《数论小火花》

被遗弃的草根

在我证明并发表的数学文章中，就有2012年11月发表在数学杂志"Advances in Theoretical and Applieed Mathematics"第4期上的哥德巴赫猜想证明，到目前都还没有得到数学界的普遍认可，但也未见有人否定。

关于张益唐先生对孪生素数猜想的预想证明，在他向“Annals of Mathematics"投稿之前，我对该猜想及以素数数目和间隔不同而命名的猜想的证明就已经发表在2013年1月数学杂志"Advances in Theoretical and Applieed Mathematics"第1期上了，到目前都还没有得到数学界的普遍认可，但也未见有人否定。

小草

被遗弃的草根 发表于 2026-5-9 00:38
在我证明并发表的数学文章中，就有2012年11月发表在数学杂志"Advances in Theoretical and Applieed Mathem ...

是金子总会发光，蒙上灰尘也仍然发光。

小草

T(2^3)=2=2^1
T(2^5)=5>2^2=4
T(2^7)=10>2^3=8
T(2^8)=17>2^4=16
T(2^10)=36>2^5=32
T(2^12)=107>2^6=64
T(2^13)=177>2^7=128
T(2^14)=290>2^8=256
T(2^16)=860>2^9=512
T(2^17)=1526>2^10=1024
T(2^18)=2679>2^11=2048
T(2^19)=4750>2^12=4096
T(2^20)=8535>2^13=8192
T(2^22)=27995>2^14=16384
T(2^23)=50638>2^15=32768
T(2^24)=92246>2^16=65536
T(2^25)=168617>2^17=131072
T(2^26)=309561>2^18=262144
T(2^27)=571313>2^19=524288
T(2^28)=1056281>2^20=1048576
T(2^30)=3650557>2^21=2097152
T(2^31)=6810670>2^22=4194304
T(2^32)=12739574>2^23=8388608
T(2^33)=23878645>2^24=16777216
T(2^34)=44849427>2^25=33554432
T(2^35)=84384508>2^26=67108864
T(2^36)=159082253>2^27=134217728
T(2^37)=300424743>2^28=268435456
T(2^38)=568237005>2^29=536870912
T(2^39)=1076431099>2^30=1073741824
T(2^41)=3879202049>2^31=2147483648
T(2^42)=7378928530>2^32=4294967296
T(2^43)=14053179903>2^33=8589934592
T(2^44)=26795709320>2^34=17179869184
T(2^45)=51149458583>2^35=34359738368
T(2^46)=97741674629>2^36=68719476736
T(2^47)=186965900951>2^37=137438953472
T(2^48)=357988002871>2^38=274877906944
T(2^49)=686087457349>2^39=549755813888
T(2^50)=1316068371494>2^40=1099511627776
T(2^51)=2526674510802>2^41=2199023255552
T(2^52)=4854867527890>2^42=4398046511104
T(2^53)=9335730886226>2^43=8796093022208
T(2^54)=17965892577331>2^44=17592186044416
T(2^56)=66678992679955>2^45=35184372088832
T(2^57)=128589588118191>2^46=70368744177664
T(2^58)=248145307510177>2^47=140737488355328
T(2^59)=479159158312507>2^48=281474976710656
T(2^60)=925800651712810>2^49=562949953421312
T(2^61)=1789823239135382>2^50=1125899906842624

小草

小草 发表于 2026-5-9 02:29
是金子总会发光，蒙上灰尘也仍然发光。

要被别人认可，也许比自己证明命题更难，许多大数学家也曾遭受过同样的磨难。

小草

10^n内素数个数
主项a_k^(k+1)
余项π(10^(k+1))-a_k^(k+1)=(b_k+1)^(k+1)


π(10^1)=4
π(10^2)=25=4^2+3^2=5^2
π(10^3)=168≈5^3+3.50340^3≈5.51785^3
π(10^4)=1229≈5.51785^4+4.16871≈5.92090^4
π(10^5)=9592≈5.92090^5+4.70889^5≈6.25723^5
π(10^6)=78498≈6.25723^6+5.14175^6≈6.54349^6
π(10^7)=664579≈6.54349^7+5.49320^7≈6.78879^7
π(10^8)=5761455≈6.78879^8+5.78234^8≈6.99949^8
π(10^9)=50847534≈6.99949^9+6.02873^9≈7.18211^9
π(10^10)=455052511≈7.18211^10+6.24248^10≈7.34186^10
π(10^11)=4118054813≈7.34186^11+6.43023^11≈7.48278^11
π(10^12)=37607912018≈7.48278^12+6.59691^12≈7.60805^12
π(10^13)=346065536839≈7.60805^13+6.74615^13≈7.72018^13
π(10^14)=3204941750802≈7.72018^14+6.88080^14≈7.82119^14
π(10^15)=29844570422669≈7.82119^15+7.00300^15≈7.91269^15
π(10^16)=279238341033925≈7.91269^16+7.11456^16≈7.99601^16
π(10^17)=2623557157654233≈7.99601^17+7.21686^17≈8.07223^17
π(10^18)=24739954287740860≈8.07223^18+7.31111^18≈8.14225^18
π(10^19)=234057667276344607≈8.14225^19+7.39826^19
≈8.20682^19
π(10^20)=2220819602560918840≈8.20682^20+7.47915^20
≈8.26658^20
π(10^21)=21127269486018731928≈8.26658^21+7.55444^21
≈8.32206^21
π(10^22)=201467286689315906290≈8.32206^22+7.62476^22
≈8.37372^22
π(10^23)=1925320391606803968923≈8.37372^23+7.69061^23
≈8.42196^23
π(10^24)=18435599767349200867866≈8.42196^24+7.75241^24
≈8.46712^24
π(10^25)=176846309399143769411680≈8.46712^25+7.81053^25
≈8.50950^25
π(10^26)=1699246750872437141327603≈8.50950^26+7.86530^26
≈8.54935^26
π(10^27)=16352460426841680446427399≈8.54935^27+7.91706^27
≈8.58690^27
π(10^28)=157589269275973410412739598≈8.58690^28+7.96607^28
≈8.62236^28
π(10^29)=1520698109714272166094258063≈8.62236^29+8.01246^29
≈8.65589^29

小草

方程z^n=x^n+y^n        （1）
(1)=z^n-x^n-y^n=0       (2)
计算方程(2)
令n=1
3-2-1=0
4-3-1=0
5-4-1=0
6-5-1=0
7-6-1=0
8-7-1=0
9-8-1=0
10-9-1=0

令n=2
取最小非负余项
3^2-2^2-1^2=4
4^2-3^2-2^2=3
【2^2+5=3^2】
5^2-4^2-3^2=0
6^2-5^2-3^2=2
7^2-6^2-3^2=4
8^2-7^2-3^2=6
9^2-8^2-4^2=1
10^2-9^2-4^2=3
11^2-10^2-4^2=5
12^2-11^2-4^2=7
【4^2+9=5^2】
13^2-12^2-5^2=0

晋源泉

小草 发表于 2026-5-12 07:23
方程z^n=x^n+y^n        （1）
(1)=z^n-x^n-y^n=0       (2)
计算方程(2)

四色猜想成立的终极证明：地图4CC成立的终极证明2024
http://www.mathchina.com/bbs/for ... &fromuid=124943
(出处: 数学中国)

小草

晋源泉 发表于 2026-5-11 23:30
四色猜想成立的终极证明：地图4CC成立的终极证明2024
http://www.mathchina.com/bbs/forum.php?mod=view ...

谢谢你的参与！你的作品值得一读，慢慢品味。

小草

T(10^1)=2
(ln10)^2=5.30190
10/5.30190=1.88612
1.88612*1.32032=2.49028
2/2.49028=0.80312

T(10^2)=8
(ln10^2)^2=21.20759
10^2/21.20759=4.71529
4.71529*1.32032=6.22569
8/6.22569=1.28500

T(10^3)=35
(ln10^3)^2=47.71708
10^3/47.71708=20.95686
20.95686*1.32032=27.66976
35/27.66976=1.26492

T(10^4)=205
(ln10^4)^2=84.83037
10^4/84.83037=117.88231
117.88231*1.32032=155.64237
205/155.64237=1.31712

T(10^5)=1224
(ln10^5)^2=132.54745
10^5/132.54745=754.44680
754.44680*1.32032=996.11120
1224/996.11120=1.22878

T(10^6)=8169
(ln10^6)^2=190.86833
10^6/190.86833=5239.21386
5239.21386*1.32032=6917.43884
8169/6917.43884=1.18093

T(10^7)=58980
(ln10^7)^2=259.79301
10^7/259.79301=38492.18268
38492.18268*1.32032=50821.99864
58980/50821.99864=1.16052

T(10^8)=440312
(ln10^8)^2=339.32148
10^8/339.32148=294705.77577
294705.77577*1.32032=389105.92986
440312/389105.92986=1.13160

T(10^9)=3424506
(ln10^9)^2=429.45375
10^9/429.45375=2328539.45274
2328539.45274*1.32032=3074417.21024
3424506/3074417.21024=1.11387

T(10^10)=27412679
(ln10^10)^2=530.18981
10^10/530.18981=18861169.73844
18861169.73844*1.32032=24902779.62906
27412679/24902779.62906=1.10079

T(10^11)=224376048
(ln10^11)^2=641.52967
10^11/641.52967=155877435.87915
155877435.87915*1.32032=205808096.13996
224376048/205808096.13996=1.09022

T(10^12)=1870585220
(ln10^12)^2=763.47333
10^12/763.47333=1309803447.88206
1309803447.88206*1.32032=1729359688.30764
1870585220/1729359688.30764=1.08166

T(10^13)=15834664872
(ln10^13)^2=896.02078
10^13/896.02078=11160455452.83001
11160455452.83001*1.32032=14735372543.48052
15834664872/14735372543.48052=1.07460

T(10^14)=135780321665
(ln10^14)^2=1039.17203
10^14/1039.17203=96230457626.92439
96230457626.92439*1.32032=127054997813.98081
135780321665/127054997813.98081=1.06867

T(10^15)=1177209242304
(ln10^15)^2=1192.92707
10^15/1192.92707=838274212353.98741
838274212353.98741*1.32032=1106790208055.21666
1177209242304/1106790208055.21666=1.06362

T(10^16)=10304195696798
(ln10^16)^2=1,357.28592
10^16/1,357.28592=7367644394336.60374
7367644394336.60374*1.32032=9727648246730.50465
10304195696798/9727648246730.50465=1.05927

T(10^17)=90948889353159
(ln10^17)^2=1532.24855
10^17/1532.24855=65263563147114.74193
65263563147114.74193*1.32032=86168787694398.53607
90948889353159/86168787694398.53607=1.05547

T(10^18)=808675888577435
(ln10^18)^2=1717.81499
10^18/1717.81499=582134866572563.78931
582134866572563.78931*1.32032=768604307033087.42230
808675888577435/768604307033087.42230=1.05214

小草

T(18)=4
(ln18)^2=8.35425
18/8.35425=2.15459
2.15459*1.32032=2.84474
4/2.84474=1.40610
4/3=1.33333

T(50)=6
(ln50)^2=15.30392
50/15.30392=3.26714
3.26714*1.32032=4.31367
6/4.31367=1.39093
6/8=0.75

T(242)=17
(ln242)^2=30.12844
242/30.12844=8.03228
8.03228*1.32032=10.60518
17/10=1.7
17/19=0.89474

T(578)=26
(ln578)^2=40.44418
578/40.44418=14.29130
14.29130*1.32032=18.86909
26/18.86909=1.37791
26/36=0.72222

T(1682)=53
(ln1682)^2=55.17130
1682/55.17130=30.48687
30.48687*1.32032=40.25242
53/40.25242=1.31669
53/65=0.81538

T(3362)=89
(ln3362)^2=65.93913
3362/65.93913=50.98642
50.98642*1.32032=67.31839
89/67.31839=1.32208
89/106=0.83962

T(6962)=162
(ln6962)^2=78.29103
6962/78.29103=88.92462
88.92462*1.32032=117.40895
162/117.40895=1.37979
162/165=0.98182

T(10082)=208
(ln10082)^2=84.98087
10082/84.98087=118.63847
118.63847*1.32032=156.64074
208/156.64074=1.32788
208/236=0.88135

T(20402)=346
(ln20402)^2=98.47363
20402/98.47363=207.18237
207.18237*1.32032=273.54703
346/273.54703=1.26486
346/337=1.02671

T(22898)=387
(ln22898)^2=100.77760
22898/100.77760=227.21319
227.21319*1.32032=299.99412
387/299.99412=1.29003
387/444=0.87162

T(37538)=564
(ln37538)^2=110.94638
37538/110.94638=338.34362
338.34362*1.32032=446.72185
564/446.72185=1.26253
564/581=0.97074

T(44402)=641
(ln44402)^2=114.51225
44402/114.51225=387.74890
387.74890*1.32032=511.95263
641/511.95263=1.25207
641/730=0.87808

T(64082)=845
(ln64082)^2=122.49883
64082/122.49883=523.12336
523.12336*1.32032=690.69023
845/690.69023=1.22341
845/909=0.92959

T(72962)=942
(ln72962)^2=125.38835
72962/125.38835=581.88819
581.88819*1.32032=768.27862
942/768.27862=1.22612
942/1100=0.85636

T(77618)=985
(ln77618)^2=126.77757
77618/126.77757=612.23764
612.23764*1.32032=808.34960
985/808.34960=1.21853
985/1297=0.75944

T(103058)=1252
(ln103058)^2=133.24194
103058/133.24194=773.46517
773.46517*1.32032=1021.22153
1252/1021.22153=1.22598
1252/1524=0.82152

T(114242)=1362
(ln114242)^2=135.63105
114242/135.63105=842.29975
842.29975*1.32032=1112.10521
1362/1112.10521=1.22470
1362/1763=0.77255

T(144722)=1649
(ln144722)^2=141.19547
144722/141.19547=1024.97623
1024.97623*1.32032=1353.29662
1649/1353.29662=1.21851
1649/2032=0.81152

T(157922)=1784
(ln157922)^2=143.27747
157922/143.27747=1102.21098
1102.21098*1.32032=1455.27120
1784/1455.27120=1.22589
1784/2313=0.77129

T(193442)=2105
(ln193442)^2=148.17543
193442/148.17543=1305.49309
1305.49309*1.32032=1723.66864
2105/1723.66864=1.22123
2105/2624=0.80221

T(240818)=2508
(ln240818)^2=153.55663
240818/153.55663=1568.26833
1568.26833*1.32032=2070.61604
2508/2070.61604=1.21123
2508/2971=0.84416

T(351122)=3429
(ln351122)^2=163.04452
351122/163.04452=2153.53450
2153.53450*1.32032=2843.35467
3429/2843.35467=1.20597
3429/3390=1.01150

T(371522)=3585
(ln371522)^2=164.48995
371522/164.48995=2258.63039
2258.63039*1.32032=2,982.11488
3585/2,982.11488=1.20217
3585/3821=0.93824

T(425042)=4003
(ln425042)^2=167.96013
425042/167.96013=2530.61247
2530.61247*1.32032=3341.21826
4003/3341.21826=1.19807
4003/4282=0.93484

T(542882)=4898
(ln542882)^2=174.36271
542882/174.36271=3113.52123
3113.52123*1.32032=4110.84435
4898/4110.84435=1.19148
4898/4803=1.01978

T(647522)=5688
(ln647522)^2=179.04870
647522/179.04870=3616.45742
3,616.45742*1.32032=4774.88106
5688/4774.88106=1.19123
5688/5372=1.05882

T(717602)=
(ln717602)^2=181.80937
717602/181.80937=3947.00229
3947.00229*1.32032=5211.30606
6189/5,211.30606=1.18761
6189/5971=1.03651

T(761378)=6483
(ln761378)^2=183.40974
761378/183.40974=4151.24082
4151.24082*1.32032=5480.96628
6483/5480.96628=1.18282
6483/6588=0.98406

T(821762)=6906
(ln821762)^2=185.48277
821762/185.48277=4430.39534
4430.39534*1.32032=5,849.53958
6906/5,849.53958=1.18061
6906/7229=0.95532

T(868562)=7242
(ln868562)^2=186.99453
868562/186.99453=4644.85245
4644.85245*1.32032=6132.69159
7242/6132.69159=1.18088
7242/7888=0.91810