判定梅森质数的卢卡斯序列

ysr

蔡家雄 发表于 2021-8-3 23:44
同邻距的三生素数
且前一组三生素数之和是后一组三生素数的首项，

1与1000000之间的素数打头有55组6生素数对: (用时119.7168秒）
/83/673/809/839/1429p=53
/479/1069/1997/2027/2617p=449
/2141/2731/6983/7013/7603p=2111
/7577/8167/23291/23321/23911p=7547
/13751/14341/41813/41843/42433p=13721
/27947/28537/84401/84431/85021p=27917
/50543/51133/152189/152219/152809p=50513
/52289/52879/157427/157457/158047p=52259
/64301/64891/193463/193493/194083p=64271
/82487/83077/248021/248051/248641p=82457
/84437/85027/253871/253901/254491p=84407
/89417/90007/268811/268841/269431p=89387
/104789/105379/314927/314957/315547p=104759
/107873/108463/324179/324209/324799p=107843
/130367/130957/391661/391691/392281p=130337
/133811/134401/401993/402023/402613p=133781
/157247/157837/472301/472331/472921p=157217
/172343/172933/517589/517619/518209p=172313
/172619/173209/518417/518447/519037p=172589
/173897/174487/522251/522281/522871p=173867
/179483/180073/539009/539039/539629p=179453
/194057/194647/582731/582761/583351p=194027
/203381/203971/610703/610733/611323p=203351
/219281/219871/658403/658433/659023p=219251
/224759/225349/674837/674867/675457p=224729
/241877/242467/726191/726221/726811p=241847
/244247/244837/733301/733331/733921p=244217
/251033/251623/753659/753689/754279p=251003
/259937/260527/780371/780401/780991p=259907
/272411/273001/817793/817823/818413p=272381
/275999/276589/828557/828587/829177p=275969
/286751/287341/860813/860843/861433p=286721
/320417/321007/961811/961841/962431p=320387
/347651/348241/1043513/1043543/1044133p=347621
/391163/391753/1174049/1174079/1174669p=391133
/439613/440203/1319399/1319429/1320019p=439583
/497339/497929/1492577/1492607/1493197p=497309
/497741/498331/1493783/1493813/1494403p=497711
/540179/540769/1621097/1621127/1621717p=540149
/553097/553687/1659851/1659881/1660471p=553067
/594551/595141/1784213/1784243/1784833p=594521
/621029/621619/1863647/1863677/1864267p=620999
/624539/625129/1874177/1874207/1874797p=624509
/651251/651841/1954313/1954343/1954933p=651221
/700241/700831/2101283/2101313/2101903p=700211
/712319/712909/2137517/2137547/2138137p=712289
/805451/806041/2416913/2416943/2417533p=805421
/843503/844093/2531069/2531099/2531689p=843473
/853079/853669/2559797/2559827/2560417p=853049
/907259/907849/2722337/2722367/2722957p=907229
/918161/918751/2755043/2755073/2755663p=918131
/920783/921373/2762909/2762939/2763529p=920753
/930719/931309/2792717/2792747/2793337p=930689
/934517/935107/2804111/2804141/2804731p=934487
/999683/1000273/2999609/2999639/3000229p=999653

ysr

蔡家雄 发表于 2021-8-3 23:56
同一个n值，

使 n(n+1) -1 与 n(n+1)+1 均为孪生素数的前100个解，，

1与100之间的素数打头有16组2生素数对: (用时2.734375E-02秒）
/5/7n=2
/11/13n=3
/29/31n=5
/41/43n=6
/71/73n=8
/239/241n=15
/419/421n=20
/461/463n=21
/599/601n=24
/1481/1483n=38
/1721/1723n=41
/2549/2551n=50
/2969/2971n=54
/3539/3541n=59
/4421/4423n=66
/8009/8011n=89

ysr

蔡家雄 发表于 2021-8-3 23:56
同一个n值，

使 n(n+1) -1 与 n(n+1)+1 均为孪生素数的前100个解，，

1与50000之间的素数打头有1033组2生素数对: (用时322.8398秒）
/5/7n=2
/11/13n=3
/29/31n=5
/41/43n=6
/71/73n=8
/239/241n=15
/419/421n=20
/461/463n=21
/599/601n=24
/1481/1483n=38
/1721/1723n=41
/2549/2551n=50
/2969/2971n=54
/3539/3541n=59
/4421/4423n=66
/8009/8011n=89
/10301/10303n=101
/17291/17293n=131
/19181/19183n=138
/20021/20023n=141
/23561/23563n=153
/24179/24181n=155
/27059/27061n=164
/31151/31153n=176
/35531/35533n=188
/41411/41413n=203
/42641/42643n=206
/43889/43891n=209
/46439/46441n=215
/47741/47743n=218
/53591/53593n=231
/55931/55933n=236
/60761/60763n=246
/83231/83233n=288
/84389/84391n=290
/95789/95791n=309
/98909/98911n=314
/123551/123553n=351
/143261/143263n=378
/156419/156421n=395
/164429/164431n=405
/205661/205663n=453
/207479/207481n=455
/208391/208393n=456
/245519/245521n=495
/250499/250501n=500
/268841/268843n=518
/281429/281431n=530
/304151/304153n=551
/314159/314161n=560
/389999/390001n=624
/415379/415381n=644
/446891/446893n=668
/471281/471283n=686
/519119/519121n=720
/530711/530713n=728
/552791/552793n=743
/579881/579883n=761
/637601/637603n=798
/681449/681451n=825
/792989/792991n=890
/838139/838141n=915
/903449/903451n=950
/949649/949651n=974
/963341/963343n=981
/1003001/1003003n=1001
/1033271/1033273n=1016
/1206701/1206703n=1098
/1278029/1278031n=1130
/1321349/1321351n=1149
/1424441/1424443n=1193
/1441199/1441201n=1200
/1588859/1588861n=1260
/1624349/1624351n=1274
/1678319/1678321n=1295
/1712171/1712173n=1308
/1804991/1804993n=1343
/1861859/1861861n=1364
/1864589/1864591n=1365
/1905779/1905781n=1380
/2020661/2020663n=1421
/2233529/2233531n=1494
/2330201/2330203n=1526
/2339369/2339371n=1529
/2397851/2397853n=1548
/2453921/2453923n=1566
/2529689/2529691n=1590
/2753939/2753941n=1659
/3050261/3050263n=1746
/3198731/3198733n=1788
/3263441/3263443n=1806
/3336101/3336103n=1826
/3416951/3416953n=1848
/3435461/3435463n=1853
/3558881/3558883n=1886
/4001999/4002001n=2000
/4220969/4220971n=2054
/4433129/4433131n=2105
/4564631/4564633n=2136
/4715411/4715413n=2171
/4859819/4859821n=2204
/4864229/4864231n=2205
/5087279/5087281n=2255
/5182451/5182453n=2276
/5375441/5375443n=2318
/5633501/5633503n=2373
/5805689/5805691n=2409
/5815331/5815333n=2411
/6004949/6004951n=2450
/6009851/6009853n=2451
/6317681/6317683n=2513
/6535691/6535693n=2556
/6561281/6561283n=2561
/6909011/6909013n=2628
/7003961/7003963n=2646
/7019849/7019851n=2649
/7030451/7030453n=2651
/7094231/7094233n=2663
/7271111/7271113n=2696
/7335971/7335973n=2708
/7450169/7450171n=2729
/7455629/7455631n=2730
/7488431/7488433n=2736
/8000411/8000413n=2828
/8360771/8360773n=2891
/8401301/8401303n=2898
/8558549/8558551n=2925
/8623031/8623033n=2936
/8979011/8979013n=2996
/9069131/9069133n=3011
/9421829/9421831n=3069
/9606899/9606901n=3099
/10052069/10052071n=3170
/10243199/10243201n=3200
/10378061/10378063n=3221
/10572251/10572253n=3251
/10598279/10598281n=3255
/11145581/11145583n=3338
/11434541/11434543n=3381
/11823281/11823283n=3438
/11899049/11899051n=3449
/11961221/11961223n=3458
/12002759/12002761n=3464
/12920429/12920431n=3594
/13238681/13238683n=3638
/14021279/14021281n=3744
/14703389/14703391n=3834
/15089339/15089341n=3884
/15252929/15252931n=3905
/15519659/15519661n=3939
/15988001/15988003n=3998
/16252991/16252993n=4031
/16455191/16455193n=4056
/17110631/17110633n=4136
/17293121/17293123n=4158
/17459861/17459863n=4178
/17610611/17610613n=4196
/17846399/17846401n=4224
/17939459/17939461n=4235
/18356939/18356941n=4284
/18926849/18926851n=4350
/19320419/19320421n=4395
/19744691/19744693n=4443
/19771361/19771363n=4446
/19789151/19789153n=4448
/20525429/20525431n=4530
/20798159/20798161n=4560
/21201419/21201421n=4604
/21339779/21339781n=4619
/21395249/21395251n=4625
/21701621/21701623n=4658
/22047719/22047721n=4695
/22075901/22075903n=4698
/22576751/22576753n=4751
/22958471/22958473n=4791
/23975711/23975713n=4896
/24805379/24805381n=4980
/25436891/25436893n=5043
/25649159/25649161n=5064
/25953929/25953931n=5094
/26383631/26383633n=5136
/26414459/26414461n=5139
/26816861/26816863n=5178
/26847941/26847943n=5181
/27284951/27284953n=5223
/27399989/27399991n=5234
/27525761/27525763n=5246
/27557249/27557251n=5249
/27599261/27599263n=5253
/27630791/27630793n=5256
/27936509/27936511n=5285
/28137719/28137721n=5304
/28520939/28520941n=5340
/28681379/28681381n=5355
/28713521/28713523n=5358
/29057489/29057491n=5390
/30431771/30431773n=5516
/30674981/30674983n=5538
/30796949/30796951n=5549
/31399211/31399213n=5603
/31815239/31815241n=5640
/32075231/32075233n=5663
/32154569/32154571n=5670
/32450111/32450113n=5696
/33114269/33114271n=5754
/34404089/34404091n=5865
/34533251/34533253n=5876
/35922041/35922043n=5993
/37167311/37167313n=6096
/37558511/37558513n=6128
/38112101/38112103n=6173
/38831591/38831593n=6231
/39507509/39507511n=6285
/39999299/39999301n=6324
/40494131/40494133n=6363
/40557791/40557793n=6368
/40596011/40596013n=6371
/40915211/40915213n=6396
/41402789/41402791n=6434
/42113609/42113611n=6489
/42386609/42386611n=6510
/42765059/42765061n=6539
/43289819/43289821n=6579
/43553399/43553401n=6599
/44149379/44149381n=6644
/44642441/44642443n=6681
/45165119/45165121n=6720
/45353489/45353491n=6734
/46219601/46219603n=6798
/46696721/46696723n=6833
/47396339/47396341n=6884
/47451431/47451433n=6888
/47810309/47810311n=6914
/49836539/49836541n=7059
/50175971/50175973n=7083
/50630339/50630341n=7115
/51272759/51272761n=7160
/51890411/51890413n=7203
/52265669/52265671n=7229
/53224319/53224321n=7295
/53501909/53501911n=7314
/54147521/54147523n=7358
/55942919/55942921n=7479
/56302511/56302513n=7503
/56618099/56618101n=7524
/56844059/56844061n=7539
/57463979/57463981n=7580
/59205329/59205331n=7694
/61551869/61551871n=7845
/61787459/61787461n=7860
/61929029/61929031n=7869
/62813549/62813551n=7925
/63624551/63624553n=7976
/63736271/63736273n=7983
/64585331/64585333n=8036
/65036159/65036161n=8064
/65359139/65359141n=8084
/65715341/65715343n=8106
/66398051/66398053n=8148
/66479561/66479563n=8153
/66724391/66724393n=8168
/68898299/68898301n=8300
/70702871/70702873n=8408
/71630831/71630833n=8463
/72940139/72940141n=8540
/72957221/72957223n=8541
/73265039/73265041n=8559
/74969621/74969623n=8658
/75160229/75160231n=8669
/76676291/76676293n=8756
/77677781/77677783n=8813
/77907101/77907103n=8826
/80667341/80667343n=8981
/80937011/80937013n=8996
/81063011/81063013n=9003
/81549929/81549931n=9030
/82074539/82074541n=9059
/82800899/82800901n=9099
/83055881/83055883n=9113
/83841491/83841493n=9156
/83988059/83988061n=9164
/85775381/85775383n=9261
/86610941/86610943n=9306
/86927651/86927653n=9323
/87319679/87319681n=9344
/87618959/87618961n=9360
/88350599/88350601n=9399
/90658961/90658963n=9521
/92092811/92092813n=9596
/92669501/92669503n=9626
/93325259/93325261n=9660
/94468679/94468681n=9719
/94935791/94935793n=9743
/95072249/95072251n=9750
/95189291/95189293n=9756
/96599411/96599413n=9828
/97249181/97249183n=9861
/99012449/99012451n=9950
/99331121/99331123n=9966
/99430811/99430813n=9971
/99510599/99510601n=9975
后面还多，超长不发了。

蔡家雄

ysr 发表于 2021-8-4 08:52
1与99000之间的素数打头有103组3生素数对: (用时74.26172秒）
/11/13n=3
/29/31n=5

漏了很多解：n=2, 6, 8, 20, 21, 455, 456, ...  

把它删除，编好程序，再把正确的发上来，，

ysr

蔡家雄 发表于 2021-8-4 01:12
漏了很多解：n=2, 6, 8, 20, 21, 455, 456, ...  

把它删除，编好程序，再把正确的发上来，，

1与2500之间的素数打头有110组2生素数对: (用时1.183594秒）
/5/7n=2
/11/13n=3
/29/31n=5
/41/43n=6
/71/73n=8
/239/241n=15
/419/421n=20
/461/463n=21
/599/601n=24
/1481/1483n=38
/1721/1723n=41
/2549/2551n=50
/2969/2971n=54
/3539/3541n=59
/4421/4423n=66
/8009/8011n=89
/10301/10303n=101
/17291/17293n=131
/19181/19183n=138
/20021/20023n=141
/23561/23563n=153
/24179/24181n=155
/27059/27061n=164
/31151/31153n=176
/35531/35533n=188
/41411/41413n=203
/42641/42643n=206
/43889/43891n=209
/46439/46441n=215
/47741/47743n=218
/53591/53593n=231
/55931/55933n=236
/60761/60763n=246
/83231/83233n=288
/84389/84391n=290
/95789/95791n=309
/98909/98911n=314
/123551/123553n=351
/143261/143263n=378
/156419/156421n=395
/164429/164431n=405
/205661/205663n=453
/207479/207481n=455
/208391/208393n=456
/245519/245521n=495
/250499/250501n=500
/268841/268843n=518
/281429/281431n=530
/304151/304153n=551
/314159/314161n=560
/389999/390001n=624
/415379/415381n=644
/446891/446893n=668
/471281/471283n=686
/519119/519121n=720
/530711/530713n=728
/552791/552793n=743
/579881/579883n=761
/637601/637603n=798
/681449/681451n=825
/792989/792991n=890
/838139/838141n=915
/903449/903451n=950
/949649/949651n=974
/963341/963343n=981
/1003001/1003003n=1001
/1033271/1033273n=1016
/1206701/1206703n=1098
/1278029/1278031n=1130
/1321349/1321351n=1149
/1424441/1424443n=1193
/1441199/1441201n=1200
/1588859/1588861n=1260
/1624349/1624351n=1274
/1678319/1678321n=1295
/1712171/1712173n=1308
/1804991/1804993n=1343
/1861859/1861861n=1364
/1864589/1864591n=1365
/1905779/1905781n=1380
/2020661/2020663n=1421
/2233529/2233531n=1494
/2330201/2330203n=1526
/2339369/2339371n=1529
/2397851/2397853n=1548
/2453921/2453923n=1566
/2529689/2529691n=1590
/2753939/2753941n=1659
/3050261/3050263n=1746
/3198731/3198733n=1788
/3263441/3263443n=1806
/3336101/3336103n=1826
/3416951/3416953n=1848
/3435461/3435463n=1853
/3558881/3558883n=1886
/4001999/4002001n=2000
/4220969/4220971n=2054
/4433129/4433131n=2105
/4564631/4564633n=2136
/4715411/4715413n=2171
/4859819/4859821n=2204
/4864229/4864231n=2205
/5087279/5087281n=2255
/5182451/5182453n=2276
/5375441/5375443n=2318
/5633501/5633503n=2373
/5805689/5805691n=2409
/5815331/5815333n=2411
/6004949/6004951n=2450
/6009851/6009853n=2451

ysr

蔡家雄 发表于 2021-8-3 23:57
同一个n值，

使 n(n+1)(n+2) -1 与 n(n+1)(n+2)+1 均为孪生素数的前100个解，，，

1与3000之间的素数打头有73组2生素数对: (用时238.6953秒）
/5/7n=1
/59/61n=3
/1319/1321n=10
/2729/2731n=13
/3359/3361n=14
/9239/9241n=20
/29759/29761n=30
/42839/42841n=34
/68879/68881n=40
/91079/91081n=44
/1367519/1367521n=110
/2196869/2196871n=129
/2515319/2515321n=135
/2743859/2743861n=139
/3723719/3723721n=154
/5451599/5451601n=175
/6751079/6751081n=188
/10793639/10793641n=220
/12166769/12166771n=229
/13651679/13651681n=238
/20570549/20570551n=273
/31554179/31554181n=315
/66923009/66923011n=405
/70957529/70957531n=413
/85765679/85765681n=440
/100544159/100544161n=464
/101194229/101194231n=465
/128023559/128023561n=503
/141420239/141420241n=520
/176557919/176557921n=560
/185192429/185192431n=569
/195111419/195111421n=579
/199176119/199176121n=583
/206424479/206424481n=590
/322828169/322828171n=685
/327082079/327082081n=688
/337152839/337152841n=695
/437244719/437244721n=758
/580092869/580092871n=833
/584276219/584276221n=835
/636055139/636055141n=859
/656234039/656234041n=868
/738762359/738762361n=903
/884735039/884735041n=959
/1080044549/1080044551n=1025
/1556861519/1556861521n=1158
/2622361559/2622361561n=1378
/3645152279/3645152281n=1538
/4204461929/4204461931n=1613
/4291013999/4291014001n=1624
/4574294339/4574294341n=1659
/4657461329/4657461331n=1669
/4750102559/4750102561n=1680
/6018634439/6018634441n=1818
/7460596709/7460596711n=1953
/8193538079/8193538081n=2015
/8882601839/8882601841n=2070
/8947092899/8947092901n=2075
/10007871719/10007871721n=2154
/10021810259/10021810261n=2155
/10303305599/10303305601n=2175
/11790078299/11790078301n=2275
/12103628039/12103628041n=2295
/12310387319/12310387321n=2308
/12503319839/12503319841n=2320
/13720576589/13720576591n=2393
/14190062039/14190062041n=2420
/17677592519/17677592521n=2604
/17779578389/17779578391n=2609
/20257110449/20257110451n=2725
/20480861519/20480861521n=2735
/22641165959/22641165961n=2828
/25025200199/25025200201n=2924

ysr

ysr 发表于 2021-8-4 01:31
1与3000之间的素数打头有73组2生素数对: (用时238.6953秒）
/5/7n=1
/59/61n=3

3000与4000之间的素数打头有17组2生素数对: (用时183.5898秒）
/28205506139/28205506141n=3043
/33199961129/33199961131n=3213
/33729572159/33729572161n=3230
/38136628529/38136628531n=3365
/39165439739/39165439741n=3395
/40565742419/40565742421n=3435
/41242417919/41242417921n=3454
/44701074599/44701074601n=3548
/45118012439/45118012441n=3559
/48827232719/48827232721n=3654
/55480713329/55480713331n=3813
/55699198439/55699198441n=3818
/56446337219/56446337221n=3835
/57736235759/57736235761n=3864
/58185542999/58185543001n=3874
/62997278759/62997278761n=3978
/63712427789/63712427791n=3993

ysr

ysr 发表于 2021-8-4 01:35
3000与4000之间的素数打头有17组2生素数对: (用时183.5898秒）
/28205506139/28205506141n=3043
/33199 ...

4000与6000之间的素数打头有28组2生素数对: (用时708.0352秒）
/64529449319/64529449321n=4010
/68870578199/68870578201n=4098
/77526747479/77526747481n=4263
/81520680719/81520680721n=4335
/81803019479/81803019481n=4340
/83510752439/83510752441n=4370
/85707785519/85707785521n=4408
/86997190559/86997190561n=4430
/87587533679/87587533681n=4440
/93576659459/93576659461n=4539
/94196370449/94196370451n=4549
/100609501799/100609501801n=4650
/125676210719/125676210721n=5008
/127947869279/127947869281n=5038
/133119725909/133119725911n=5105
/137388090839/137388090841n=5159
/141828308159/141828308161n=5214
/142318403639/142318403641n=5220
/145614589319/145614589321n=5260
/155287103999/155287104001n=5374
/164656694159/164656694161n=5480
/170492248079/170492248081n=5544
/189712895189/189712895191n=5745
/191501377979/191501377981n=5763
/198155281169/198155281171n=5829
/198563427869/198563427871n=5833
/211815312719/211815312721n=5960
/213311228399/213311228401n=5974

蔡家雄

ysr 发表于 2021-8-4 09:55
4000与6000之间的素数打头有28组2生素数对: (用时708.0352秒）
/64529449319/64529449321n=4010
/68870 ...

同一个n值，

使 n(n+1) -1 与 n(n+1)+1 均为孪生素数，

及 (n+1)(n+2) -1 与 (n+1)(n+2)+1 均为孪生素数，

的 前20个解，你能求全 吗？

ysr

蔡家雄 发表于 2021-8-4 02:07
同一个n值，

使 n(n+1) -1 与 n(n+1)+1 均为孪生素数，

1与2000之间的素数打头有5组4生素数对: (用时1.179688秒）
/5/7/11/13n=2
/29/31/41/43n=5
/419/421/461/463n=20
/207479/207481/208391/208393n=455
/1861859/1861861/1864589/1864591n=1364