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蔡家雄

克莱姆猜想不可能被推翻，否则，暗示着素数定理不成立。

蔡家雄

我的这个猜想几乎与素数定理等价，

设1<N<素数p<N^2, 至少存在一个素数p,

使    N !+N< 素数(N !+p)< N !+N^2 ，

当 N 较大时，好像是大约有 (N/ lnN) 个素数p，使之成立。

蔡家雄

我的这个猜想几乎与素数定理等价，

设1<N<素数p<N^2, 至少存在一个素数p,

使    N !+N< 素数(N !+p)< N !+N^2 ，

当 N 较大时，大约有 (N/ lnN) 个素数p，使之成立。

例：36 !+36< 素数(36 !+p)< 36 !+36^2 ，

大约有 (36/ ln36)=10 个素数p，使之成立。

蔡家雄

我的这个猜想几乎与素数定理等价，

设1<N<素数p<N^2, 至少存在一个素数p,

使    N !+N< 素数(N !+p)< N !+N^2 ，

当 N 较大时，大约有 (N/ lnN) 个素数p，使之成立。

例：100 !+100< 素数(100 !+p)< 100 !+100^2 ，

大约有 (100/ ln100)=21 个素数p，使之成立。

蔡家雄

素数定理：π(N)=N/ lnN，是也。

ysr

/67184/323861151744/94848/319378698496/129808/311524724736/141056/308478046464/156864/303768527104/205200/286267801600/220400/279798681600/231040/274995360000/280896/249472278784/290928/243735740416/304912/235403513856/343824/210159898624/395200/172191801600/5219/641774027664/10205/641697123600/17900/641480855625/28101/641011599424/28860/640968366025/31941/640781038144/34075/640640160000/44268/639841609801/56925/638560810000/60000/638201265625/65960/637450544025/70928/636770484441/76125/636006250000/88740/633926478025/93925/632979360000/98875/632025000000/104052/630974446921/104805/630817177600/122525/626788890000/127680/625499083225/132600/624218505625/150220/619235217225/163995/614906905600/166085/614217038400/169100/613206455625/181475/608868090000/187293/606722597776/191400/605167305625/197200/602913425625/207075/598921210000/209467/597924841536/214500/595791015625/219300/593708775625/224315/591484046400/225044/591156463689/241443/583506543376/251875/578360250000/254800/576878225625/256824/575842698649/278396/564296932809/281285/562680014400/281996/562279521609/286875/559504000000/291525/556814440000/296380/553960161225/298680/552591523225/308125/546860250000/312936/543872325529/313635/543434352400/317520/540982315225/323000/537472265625/334565/529867526400/337364/527986797129/339300/526676775625/348517/520337166336/351973/517916272896/367965/506403024400/372387/503129187856/377000/499672265625/381597/496184995216/392700/487587975625/397900/483476855625/401563/480548422656/402220/480020337225/406725/476376040000/415484/469174311369/417600/467411505625/422045/463679283600/426275/460090890000/431325/455760010000/433920/453514699225/452980/436610385225/454740/435012798025/457275/432700840000/466235/424426190400/472472/418571474841/480675/410752810000/484840/406731440025/488800/402875825625/494875/396900000000/502860/388933086025/503451/388338356224/507500/384245015625/515355/376210489600/525000/366176265625/527325/363729610000/528931/362033262864/531811/358978325904/539400/350848905625/548709/340719698944/552500/336545015625/556100/332554055625/559845/328374841600/560388/327766555081/7995/241729555600/17875/241473960000/20915/241356038400/25236/241156619929/28900/240958265625/36667/240449006736/38760/240291138025/46515/239629830400/46725/239610250000/54468/238826712601/72197/236581068816/75205/236137683600/83096/234888530409/92204/233291898009/92820/233177923225/100045/231784473600/100659/231661241344/103635/231053262400/109701/229759166224/113275/228962250000/117480/227991925225/120432/227289609001/121040/227142794025/128773/225210990096/137683/222836867136/138285/222670734400/145340/220669760025/154752/217845294121/165189/214506069904/165581/214376408064/172500/212037225625/181720/208771317225/181916/208700044569/189125/206025210000/192507/204734530576/196480/203189085225/205500/199563225625/208260/198421248025/208828/198184342041/215475/195364000000/224315/191476256400/231400/188247515625/234080/187000029225/242724/182878535449/249645/179470849600/256320/176093533225/256500/176001225625/263109/172567129744/264880/171632061225/271405/168132801600/278036/164489458329/280540/163090784025/288600/158503515625/294533/155043787536/295035/154747824400/301392/150956337961/308652/146527418521/309140/146225936025/311500/144761225625/314835/142672398400/317645/140895129600/322363/137875571856/325125/136087210000/330616/132486536169/330924/132282781849/331080/132179509225/343629/123712585984

ysr

/8415/173472250000/9308/173456423361/11900/173401452225/17719/173229099264/29601/172666843024/31200/172569622225/39585/171976090000/48841/171157618944/51415/170899560000/51927/170846648896/55384/170475674769/57188/170272594881/60639/169865973904/63713/169483715856/68952/168788683921/72016/168356757969/75447/167850812416/87932/165811025601/94367/164637931536/99528/163637239441/102544/163027790289/107679/161948295184/111540/161101890625/114036/160538852929/119625/159232921600/122960/158423900625/130975/156388611600/132496/155987872209/140447/153817702416/143724/152886474049/149175/151289881600/151593/150562624576/160225/147871011600/165584/146125001169/167960/145332500625/168777/145057386496/176436/142413400129/184023/139678597696/185460/139147650625/187144/138520185489/188575/137982531600/196040/135111380625/203425/132161331600/204204/131843788609/206460/130917330625/206908/130732141761/211497/128812081216/217152/126388071121/221663/124408576656/224289/123237506704/237783/117002307136/240329/115785033984/243168/114412386001/244644/113692375489/247457/112308095376/249951/111067559824/254176/108937623249/256632/107683078801/257335/107321760000/259369/106270784064/263900/103899852225/273000/99014062225/274209/98352486544/280488/94869544081/287300/91001772225/289172/89922616641/293335/87497640000

Treenewbee

蔡家雄 发表于 2023-2-10 20:55
我的这个猜想几乎与素数定理等价，

设1

n=100
n/ln(n)=21.71
Primes of 100!+p: 30
[229, 439, 547, 613, 1103, 1553, 1657, 2741, 2851, 3229, 3331, 3547, 3607, 3907, 4019, 4271, 4513, 4523, 4759, 5503, 5867, 6551, 7001, 7109, 7309, 8123, 8737, 8971, 9371, 9817]

ysr

s = "/67184/323861151744/94848/319378698496/129808/311524724736/141056/308478046464/156864/303768527104/205200/286267801600/220400/279798681600/231040/274995360000/280896/249472278784/290928/243735740416/304912/235403513856/343824/210159898624/395200/172191801600/5219/641774027664/10205/641697123600/17900/641480855625/28101/641011599424/28860/640968366025/31941/640781038144/34075/640640160000/44268/639841609801/56925/638560810000/60000/638201265625/65960/637450544025/70928/636770484441/76125/636006250000/88740/633926478025/93925/632979360000/98875“"
s = s & "/632025000000/104052/630974446921/104805/630817177600/122525/626788890000/127680/625499083225/132600/624218505625/150220/619235217225/163995/614906905600/166085/614217038400/169100/613206455625/181475/608868090000/187293/606722597776/191400/605167305625/197200/602913425625/207075/598921210000/209467/597924841536/214500/595791015625/219300/593708775625/224315/591484046400/225044/591156463689/241443/583506543376/251875"
s = s & "/578360250000/254800/576878225625/256824/575842698649/278396/564296932809/281285/562680014400/281996/562279521609/286875/559504000000/291525/556814440000/296380/553960161225/298680/552591523225/308125/546860250000/312936/543872325529/313635/543434352400/317520/540982315225/323000/537472265625/334565/529867526400/337364/527986797129/339300/526676775625/348517/520337166336/351973/517916272896/367965/506403024400/372387/503129187856/377000/499672265625/381597/496184995216/392700/487587975625/397900/483476855625/401563/480548422656"
s = s & "/402220/480020337225/406725/476376040000/415484/469174311369/417600/467411505625/422045/463679283600/426275/460090890000/431325/455760010000/433920/453514699225/452980/436610385225/454740/435012798025/457275/432700840000/466235/424426190400/472472/418571474841/480675/410752810000/484840/406731440025/488800/402875825625/494875/396900000000/502860/388933086025/503451/388338356224/507500/384245015625/515355/376210489600/525000/366176265625/527325/363729610000/528931/362033262864/531811/358978325904/539400/350848905625/548709/340719698944/552500/336545015625/556100/332554055625/559845/328374841600/560388/327766555081"
s = s & "/7995/241729555600/17875/241473960000/20915/241356038400/25236/241156619929/28900/240958265625/36667/240449006736/38760/240291138025/46515/239629830400/46725/239610250000/54468/238826712601/72197/236581068816/75205/236137683600/83096/234888530409/92204/233291898009/92820/233177923225/100045/231784473600/100659/231661241344/103635/231053262400/109701/229759166224/113275/228962250000/117480/227991925225/120432/227289609001/121040/227142794025/128773/225210990096/137683/222836867136/138285/222670734400/145340/220669760025/154752/217845294121/165189/214506069904/165581/214376408064/172500/212037225625/181720"
s = s & "/208771317225/181916/208700044569/189125/206025210000/192507/204734530576/196480/203189085225/205500/199563225625/208260/198421248025/208828/198184342041/215475/195364000000/224315/191476256400/231400/188247515625/234080/187000029225/242724/182878535449/249645/179470849600/256320/176093533225/256500/176001225625/263109/172567129744/264880/171632061225/271405/168132801600/278036/164489458329/280540/163090784025/288600/158503515625/294533/155043787536/295035/154747824400/301392/150956337961/308652/146527418521/309140/146225936025/311500/144761225625/314835/142672398400/317645/140895129600/322363/137875571856/325125/136087210000/330616/132486536169/330924/132282781849/331080/132179509225/343629/123712585984"

s4 = Split(s, "/")
j = UBound(s4)

ysr

a = Val(ak(k))
            B = Val(bk(i))
            c = Val(cr(i1))
            d = Val(a ^ 2 + B ^ 2)
            e = Val(B ^ 2 + c ^ 2)
            g = Val(a ^ 2 + B ^ 2 + c ^ 2)
            f = Val(a ^ 2 + c ^ 2)