
/1339901/1339903/1339907/1339909k=12761
/1340321/1340323/1340327/1340329k=12765
/1351241/1351243/1351247/1351249k=12869
/1358801/1358803/1358807/1358809k=12941
/1368461/1368463/1368467/1368469k=13033
/1381271/1381273/1381277/1381279k=13155
/1400801/1400803/1400807/1400809k=13341
/1447001/1447003/1447007/1447009k=13781
/1451831/1451833/1451837/1451839k=13827
/1468631/1468633/1468637/1468639k=13987
/1524071/1524073/1524077/1524079k=14515
/1525961/1525963/1525967/1525969k=14533
/1571741/1571743/1571747/1571749k=14969
/1588751/1588753/1588757/1588759k=15131
/1615841/1615843/1615847/1615849k=15389
/1621721/1621723/1621727/1621729k=15445
/1627601/1627603/1627607/1627609k=15501
/1659101/1659103/1659107/1659109k=15801
/1691861/1691863/1691867/1691869k=16113
/1711811/1711813/1711817/1711819k=16303
/1727771/1727773/1727777/1727779k=16455
/1747721/1747723/1747727/1747729k=16645
/1780481/1780483/1780487/1780489k=16957
/1834031/1834033/1834037/1834039k=17467
/1837391/1837393/1837397/1837399k=17499
/1890521/1890523/1890527/1890529k=18005
/1910261/1910263/1910267/1910269k=18193
/1915931/1915933/1915937/1915939k=18247
/1925381/1925383/1925387/1925389k=18337
/1943651/1943653/1943657/1943659k=18511
/1954151/1954153/1954157/1954159k=18611
/1954361/1954363/1954367/1954369k=18613
/1979141/1979143/1979147/1979149k=18849
/2007911/2007913/2007917/2007919k=19123
/2020721/2020723/2020727/2020729k=19245
/2050331/2050333/2050337/2050339k=19527
/2063771/2063773/2063777/2063779k=19655
/2083511/2083513/2083517/2083519k=19843
/2107661/2107663/2107667/2107669k=20073
/2202791/2202793/2202797/2202799k=20979
/2225051/2225053/2225057/2225059k=21191
/2256341/2256343/2256347/2256349k=21489
/2266631/2266633/2266637/2266639k=21587
/2303591/2303593/2303597/2303599k=21939
/2381081/2381083/2381087/2381089k=22677
/2413421/2413423/2413427/2413429k=22985
/2418671/2418673/2418677/2418679k=23035
/2470331/2470333/2470337/2470339k=23527
/2478521/2478523/2478527/2478529k=23605
/2499941/2499943/2499947/2499949k=23809
/2541941/2541943/2541947/2541949k=24209
/2552651/2552653/2552657/2552659k=24311
/2561261/2561263/2561267/2561269k=24393
/2576591/2576593/2576597/2576599k=24539
/2604731/2604733/2604737/2604739k=24807
/2679491/2679493/2679497/2679499k=25519
/2696921/2696923/2696927/2696929k=25685
/2704901/2704903/2704907/2704909k=25761
/2759291/2759293/2759297/2759299k=26279
/2764121/2764123/2764127/2764129k=26325
/2822711/2822713/2822717/2822719k=26883
/2839931/2839933/2839937/2839939k=27047
/2846861/2846863/2846867/2846869k=27113
/2893481/2893483/2893487/2893489k=27557
/2989031/2989033/2989037/2989039k=28467
/3047411/3047413/3047417/3047419k=29023
/3076391/3076393/3076397/3076399k=29299
/3092561/3092563/3092567/3092569k=29453
/3103271/3103273/3103277/3103279k=29555
/3171731/3171733/3171737/3171739k=30207
/3207431/3207433/3207437/3207439k=30547
/3224861/3224863/3224867/3224869k=30713
/3243341/3243343/3243347/3243349k=30889
/3366821/3366823/3366827/3366829k=32065
/3371441/3371443/3371447/3371449k=32109
/3400211/3400213/3400217/3400219k=32383
/3512981/3512983/3512987/3512989k=33457
/3586901/3586903/3586907/3586909k=34161
/3735161/3735163/3735167/3735169k=35573
/3837851/3837853/3837857/3837859k=36551
/3849821/3849823/3849827/3849829k=36665
/3974351/3974353/3974357/3974359k=37851
/4015931/4015933/4015937/4015939k=38247
/4016561/4016563/4016567/4016569k=38253
/4039661/4039663/4039667/4039669k=38473
/4042601/4042603/4042607/4042609k=38501
/4059191/4059193/4059197/4059199k=38659
/4098461/4098463/4098467/4098469k=39033
/4157891/4157893/4157897/4157899k=39599

ysr

110000与120000之间的k*825有8组4生素数对: (用时28.30859秒）
/91065971/91065973/91065977/91065979k=110383
/91557671/91557673/91557677/91557679k=110979
/91696271/91696273/91696277/91696279k=111147
/91867871/91867873/91867877/91867879k=111355
/92202821/92202823/92202827/92202829k=111761
/94722371/94722373/94722377/94722379k=114815
/96834371/96834373/96834377/96834379k=117375
/98538821/98538823/98538827/98538829k=119441
110000与120000之间的k*105有17组4生素数对: (用时13.23047秒）
/11622131/11622133/11622137/11622139k=110687
/11652161/11652163/11652167/11652169k=110973
/11664551/11664553/11664557/11664559k=111091
/11779211/11779213/11779217/11779219k=112183
/11911511/11911513/11911517/11911519k=113443
/11927471/11927473/11927477/11927479k=113595
/12039821/12039823/12039827/12039829k=114665
/12172751/12172753/12172757/12172759k=115931
/12216431/12216433/12216437/12216439k=116347
/12279011/12279013/12279017/12279019k=116943
/12300641/12300643/12300647/12300649k=117149
/12320171/12320173/12320177/12320179k=117335
/12407111/12407113/12407117/12407119k=118163
/12421391/12421393/12421397/12421399k=118299
/12451841/12451843/12451847/12451849k=118589
/12511901/12511903/12511907/12511909k=119161
/12528281/12528283/12528287/12528289k=119317

ysr

蔡家雄 发表于 2021-7-22 08:39
定义：若 15k±2 和 15k±4 是 四生素数，则称 15k 为 双中数。

奇数双中比猜想：一奇数均可表为两个双 ...

就是说k2/k1=105吧？这个可能有很多。由于105/15=7，所以在15k中，只要k是7的倍数，都是所求的解。

ysr

ysr 发表于 2021-7-22 13:17
就是说k2/k1=105吧？这个可能有很多。由于105/15=7，所以在15k中，只要k是7的倍数，都是所求的解。

100与500之间的k*15有5组4生素数对: (用时0.0625秒）
/1873/1877/1871/1879k=125
/2083/2087/2081/2089k=139
/3253/3257/3251/3259k=217
/3463/3467/3461/3469k=231
/5653/5657/5651/5659k=377
其中217/7=31，231/7=33.
105=217*15/31

ysr

ysr 发表于 2021-7-22 13:17
就是说k2/k1=105吧？这个可能有很多。由于105/15=7，所以在15k中，只要k是7的倍数，都是所求的解。

要想k2/k1=105，则需k2/7=105的倍数，217*15/7=31*15

ysr

蔡家雄 发表于 2021-7-22 08:39
定义：若 15k±2 和 15k±4 是 四生素数，则称 15k 为 双中数。

奇数双中比猜想：一奇数均可表为两个双 ...

10000与40000之间的k*105有107组4生素数对: (用时22.55859秒）
/1063961/1063963/1063967/1063969k=10133
/1065011/1065013/1065017/1065019k=10143
/1091261/1091263/1091267/1091269k=10393
/1093991/1093993/1093997/1093999k=10419
/1122131/1122133/1122137/1122139k=10687
/1137881/1137883/1137887/1137889k=10837
/1157831/1157833/1157837/1157839k=11027
/1163711/1163713/1163717/1163719k=11083
/1167701/1167703/1167707/1167709k=11121
/1172531/1172533/1172537/1172539k=11167
/1173581/1173583/1173587/1173589k=11177
/1228391/1228393/1228397/1228399k=11699
/1233431/1233433/1233437/1233439k=11747
/1246241/1246243/1246247/1246249k=11869
/1272281/1272283/1272287/1272289k=12117
/1285511/1285513/1285517/1285519k=12243
/1298111/1298113/1298117/1298119k=12363
/1324571/1324573/1324577/1324579k=12615
…………
由于12615/15=841，所以，12615*7/105=841.

（没有找到，要想k2/k1=105，则需k2=105或k2/7=105或者k2/13=105等等）

蔡家雄

定义：若 m±2 和 m±4 是 四生素数，则称 m 为 双中数。

奇数双中比猜想：一奇数均可表为两个双中数之比。

奇数双中数 105 表为两个 更大的 双中数之比，（ 绝对有解 ）

即：105 = (105m) / m , 求：105m 与 m 都是双中数，m = ?