ysr
发表于 2025-5-24 14:32
168802853 168802901 168802961 168803321 168803381
168803501 168803597 168803741 168803777 168803801
168803861 168803933 168804017 168804161 168804281
168804437 168804761 168804821 168804833 168804893
168805001 168805097 168805157 168805493 168805517
168805577 168805853 168805913 168805997 168806117
168806201 168806237 168806513 168806633 168806741
168806801 168806861 168806921 168807113 168807377
168807497 168807857 168807893 168808061 168808253
168808301 168808313 168808373 168808481 168808517
168808613 168808697 168808721 168808817 168808877
168808973 168809033 168809057 168809141 168809681
168809777 168809897 168809981 168810077 168810101
168810401 168810413 168810557 168810581 168810641
168810737 168810893 168811061 168811121 168811133
168811157 168811193 168811277 168811301 168811397
168811781 168811901 168811961 168812141 168812201
168812513 168812753 168812933 168812957 168813053
168813173 168813581 168813653 168813677 168813773
168813833 168814157 168814337 168814493 168814661
168814817 168815417 168815453 168815477 168815501
168815693 168815753 168815861 168815897 168815981
168816101 168816161 168816353 168816413 168816677
168816701 168816761 168816797 168816821 168817013
168817037 168817133 168817193 168817241 168817277
168817301 168817457 168817577 168818081 168818261
168818297 168818393 168818513 168818561 168818633
168818693 168818861 168818921 168818981 168819113
168819173 168819653 168819713 168819773 168819821
168819881 168819941 168819953 168820097 168820121
168820277 168820313 168820433 168820721 168820781
168820913 168820937 168820961 168821057 168821201
168821297 168821573 168821621 168821693 168821717
168821921 168821993 168822221 168822233 168822293
168822317 168822341 168822377 168822413 168822473
168822557 168822701 168822821 168822881 168822977
168823097 168823253 168823337 168823373 168823517
168823601 168823673 168823817 168823913 168823997
168824261 168824333 168824477 168824561 168824741
168824753 168824801 168824933 168824993 168825053
168825197 168825233 168825281 168825341 168825581
168825593 168825653 168826013 168826061 168826157
168826421 168826517 168826673 168826793 168826841
168827081 168827093 168827117 168827177 168827201
168827213 168827237 168827297 168827453 168827501
168827777 168827921 168828017 168828113 168828137
168828221 168828353 168828497 168828761 168828833
168828941 168828953 168829061 168829181 168829301
168829313 168829613 168829673 168829901 168829961
168830033 168830177 168830201 168830237 168830273
168830633 168830861 168830897 168830933 168831197
168831353 168831461 168831521 168831557 168831833
168831917 168831941 168832241 168832373 168833057
168833237 168833321 168833453 168833921 168834041
168834077 168834101 168834257 168834377 168834461
168834557 168834581 168834593 168834833 168834917
168835001 168835061 168835241 168835301 168835493
168835613 168835637 168835661 168835817 168835841
168836093 168836141 168836441 168836453 168836501
168836561 168836621 168836873 168837017 168837161
168837257 168837533 168837593 168837653 168837941
168838001 168838013 168838037 168838097 168838133
168838181 168838217 168838277 168838601 168838913
168839081 168839093 168839117 168839381 168839477
168839501 168839717 168839813 168839837 168839861
168839873 168840101 168840257 168840281 168840293
168840341 168840437 168840461 168840521 168840533
168840761 168840941 168840977 168841037 168841073
168841193 168841301 168841313 168841373 168841457
168841553 168841661 168841721 168841793 168842081
168842237 168842393 168842477 168842621 168842717
168842741 168843053 168843113 168843197 168843221
168843377 168843401 168843533 168843581 168843593
168843641 168843797 168843977 168844133 168844337
168844421 168844433 168844733 168844937 168845021
168845057 168845141 168845657 168845681 168845753
168845777 168845813 168846221 168846317 168846401
168846581 168846593 168846761 168846857 168846893
168846917 168847013 168847037 168847097 168847121
168847337 168847361 168847373 168847517 168848021
168848177 168848213 168848261 168848333 168848357
168848417 168848441 168848597 168848921 168849101
168849137 168849353 168849377 168849617 168849677
168849701 168849773 168849953 168850037 168850133
168850373 168850457 168850541 168850697 168850733
168850841 168850901 168851201 168851597 168851621
168851741 168851897 168852017 168852077 168852161
168852353 168852377 168852617 168852713 168852737
168852773 168852953 168853121 168853193 168853541
168853613 168853637 168853661 168853901 168853913
168853961 168854141 168854261 168854297 168854393
168854633 168854681 168854813 168854921 168855041
168855053 168855077 168855317 168855341 168855353
168855437 168856277 168856361 168856421 168856637
168856661 168856697 168856841 168857033 168857477
168857573 168857657 168857813 168857873 168857993
168858077 168858101 168858197 168858233 168858461
168858653 168858737 168858761 168858917 168858941
168859133 168859193 168859661 168859781 168859913
168860141 168860333 168860357 168860381 168860777
168861041 168861197 168861281 168861353 168861521
168861617 168861677 168862061 168862073 168862097
168862361 168862373 168862433 168862553 168862601
168862613 168862697 168862721 168862817 168862913
168862961 168862973 168863237 168863333 168863573
168863633 168863657 168863741 168863801 168863993
168864401 168864461 168864473 168864497 168864557
168864701 168864821 168864953 168864977 168865013
168865061 168865181 168865421 168865481 168865721
168865937 168865973 168865997 168866057 168866177
168866297 168866381 168866501 168866561 168866573
168866981 168867113 168867197 168867317 168867521
168867641 168867701 168867773 168867821 168867833
168867857 168868013 168868121 168868373 168868433
168868517 168868673 168868793 168868961 168869081
168869153 168869237 168869297 168869333 168869417
168869621 168869717 168869837 168870017 168870101
168870437 168870473 168870497 168870593 168870641
168870941 168871061 168871253 168871301 168871337
168871361 168871457 168871541 168871613 168871721
168871841 168871853 168872021 168872117 168872177
168872201 168872213 168872357 168872453 168872621
168872633 168872933 168873161 168873401 168873557
168873917 168874001 168874133 168874193 168874217
168874397 168874553 168874637 168874661 168874721
168874817 168874841 168874877 168874973 168875261
168875393 168875513 168875537 168875717 168875753
168875801 168875981 168876017 168876137 168876173
168876221 168876293 168876377 168876401 168876413
168876677 168876713 168876761 168876857 168876941
168877061 168877217 168877253 168877421 168877481
168877601 168877637 168877697 168877781 168877853
168877997 168878033 168878081 168878141 168878201
168878477 168878597 168878681 168878753 168878813
168878981 168879257 168879281 168879437 168879617
168879701 168879761 168879773 168879833 168879881
168880001 168880073 168880277 168880301 168880457
168880781 168880853 168880961 168880997 168881057
168881117 168881261 168881477 168881561 168881693
168881717 168881957 168882041 168882101 168882173
168882281 168882401 168882521 168882533 168882617
168882941 168883061 168883217 168883241 168883373
168883601 168883973 168884117 168884201 168884213
168884381 168884393 168884501 168884537 168884633
168884657 168884741 168884801 168884873 168884921
168885161 168885377 168885461 168885557 168885653
168885677 168885917 168886013 168886061 168886073
168886397 168886433 168886457 168886577 168886793
168886961 168886973 168887093 168887141 168887153
168887261 168887393 168887417 168887501 168887513
168887657 168887777 168887921 168887933 168888101
168888281 168888413 168888497 168888521 168888773
168888893 168889181 168889241 168889277 168889361
168889397 168889421 168889481 168889517 168889733
168889937 168890093 168890177 168890261 168890417
168890441 168890453 168890717 168890741 168890921
168890993 168891137 168891161 168891197 168891521
168891581 168891677 168891713 168891773 168891857
168892001 168892037 168892133 168892181 168892481
168892517 168892553 168892721 168892733 168892793
168892877 168893237 168893321 168893357 168893381
168893693 168893741 168893873 168893897 168894017
168894533 168894581 168894617 168894797 168894953
168895073 168895157 168895193 168895361 168895553
168895613 168895637 168895673 168895757 168895817
168895841 168896081 168896393 168896501 168896657
168896801 168896873 168897221 168897233 168897317
168897473 168897557 168897713 168897893 168898073
168898157 168898253 168898781 168898841 168898901
168898973 168898997 168899021 168899033 168899201
168899261 168899321 168899441 168899513 168899681
168899693 168899813 168899921 168899933 168900161
168900257 168900461 168900701 168900737 168900821
168900857 168900881 168900917 168901097 168901433
168901517 168901553 168901637 168901661 168901757
168901853 168901877 168902033 168902057 168902081
168902273 168902441 168902453 168902561 168902621
168902693 168902813 168902861 168902897 168902933
ysr
发表于 2025-5-24 14:35
后面还有很多，不发了，不算了，第53个梅森素数的指数很大概率就可能是在前面这些数值中，后面的不用计算了，后面的就没有参考价值了。
ysr
发表于 2025-5-24 14:46
M48～M52的指数p的特征：
序号 p p-1的特征 p+1的特征
48 57,885,161 57885160=2^3*5*29*139*359 57885162=2*3*9647527
49* 74,207,281 74207280=2^4*3*5*7*44171 74207282=2*107*346763
50* 77,232,917 77232916=2^2*29*665801 77232918=2*3*7^2*262697
51* 82,589,933 82589932=2^2*103*200461 82589934=2*3*7*1966427
52 136,279,841136279840= 2^5*5*851749 136279842=2*3*1381*16447
有类似特征的素数p就可能是梅森素数的指数p
特征就是：
1：在p-1中素因子2的次数在2以上，而在p+1中素因子2的次数仅仅是1.
2：在p-1和p+1中，不同的素因子个数在3个以上，除了素因子2以外，其他不同的素因子的个数在2个以上。
上线公式：f(x1)=(3.14*x1)/ln([（X1+2）/50]*0.5+x1+5)-0.8,x1=1,2,3,……,其中[]为高斯函数，
P=1.618^f(x1)
下限公式：y=302887e ^(0.1106x)，R ^2=0.8477.
按前一个计算得到p53=239813977
按第二个公式计算得到p53=106421169
接近实际的上线公式：f(x1)=(3.14*x1)/ln([（X1+2）/50]+x1+5)-0.8,x1=1,2,3,……,其中[]为高斯函数，
P=1.618^f(x1)
按这个公式计算得到p53=230162709
239813977+106421169=346235146，346235146/2=173117573
230162709+106421169=336583878，336583878/2=168291939
则，预测第53个梅森素数的指数p的值在168291939~173117573之间
或者略低于168291939
判断一下在168291939~173117573之间的素数的特征，就有可能找到第53个梅森素数。
ysr
发表于 2025-5-24 14:55
在168291939 与 168299939之间的素数个数有：424个，其间可能的梅森指数p有 107 个：
168291961 s=1 p1=2^3*3*5*47*53*563 p2=2*41*79*83*313
168291997 s=2 p1=2^2*3*14024333 p2=2*7*2113*5689
168292057 s=3 p1=2^3*3*31*226199 p2=2*11*23*37*89*101
168292213 s=4 p1=2^2*3*11*1274941 p2=2*17^2*491*593
168292309 s=5 p1=2^2*3*59*237701 p2=2*5*19*199*4451
168292321 s=6 p1=2^5*3*5*7*50087 p2=2*11*7649651
168292417 s=7 p1=2^6*3*876523 p2=2*7*17*707111
168292573 s=8 p1=2^2*3*7*2003483 p2=2*769*109423
168292589 s=9 p1=2^2*17*313*7907 p2=2*3*5*487*11519
168292609 s=10 p1=2^8*3*11^2*1811 p2=2*5*23*67^2*163
168292849 s=11 p1=2^4*3*3506101 p2=2*5^2*11^2*27817
168292921 s=12 p1=2^3*3*5*617*2273 p2=2*7*773*15551
168292981 s=13 p1=2^2*3^2*5*934961 p2=2*11*13*588437
168293009 s=14 p1=2^4*13*809101 p2=2*3*5*157*35731
168293029 s=15 p1=2^2*3*41*342059 p2=2*5*17*989959
168293113 s=16 p1=2^3*3*13*539401 p2=2*11*571*13397
168293137 s=17 p1=2^4*3*11*318737 p2=2*13*139*46567
168293173 s=18 p1=2^2*3*31*452401 p2=2*7*263*45707
168293269 s=19 p1=2^2*3^3*11*13*17*641 p2=2*5*101*166627
168293329 s=20 p1=2^4*3*7*500873 p2=2*5*1429*11777
168293341 s=21 p1=2^2*3^2*5*293*3191 p2=2*7^2*131*13109
168293413 s=22 p1=2^2*3^2*7*19*35149 p2=2*67*149*8429
168293509 s=23 p1=2^2*3*14024459 p2=2*5*7*11*61*3583
168293533 s=24 p1=2^2*3*11*983*1297 p2=2*1103*76289
168293549 s=25 p1=2^2*67*627961 p2=2*3*5^2*53*21169
168293569 s=26 p1=2^6*3*876529 p2=2*5*233*72229
168293581 s=27 p1=2^2*3*5*7*13^2*2371 p2=2*167*461*1093
168293869 s=28 p1=2^2*3*19^2*53*733 p2=2*5*373*45119
168294073 s=29 p1=2^3*3*7012253 p2=2*13*587*11027
168294097 s=30 p1=2^4*3^2*19*61511 p2=2*7*12021007
168294149 s=31 p1=2^2*11*3824867 p2=2*3^2*5^2*373987
168294193 s=32 p1=2^4*3*11*29^2*379 p2=2*89*945473
168294209 s=33 p1=2^6*557*4721 p2=2*3*5*7*19*42179
168294277 s=34 p1=2^2*3^2*4674841 p2=2*37*2274247
168294361 s=35 p1=2^3*3*5*13*107881 p2=2*19*137*32327
168294449 s=36 p1=2^4*7*1502629 p2=2*3*5^2*23*48781
168294541 s=37 p1=2^2*3*5*29*311^2 p2=2*13*23*281429
168294589 s=38 p1=2^2*3*7*11*23*7919 p2=2*5*19^2*46619
168294697 s=39 p1=2^3*3*17*412487 p2=2*11*13*199*2957
168294793 s=40 p1=2^3*3*7012283 p2=2*271*310507
168294937 s=41 p1=2^3*3*151*46439 p2=2*7*12021067
168294961 s=42 p1=2^4*3^2*5*233743 p2=2*11*643*11897
168295021 s=43 p1=2^2*3*5*2804917 p2=2*7*59*67*3041
168295093 s=44 p1=2^2*3*7*37*173*313 p2=2*11*23*31*10729
168295273 s=45 p1=2^3*3*631*11113 p2=2*7*17*19*37217
168295333 s=46 p1=2^2*3*14024611 p2=2*733*114799
168295349 s=47 p1=2^2*13*3236449 p2=2*3*5^2*19*59051
168295417 s=48 p1=2^3*3*23*304883 p2=2*71*1185179
168295453 s=49 p1=2^2*3*13*1078817 p2=2*6779*12413
168295469 s=50 p1=2^2*11*29*131893 p2=2*3*5*7*801407
168295513 s=51 p1=2^3*3*7*11^2*17*487 p2=2*73*1021*1129
168295549 s=52 p1=2^2*3*14024629 p2=2*5^2*43*78277
168295681 s=53 p1=2^8*3^2*5*7*2087 p2=2*17^2*291169
168295709 s=54 p1=2^2*7*379*15859 p2=2*3*5*11*211*2417
168295837 s=55 p1=2^2*3*157*89329 p2=2*31*2714449
168296113 s=56 p1=2^4*3^2*83*14081 p2=2*7*797*15083
168296137 s=57 p1=2^3*3*1579*4441 p2=2*283*409*727
168296189 s=58 p1=2^2*1429*29443 p2=2*3*5*47*119359
168296197 s=59 p1=2^2*3*139*163*619 p2=2*7*23*522659
168296389 s=60 p1=2^2*3*13*347*3109 p2=2*5*41*73*5623
168296521 s=61 p1=2^3*3*5*7*23*31*281 p2=2*163*516247
168296629 s=62 p1=2^2*3*29*483611 p2=2*5*67*239*1051
168296641 s=63 p1=2^6*3*5*175309 p2=2*19*4428859
168296701 s=64 p1=2^2*3*5^2*11*13*3923 p2=2*7*17*79*8951
168296729 s=65 p1=2^3*2053*10247 p2=2*3*5*7*53*15121
168296749 s=66 p1=2^2*3*131*151*709 p2=2*5^3*23*29269
168296833 s=67 p1=2^7*3^3*11*19*233 p2=2*3011*27947
168296917 s=68 p1=2^2*3*823*17041 p2=2*29*1151*2521
168296929 s=69 p1=2^5*3*1753093 p2=2*5*743*22651
168296977 s=70 p1=2^4*3^2*29*191*211 p2=2*7127*11807
168297001 s=71 p1=2^3*3*5^3*56099 p2=2*113*744677
168297133 s=72 p1=2^2*3*14024761 p2=2*97*867511
168297329 s=73 p1=2^4*97*108439 p2=2*3*5*5609911
168297373 s=74 p1=2^2*3^3*1558309 p2=2*7*41*293201
168297449 s=75 p1=2^3*11^2*173861 p2=2*3*5^2*17*31*2129
168297517 s=76 p1=2^2*3^2*19*246049 p2=2*17*107*46261
168297709 s=77 p1=2^2*3*797*17597 p2=2*5*7*2404253
168297781 s=78 p1=2^2*3*5*7*61*6569 p2=2*19*181*24469
168297889 s=79 p1=2^5*3*11*197*809 p2=2*5*16829789
168297901 s=80 p1=2^2*3*5^2*23*24391 p2=2*61*1379491
168297937 s=81 p1=2^4*3*3506207 p2=2*83*1013843
168298057 s=82 p1=2^3*3^2*659*3547 p2=2*131*642359
168298093 s=83 p1=2^2*3^2*4674947 p2=2*4159*20233
168298213 s=84 p1=2^2*3*14024851 p2=2*7*53*226817
168298297 s=85 p1=2^3*3*7012429 p2=2*7*97*123931
168298309 s=86 p1=2^2*3^2*919*5087 p2=2*5*29*580339
168298357 s=87 p1=2^2*3*14024863 p2=2*41^2*113*443
168298369 s=88 p1=2^7*3*7*17*29*127 p2=2*5*16829837
168298381 s=89 p1=2^2*3^2*5*31*30161 p2=2*7*739*16267
168298393 s=90 p1=2^3*3*2309*3037 p2=2*11*467*16381
168298441 s=91 p1=2^3*3*5*41*79*433 p2=2*13*31*208807
168298477 s=92 p1=2^2*3*457*30689 p2=2*163*516253
168298549 s=93 p1=2^2*3*11*1274989 p2=2*5^2*7*480853
168298649 s=94 p1=2^3*7*463*6491 p2=2*3^2*5^2*13^2*2213
168298717 s=95 p1=2^2*3*29*563*859 p2=2*7*37*324901
168298777 s=96 p1=2^3*3^3*17*45833 p2=2*149*564761
168298813 s=97 p1=2^2*3^2*11*424997 p2=2*31*509*5333
168298849 s=98 p1=2^5*3^2*313*1867 p2=2*5^2*41*53*1549
168299029 s=99 p1=2^2*3^2*4674973 p2=2*5*16829903
168299041 s=100 p1=2^5*3*5*7*13*3853 p2=2*67*1255963
168299189 s=101 p1=2^2*19*23*96281 p2=2*3^2*5*1869991
168299249 s=102 p1=2^4*13*31*43*607 p2=2*3*5^3*7*32057
168299413 s=103 p1=2^2*3*29*483619 p2=2*1409*59723
168299641 s=104 p1=2^3*3^3*5*155833 p2=2*7*12021403
168299669 s=105 p1=2^2*47*895211 p2=2*3*5*7*11*41*1777
168299849 s=106 p1=2^3*1801*11681 p2=2*3*5^2*43*97*269
168299909 s=107 p1=2^2*7^2*858673 p2=2*3^3*5*19*53*619
重点是这些数值，还有下面这些数值：
在168291939 与 168299939之间的素数个数有：424个，其间可能的梅森指数p有 75 个：
168291941 s=1 p1=2^2*5*67*125591 p1有3个*号， p2=2*3*7*13*17*18131
168292001 s=2 p1=2^5*5^3*42073 p1有2个*号， p2=2*3*2297*12211
168292037 s=3 p1=2^2*11*907*4217 p1有3个*号， p2=2*3*28048673
168292097 s=4 p1=2^8*7*93913 p1有2个*号， p2=2*3^2*13*719197
168292277 s=5 p1=2^2*6397*6577 p1有2个*号， p2=2*3^2*7*11*29*53*79
168292301 s=6 p1=2^2*5^2*11*152993 p1有3个*号， p2=2*3*73*223*1723
168292433 s=7 p1=2^4*7*11*136601 p1有3个*号， p2=2*3*28048739
168292661 s=8 p1=2^2*5*461*18253 p1有3个*号， p2=2*3*59*475403
168292781 s=9 p1=2^2*5*59*127*1123 p1有4个*号， p2=2*3^3*7*41*10859
168292793 s=10 p1=2^3*17^2*83*877 p1有3个*号， p2=2*3*23*919*1327
168292913 s=11 p1=2^4*193*54499 p1有2个*号， p2=2*3*53*167*3169
168292997 s=12 p1=2^2*17*2474897 p1有2个*号， p2=2*3^3*3116537
168293201 s=13 p1=2^4*5^2*17*24749 p1有3个*号， p2=2*3*7*11*364271
168293381 s=14 p1=2^2*5*29*290161 p1有3个*号， p2=2*3*28048897
168293441 s=15 p1=2^6*5*7^2*10733 p1有3个*号， p2=2*3*28048907
168293453 s=16 p1=2^2*107*393209 p1有2个*号， p2=2*3*7*719*5573
168293717 s=17 p1=2^2*19*307*7213 p1有3个*号， p2=2*3^2*9349651
168293753 s=18 p1=2^3*11*1912429 p1有2个*号， p2=2*3^3*19*61*2689
168293777 s=19 p1=2^4*7*479*3137 p1有3个*号， p2=2*3*17*1171*1409
168293837 s=20 p1=2^2*97*433747 p1有2个*号， p2=2*3*89*113*2789
168294041 s=21 p1=2^3*5*31*135721 p1有3个*号， p2=2*3^2*7*1335667
168294281 s=22 p1=2^3*5*7*11*101*541 p1有5个*号， p2=2*3*13*71*30389
168294293 s=23 p1=2^2*53*793841 p1有2个*号， p2=2*3^3*7*431*1033
168294317 s=24 p1=2^2*4691*8969 p1有2个*号， p2=2*3*28049053
168294677 s=25 p1=2^2*11*3824879 p1有2个*号， p2=2*3*701*40013
168294941 s=26 p1=2^2*5*11*764977 p1有3个*号， p2=2*3^3*3116573
168294953 s=27 p1=2^3*7*3005267 p1有2个*号， p2=2*3*28049159
168294977 s=28 p1=2^6*433*6073 p1有2个*号， p2=2*3^2*223*41927
168295013 s=29 p1=2^2*1753*24001 p1有2个*号， p2=2*3^2*9349723
168295073 s=30 p1=2^5*11*478111 p1有2个*号， p2=2*3*28049179
168295181 s=31 p1=2^2*5*1511*5569 p1有3个*号， p2=2*3*11*2549927
168295313 s=32 p1=2^4*19^2*29137 p1有2个*号， p2=2*3*11*37*68917
168295397 s=33 p1=2^2*281*149729 p1有2个*号， p2=2*3*571*49123
168295481 s=34 p1=2^3*5*1303*3229 p1有3个*号， p2=2*3^6*115429
168295493 s=35 p1=2^2*101*416573 p1有2个*号， p2=2*3*59*199*2389
168295601 s=36 p1=2^4*5^2*11*23*1663 p1有4个*号， p2=2*3*241*116387
168295637 s=37 p1=2^2*43*978463 p1有2个*号， p2=2*3*7*4007039
168295661 s=38 p1=2^2*5*13*73*8867 p1有4个*号， p2=2*3^2*971*9629
168295781 s=39 p1=2^2*5*83*101383 p1有3个*号， p2=2*3*109*277*929
168295817 s=40 p1=2^3*13*29*41*1361 p1有4个*号， p2=2*3*17*1649959
168295973 s=41 p1=2^2*13*181*17881 p1有3个*号， p2=2*3*7*11*89*4093
168296081 s=42 p1=2^4*5*701*3001 p1有3个*号， p2=2*3*127*220861
168296201 s=43 p1=2^3*5^2*53*15877 p1有3个*号， p2=2*3^2*37*59*4283
168296321 s=44 p1=2^7*5*59*4457 p1有3个*号， p2=2*3*28049387
168296441 s=45 p1=2^3*5*13*323647 p1有3个*号， p2=2*3*28049407
168296477 s=46 p1=2^2*173*243203 p1有2个*号， p2=2*3*7^2*572437
168296501 s=47 p1=2^2*5^3*336593 p1有2个*号， p2=2*3*11*101*25247
168296741 s=48 p1=2^2*5*8414837 p1有2个*号， p2=2*3^2*2281*4099
168296873 s=49 p1=2^3*17*109*11353 p1有3个*号， p2=2*3*179*349*449
168297317 s=50 p1=2^2*11*3824939 p1有2个*号， p2=2*3^3*7*47*9473
168297377 s=51 p1=2^5*13*137*2953 p1有3个*号， p2=2*3*28049563
168297401 s=52 p1=2^3*5^2*307*2741 p1有3个*号， p2=2*3*7*13*19*16223
168297557 s=53 p1=2^2*7^2*29^2*1021 p1有3个*号， p2=2*3*11*13*73*2687
168297593 s=54 p1=2^3*19*727*1523 p1有3个*号， p2=2*3*5099*5501
168297641 s=55 p1=2^3*5*7*647*929 p1有4个*号， p2=2*3^3*3116623
168297797 s=56 p1=2^2*131*509*631 p1有3个*号， p2=2*3*28049633
168297821 s=57 p1=2^2*5*19*211*2099 p1有4个*号， p2=2*3^2*7*11*31*3917
168297881 s=58 p1=2^3*5*103*40849 p1有3个*号， p2=2*3*47*199*2999
168297917 s=59 p1=2^2*101*416579 p1有2个*号， p2=2*3*28049653
168298157 s=60 p1=2^2*13*3236503 p1有2个*号， p2=2*3*7*4007099
168298217 s=61 p1=2^3*43*489239 p1有2个*号， p2=2*3^2*11*849991
168298433 s=62 p1=2^6*821*3203 p1有2个*号， p2=2*3^2*73*263*487
168298457 s=63 p1=2^3*673*31259 p1有2个*号， p2=2*3*2237*12539
168298541 s=64 p1=2^2*5*47*179041 p1有3个*号， p2=2*3^2*19*29*71*239
168298553 s=65 p1=2^3*173*277*439 p1有3个*号， p2=2*3*28049759
168299141 s=66 p1=2^2*5*8414957 p1有2个*号， p2=2*3*11^2*23*10079
168299177 s=67 p1=2^3*67*313991 p1有2个*号， p2=2*3*41*89*7687
168299333 s=68 p1=2^2*1901*22133 p1有2个*号， p2=2*3^2*7*43*31063
168299477 s=69 p1=2^2*1223*34403 p1有2个*号， p2=2*3^3*3116657
168299501 s=70 p1=2^2*5^3*336599 p1有2个*号， p2=2*3*7*4007131
168299561 s=71 p1=2^3*5*11*13*29423 p1有4个*号， p2=2*3*28049927
168299693 s=72 p1=2^2*11*3824993 p1有2个*号， p2=2*3^4*17*23*2657
168299741 s=73 p1=2^2*5*7*23*52267 p1有4个*号， p2=2*3*13*59*36571
168299921 s=74 p1=2^4*5*2103749 p1有2个*号， p2=2*3*7*4007141
168299933 s=75 p1=2^2*17*2474999 p1有2个*号， p2=2*3*11*29*87931
ysr
发表于 2025-5-24 18:05
Private Sub Command1_Click()
Dim x, p
x = Val(Text1)
X1 = Val(Text2)
X2 = x
Do While x <= X1
p = fenjieyinzi(Val(x))
If InStr(Trim(p), "*") = 0 Then
s2 = s2 + 1
p1 = x - 1: p2 = x + 1: p3 = fenjieyinzi0(Val(p1)): p4 = fenjieyinzi0(Val(p2))
j = Split(p3, "*"): j2 = UBound(j): j1 = Split(p4, "*"): j3 = UBound(j1)
If p1 Mod 4 = 0 And p2 Mod 4 <> 0 And j2 >= 2 And j3 >= 2 Then
If p1 Mod 6 <> 0 And p2 Mod 10 <> 0 Then
s = s
Else
s = s + 1
t = t & x & " s=" & s
t = t & " p1=" & p3 & " p2=" & p4 & vbCrLf
End If
Else
s = s
End If
Else
x = x
End If
x = x + 2
Loop
If s > 0 Then
Text3 = "在" & X2 & " 与 " & X1 & "之间的素数个数有：" & s2 & "个，其间可能的梅森指数p有 " & s & " 个：" & vbCrLf & t
Else
Text3 = "wujie"
End If
End Sub
Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
End Sub
Private Function fenjieyinzi(sa As String) As String
Dim x, a, b
x = sa
b = Int(Sqr(Val(x)) / 2)
If x = 3 Or x = 2 Then
a = True
Else
If x Mod 2 = 0 Then
a = False
Else
For i = 3 To 2 * b + 1 Step 2
If x Mod i = 0 Then
a = False
Exit For
Else: a = True
End If
Next
End If
End If
If a = True Then
fenjieyinzi = "这是个素数"
Else
fenjieyinzi = "2*2"
End If
End Function
Private Function fenjieyinzi0(sa As String) As String
Dim r As String
Dim i, c As Long
r = ""
a = sa
For i = 2 To Sqr(sa)
c = 0
Do While a Mod i = 0
c = c + 1
a = a / i
Loop
If c > 0 Then
r = r & i
If c > 1 Then
r = r & "^" & c
End If
If a > 1 Then
r = r & "*"
End If
End If
Next i
If a > 1 Then
r = r & a
End If
fenjieyinzi0 = r
End Function
ysr
发表于 2025-5-24 18:05
Private Sub Command1_Click()
Dim x, p
x = Val(Text1)
X1 = Val(Text2)
X2 = x
Do While x <= X1
p = fenjieyinzi(Val(x))
If InStr(Trim(p), "*") = 0 Then
s2 = s2 + 1
p1 = x - 1: p2 = x + 1: p3 = fenjieyinzi0(Val(p1)): p4 = fenjieyinzi0(Val(p2))
j = Split(p3, "*"): j2 = UBound(j): j1 = Split(p4, "*"): j3 = UBound(j1)
If p1 Mod 4 = 0 And p2 Mod 4 <> 0 And j2 >= 2 And j3 >= 2 Then
If p1 Mod 6 <> 0 And p2 Mod 10 <> 0 Then
s = s + 1
If s Mod 5 = 0 Then
t = t & " " & x & vbCrLf
Else
t = t & " " & x
End If
Else
s = s
End If
Else
s = s
End If
Else
x = x
End If
x = x + 2
Loop
If s > 0 Then
Text3 = "在" & X2 & " 与 " & X1 & "之间的素数个数有：" & s2 & "个，其间可能的梅森指数p有 " & s & " 个：" & vbCrLf & t
Else
Text3 = "wujie"
End If
End Sub
Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
End Sub
Private Function fenjieyinzi0(sa As String) As String
Dim r As String
Dim i, c As Long
r = ""
a = sa
For i = 2 To Sqr(sa)
c = 0
Do While a Mod i = 0
c = c + 1
a = a / i
Loop
If c > 0 Then
r = r & i
If c > 1 Then
r = r & "^" & c
End If
If a > 1 Then
r = r & "*"
End If
End If
Next i
If a > 1 Then
r = r & a
End If
fenjieyinzi0 = r
End Function
Private Function fenjieyinzi(sa As String) As String
Dim x, a, b
x = sa
b = Int(Sqr(Val(x)) / 2)
If x = 3 Or x = 2 Then
a = True
Else
If x Mod 2 = 0 Then
a = False
Else
For i = 3 To 2 * b + 1 Step 2
If x Mod i = 0 Then
a = False
Exit For
Else: a = True
End If
Next
End If
End If
If a = True Then
fenjieyinzi = "这是个素数"
Else
fenjieyinzi = "2*2"
End If
End Function
ysr
发表于 2025-5-24 20:05
梅森数的验证必须用卢卡斯-莱莫测试，一般都是第p-1项的余数为0，所以最高项就是p-1.
我们知道，梅森素数的判定用到卢卡斯莱默法，即递推数列：
S0=4，SN=S(N-1)^2-2,（程序可以这样写：S=4,S=S^2-2）每项MOD梅森数MP，若P-1项中有一项余数为0，则MP为素数，数列的数据增长太快，一般的是用前一项的余数的平方再-2来做为后一项来判断，这个可以证明是成立的。就是通项为S=(S MODMP )^2-2，再判断S MODMP 是否为0.
一般的，最多算P-1项就可以判定了。
ysr
发表于 2025-5-24 20:06
例：M89=618970019642690137449562111，素性测试结果如下：
这是个素数4(1)
14(2)
194(3)
37634(4)
1416317954(5)
2005956546822746114(6)
598028640278675810224740676(7)
480114390397887436345871973(8)
256286478379806120980640370(9)
503856043838036255396725647(10)
511097357768708595775143636(11)
168909432968702305299180947(12)
606396047570974655444193748(13)
384259961875522880452984663(14)
400988785643977730394319793(15)
451946598706049129545781082(16)
519056096255902175211532475(17)
121085530627461043345077875(18)
71186560963388750687096830(19)
36000517785442762303479300(20)
523566428507141573725342798(21)
424152844029608571078391252(22)
451425083283677785701240528(23)
471604984152655775544654653(24)
149504332299367259583502770(25)
2661688372237296008669225(26)
14651690105229857026329789(27)
118366775657027743761992789(28)
78447114542527441733697497(29)
414825479001522844830957808(30)
140234396746501638380162556(31)
524724811145776165191705380(32)
454239684978083396425387798(33)
443190129321733552688414291(34)
193246662398964773806577169(35)
90276720159245463714588945(36)
325532186394213993941115709(37)
184428441183694588040637933(38)
20227257621080411005543513(39)
492178310326013754654519350(40)
98383234722633752804518339(41)
422539297718609229503207527(42)
239699647065516513819077229(43)
451540821309242236737612159(44)
386616582127510358048893037(45)
111015693969297793247714068(46)
526524283201479916042588129(47)
64862389039487459674212268(48)
222734658450663017797297098(49)
527979459006852476995019463(50)
597546382855243971575029724(51)
432108610907467792010713113(52)
267528776084781116062417378(53)
539136831481300028111816217(54)
451247597566784449829767505(55)
437168526145243171726687748(56)
598500912756632689317072800(57)
524692914241987400050525363(58)
332189870719179258780519572(59)
412661427218334854756142421(60)
321992305401224654215082066(61)
435970785565830723987708026(62)
381742226819095467298228805(63)
170103210134157444573479299(64)
529650761375006727395831727(65)
588636842041150882786657416(66)
532115895320758084925029926(67)
501541201809618824302560067(68)
339657887315362077441027847(69)
99498791857820493810407653(70)
267353229805674813483082782(71)
153775828163901691352640258(72)
645734370591155030147282(73)
239072406272077525999142496(74)
386211355975098724888629576(75)
589820547708179745896185533(76)
426471425099610829450724237(77)
14792991384462166970694984(78)
574596879853011245099388238(79)
269783273665984523074966550(80)
98263195276941167273641778(81)
288575740080467405879843347(82)
592120439037291200756916902(83)
248352176262993969312953851(84)
496815502059771466001738628(85)
309566686160249986820679689(86)
618970019642654953077473279(87)
0(88)
8(89)
62(90)
ysr
发表于 2025-5-25 13:51
本帖最后由 ysr 于 2025-5-25 12:43 编辑
Private Sub Command1_Click()
Dim x, p
x = Val(Text1)
X1 = Val(Text2)
X2 = x
Do While x <= X1
p = fenjieyinzi(Val(x))
If InStr(Trim(p), "*") = 0 Then
s2 = s2 + 1
p1 = x - 1: p2 = x + 1: p3 = fenjieyinzi0(Val(p1)): p4 = fenjieyinzi0(Val(p2))
j = Split(p3, "*"): j2 = UBound(j): j1 = Split(p4, "*"): j3 = UBound(j1)
If p1 Mod 4 = 0 And p2 Mod 4 <> 0 And j2 >= 2 And j3 >= 2 Then
If p1 Mod 6 <> 0 And p2 Mod 10 <> 0 Then
s = s
Else
For i = 0 To UBound(j)
Print j(i)
Next
s = s + 1
If s Mod 5 = 0 Then
t = t & " " & x & vbCrLf
Else
t = t & " " & x
End If
End If
Else
s = s
End If
Else
x = x
End If
x = x + 2
Loop
If s > 0 Then
Text3 = "在" & X2 & " 与 " & X1 & "之间的素数个数有：" & s2 & "个，其间可能的梅森指数p有 " & s & " 个：" & vbCrLf & t
Else
Text3 = "wujie"
End If
End Sub
Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
Me.Cls
End Sub
Private Function fenjieyinzi0(sa As String) As String
Dim r As String
Dim i, c As Long
r = ""
a = sa
For i = 2 To Sqr(sa)
c = 0
Do While a Mod i = 0
c = c + 1
a = a / i
Loop
If c > 0 Then
r = r & i
If c > 1 Then
r = r & "^" & c
End If
If a > 1 Then
r = r & "*"
End If
End If
Next i
If a > 1 Then
r = r & a
End If
fenjieyinzi0 = r
End Function
Private Function fenjieyinzi(sa As String) As String
Dim x, a, b
x = sa
b = Int(Sqr(Val(x)) / 2)
If x = 3 Or x = 2 Then
a = True
Else
If x Mod 2 = 0 Then
a = False
Else
For i = 3 To 2 * b + 1 Step 2
If x Mod i = 0 Then
a = False
Exit For
Else: a = True
End If
Next
End If
End If
If a = True Then
fenjieyinzi = "这是个素数"
Else
fenjieyinzi = "2*2"
End If
End Function
ysr
发表于 2025-5-25 20:42
Private Sub Command1_Click()
Dim x, p
x = Val(Text1)
X1 = Val(Text2)
X2 = x
Do While x <= X1
p = fenjieyinzi(Val(x))
If InStr(Trim(p), "*") = 0 Then
s2 = s2 + 1
p1 = x - 1: p2 = x + 1: p3 = fenjieyinzi0(Val(p1)): p4 = fenjieyinzi0(Val(p2))
j = Split(p3, "*"): j2 = UBound(j): j1 = Split(p4, "*"): j3 = UBound(j1)
If p1 Mod 4 = 0 And p2 Mod 4 <> 0 And j2 >= 2 And j3 >= 2 Then
If p1 Mod 6 <> 0 And p2 Mod 10 <> 0 Then
s = s
Else
For i = 0 To 2
Print j(i), j1(i)
Next
s = s + 1
If s Mod 5 = 0 Then
t = t & " " & x & vbCrLf
Else
t = t & " " & x
End If
End If
Else
s = s
End If
Else
x = x
End If
x = x + 2
Loop
If s > 0 Then
Text3 = "在" & X2 & " 与 " & X1 & "之间的素数个数有：" & s2 & "个，其间可能的梅森指数p有 " & s & " 个：" & vbCrLf & t
Else
Text3 = "wujie"
End If
End Sub
Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
Me.Cls
End Sub
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