勾股数新公式

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蔡家雄 发表于 2023-3-19 19:23
若 16^k+13 是素数，

则 2 是素数 16^k+13 的最小原根。

{{1, 2}, {2, 2}, {5, 2}, {16, 2}, {20, 2}, {73, 2}}

P=283时不确定

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蔡家雄 发表于 2023-3-19 19:23
若 16^k+13 是素数，

则 2 是素数 16^k+13 的最小原根。

{{1, 2}, {3, 2}, {4, 2}, {7, 2}, {21, 2}, {57, 2}}

p={196, 426, 502}时，不确定

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蔡家雄 发表于 2023-3-19 20:54
若 (6n+3)^2 -2 是素数，

则 3 是素数 (6n+3)^2 -2 的最小原根。

若 (6n+3)^2 -2 是素数，

则 3 是素数 (6n+3)^2 -2 的最小原根。

{{1,3},{2,3},{3,15},{4,5},{5,3},{10,6},{11,3},{12,5},{15,3},{19,3},{22,3},{29,6},{30,6},{38,3},{39,3},{44,3},{45,3},{46,3},{47,5},{50,3},{51,17},{52,3},{59,3},{64,6},{66,12},{67,3},{71,3},{72,10},{73,3},{74,3},{81,3},{82,6},{85,6},{87,3},{88,3},{93,3},{95,3},{101,6},{102,3},{103,3},{107,3},{110,3},{124,5},{131,3},{134,5},{137,13},{149,3},{157,6},{158,11},{164,3},{165,3},{170,3},{171,3},{172,3},{178,3},{183,3},{185,3},{186,6},{187,3},{190,6},{191,6},{193,3},{199,3},{205,3},{206,3},{208,3},{214,3},{218,6},{226,11},{227,3},{240,3},{243,6},{248,3},{253,6},{257,6},{260,3},{268,3},{269,11},{275,3},{282,17},{283,3},{289,6},{291,3},{297,3},{299,3},{304,3},{306,3},{312,5},{318,13},{320,3},{324,5},{325,3},{327,3},{331,3},{333,3},{338,3},{339,6},{340,3},{345,3},{348,7},{351,3},{355,3},{358,6},{360,3},{368,19},{373,15},{374,3},{379,3},{380,3},{389,3},{403,3},{411,3},{418,3},{421,6},{423,3},{429,3},{431,6},{436,13},{439,6},{444,3},{446,3},{450,3},{452,5},{453,3},{456,3},{478,3},{480,3},{481,3},{487,3},{488,11},{492,5},{495,3},{499,3},{505,3},{506,13},{512,5},{513,3},{515,5},{521,11},{522,6},{523,3},{527,3},{540,3},{542,5},{548,3},{550,5},{569,3},{571,6},{572,3},{575,3},{576,3},{577,3},{579,5},{584,6},{591,6},{592,5},{593,3},{603,3},{611,6},{617,3},{618,3},{620,3},{627,5},{628,3},{634,5},{642,5},{645,6},{646,3},{647,6},{649,5},{654,3},{677,3},{682,3},{684,5},{691,3},{694,3},{695,3},{696,3},{701,6},{703,3},{708,6},{710,6},{711,3},{717,3},{718,6},{730,3},{732,3},{739,3},{746,3},{751,3},{752,3},{753,3},{758,3},{760,3},{761,6},{771,3},{779,3},{786,3},{787,5},{792,7},{801,3},{807,5},{810,3},{815,5},{817,3},{822,3},{827,6},{835,5},{837,3},{838,3},{845,13},{850,3},{852,3},{855,5},{856,6},{863,3},{866,6},{873,3},{879,3},{880,5},{883,3},{884,11},{886,3},{887,5},{898,3},{899,3},{900,5},{901,6},{914,6},{919,3},{920,3},{921,11},{922,3},{929,3},{935,3},{940,3},{943,7},{947,3},{962,3},{969,5},{971,3},{975,5},{977,5},{981,7},{983,6},{989,3},{990,3},{992,5},{996,3}}

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若 (6n+3)^2+8 是素数，

则 3 是素数 (6n+3)^2+8 的最小原根。
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{{1,3},{2,3},{3,3},{5,3},{8,3},{9,3},{13,3},{14,3},{18,3},{19,3},{20,3},{21,3},{22,3},{23,3},{24,3},{25,3},{29,3},{31,3},{35,3},{36,3},{42,3},{46,3},{47,3},{52,3},{53,3},{54,3},{57,3},{58,3},{60,3},{66,3},{69,3},{77,3},{78,3},{79,3},{80,3},{82,3},{91,3},{96,3},{97,3},{104,3},{109,3},{110,3},{111,3},{120,3},{122,3},{123,3},{124,3},{126,3},{128,3},{130,3},{131,3},{134,3},{137,3},{139,3},{142,3},{146,3},{148,3},{150,6},{151,3},{155,3},{156,3},{157,3},{161,3},{162,3},{164,5},{166,3},{167,3},{168,3},{172,3},{173,3},{175,3},{181,3},{195,3},{200,3},{207,3},{208,3},{209,3},{211,6},{219,3},{223,3},{225,5},{231,3},{232,3},{233,3},{240,3},{243,3},{247,3},{252,3},{260,3},{261,3},{264,3},{267,3},{269,3},{278,3},{282,3},{283,3},{291,3},{295,3},{298,3},{300,3},{302,3},{304,6},{307,3},{316,3},{318,3},{319,3},{321,3},{326,3},{327,3},{329,3},{333,3},{341,3},{343,3},{344,3},{348,3},{350,3},{351,3},{355,3},{363,3},{364,3},{365,3},{375,3},{381,3},{383,3},{384,3},{386,3},{388,3},{394,3},{403,3},{404,3},{409,3},{414,3},{415,3},{418,3},{419,3},{426,3},{428,6},{431,3},{432,3},{434,3},{436,3},{437,3},{438,3},{439,3},{447,3},{449,3},{450,3},{451,3},{456,3},{469,3},{472,3},{480,3},{483,3},{487,3},{491,3},{494,3},{497,3},{498,3},{504,3},{506,3},{507,5},{508,3},{516,3},{518,3},{519,3},{533,3},{538,6},{550,3},{555,3},{557,3},{559,3},{569,3},{570,3},{573,3},{575,3},{580,3},{582,3},{583,3},{586,3},{588,3},{597,3},{601,3},{603,3},{605,3},{606,3},{610,3},{613,3},{623,3},{627,3},{630,3},{636,3},{637,3},{639,3},{640,5},{641,3},{643,3},{647,3},{651,3},{654,3},{659,3},{669,3},{670,3},{673,3},{678,3},{682,3},{683,3},{684,3},{685,3},{693,3},{694,3},{698,3},{703,11},{704,3},{706,3},{709,3},{712,3},{715,3},{717,3},{723,3},{724,3},{726,3},{735,5},{737,3},{740,3},{744,3},{745,3},{746,3},{753,3},{755,3},{758,3},{760,3},{766,6},{772,3},{777,3},{780,3},{788,3},{792,3},{793,3},{797,3},{800,3},{801,6},{806,3},{810,3},{812,3},{817,3},{819,3},{823,3},{834,3},{846,3},{854,3},{855,3},{857,3},{860,3},{861,3},{865,3},{869,3},{870,3},{877,3},{878,3},{879,3},{887,3},{893,3},{896,3},{898,3},{905,3},{909,3},{910,3},{911,3},{913,3},{914,3},{924,3},{927,3},{940,3},{943,3},{944,3},{946,3},{954,3},{956,3},{964,3},{965,3},{967,3},{971,3},{975,3},{982,3},{984,3},{988,3},{990,3}}

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蔡家雄 发表于 2023-3-19 18:44
最小原根问题

若 (2n+1)^2+4 是素数，

{{1,2},{2,2},{3,2},{6,2},{7,6},{8,2},{13,6},{16,5},{17,2},{18,2},{22,2},{23,2},{28,2},{32,2},{33,2},{36,2},{42,2},{43,2},{47,2},{48,3},{51,2},{57,2},{58,6},{62,2},{67,2},{68,2},{73,2},{77,2},{81,2},{83,2},{88,5},{91,2},{96,2},{101,2},{103,2},{107,2},{108,2},{116,2},{117,2},{121,15},{122,2},{126,2},{127,2},{132,2},{133,5},{137,2},{138,2},{143,2},{146,2},{151,2},{153,2},{156,2},{158,2},{173,2},{178,2},{186,2},{187,2},{192,2},{201,2},{203,2},{211,5},{212,2},{213,2},{217,2},{223,5},{226,2},{227,2},{231,2},{237,2},{238,2},{241,2},{243,2},{247,2},{251,2},{253,2},{266,2},{273,2},{286,2},{288,2},{296,2},{302,2},{303,2},{306,2},{307,6},{311,2},{331,5},{332,2},{333,2},{338,2},{342,2},{351,2},{353,2},{356,2},{358,6},{371,2},{372,2},{376,2},{377,2},{381,2},{383,2},{392,2},{393,2},{397,2},{402,2},{406,2},{411,2},{413,2},{418,2},{422,3},{423,2},{426,2},{441,2},{448,6},{451,2},{452,3},{467,2},{472,2},{476,2},{481,2},{483,2},{486,2},{491,2},{496,2},{498,2},{513,3},{517,10},{527,3},{528,2},{536,3},{537,2},{541,2},{543,2},{552,2},{558,2},{561,2},{572,2},{578,2},{587,2},{588,2},{591,2},{592,2},{597,2},{598,2},{601,2},{617,2},{618,2},{623,2},{627,3},{628,5},{631,2},{637,2},{642,2},{656,2},{657,2},{662,2},{668,2},{672,2},{673,2},{676,5},{681,2},{682,2},{683,3},{688,2},{691,5},{696,2},{697,2},{702,2},{706,2},{707,2},{711,3},{721,2},{723,2},{728,2},{733,2},{737,2},{748,6},{753,2},{758,2},{761,2},{762,2},{763,5},{766,2},{771,2},{792,2},{796,2},{797,2},{806,2},{813,2},{816,3},{818,2},{821,2},{822,2},{823,2},{836,2},{847,2},{852,2},{861,2},{876,2},{877,2},{878,2},{881,2},{886,2},{892,2},{902,2},{926,2},{928,14},{932,3},{941,2},{942,3},{948,2},{952,2},{961,2},{962,2},{977,2},{978,3},{993,2}}

蔡家雄

完全循环节问题

若 16^k+3 是素数，

则 10 是素数 16^k+3 的原根，

简记为  \(g(16^k+3)=10\) .

蔡家雄

完全循环节问题

若 16^k+7 是素数，

则 10 是素数 16^k+7 的原根，

简记为  \(g(16^k+7)=10\) .

蔡家雄

完全循环节问题

若 16^k+13 是素数，

则 10 是素数 16^k+13 的原根，

简记为  \(g(16^k+13)=10\) .

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蔡家雄 发表于 2023-3-19 21:44
完全循环节问题

若 16^k+3 是素数，

{{1, 10}, {3, 10}, {4, 10}, {7, 10}, {21, 10}, {57, 10}}

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蔡家雄 发表于 2023-3-19 21:46
完全循环节问题

若 16^k+7 是素数，

{{1, 10}, {2, 10}, {4, 10}, {5, 10}, {7, 10}, {11, 10}, {22, 10}, {40, 10}, {51, 10}}