设 k 为正整数,
若 30k+1 和 65536*(30k+1)+1 都是素数,
则 10 是素数 65536*(30k+1)+1 的原根。
10000内的503个数均符合条件:
{14,18,19,20,27,33,49,51,54,74,76,89,118,135,152,184,210,219,252,284,286,294,308,313,314,324,363,390,391,413,448,467,503,509,515,564,597,599,635,646,656,660,670,685,700,704,762,767,777,779,781,802,819,821,828,844,852,866,907,912,935,936,987,1041,1073,1078,1106,1139,1175,1183,1231,1244,1262,1279,1287,1306,1315,1341,1349,1372,1376,1378,1383,1398,1470,1528,1546,1568,1572,1647,1670,1686,1700,1701,1705,1736,1766,1776,1780,1787,1805,1887,1897,1909,1911,1944,1948,1976,1978,2043,2086,2099,2113,2120,2130,2139,2238,2260,2277,2284,2296,2322,2350,2365,2398,2401,2407,2414,2445,2452,2484,2533,2548,2555,2581,2583,2585,2641,2673,2687,2692,2706,2711,2769,2788,2793,2802,2804,2821,2827,2847,2854,2861,2867,2883,2904,2923,2924,2956,2960,3017,3021,3036,3057,3065,3075,3089,3092,3129,3155,3199,3231,3257,3275,3322,3350,3360,3372,3374,3378,3400,3408,3429,3455,3476,3483,3485,3497,3525,3542,3547,3554,3569,3607,3633,3672,3694,3724,3771,3779,3859,3882,3924,3961,3989,4024,4029,4053,4071,4090,4092,4120,4121,4185,4198,4209,4220,4253,4300,4304,4321,4328,4339,4367,4370,4375,4381,4389,4421,4445,4461,4472,4513,4526,4562,4634,4660,4673,4674,4676,4692,4702,4706,4716,4717,4720,4737,4741,4750,4766,4793,4802,4808,4815,4816,4825,4849,4856,4874,4927,4934,4949,4972,4991,5003,5030,5033,5089,5137,5156,5166,5173,5182,5184,5226,5236,5252,5259,5312,5327,5329,5331,5340,5362,5382,5387,5459,5497,5511,5518,5530,5569,5574,5578,5599,5605,5621,5630,5661,5663,5696,5718,5719,5739,5781,5803,5808,5884,5885,5927,5952,5956,5961,6012,6017,6050,6122,6185,6199,6207,6215,6220,6262,6276,6277,6297,6389,6397,6409,6421,6440,6508,6523,6533,6561,6578,6599,6619,6628,6650,6671,6689,6704,6722,6746,6753,6754,6782,6794,6799,6817,6831,6839,6918,6922,6937,6974,7012,7058,7072,7145,7146,7159,7173,7195,7202,7203,7214,7222,7247,7252,7256,7287,7292,7369,7380,7398,7431,7443,7467,7468,7475,7496,7520,7525,7529,7541,7567,7571,7606,7615,7639,7678,7681,7692,7711,7716,7753,7756,7769,7797,7818,7819,7826,7905,7910,7919,7930,7942,7987,8019,8062,8070,8110,8126,8134,8189,8213,8217,8222,8231,8281,8369,8374,8383,8405,8413,8444,8497,8528,8559,8566,8574,8580,8589,8607,8624,8633,8640,8644,8651,8698,8735,8741,8754,8770,8784,8801,8820,8833,8861,8880,8894,8899,8920,8939,8959,8995,9042,9067,9092,9106,9120,9183,9188,9196,9258,9287,9333,9345,9347,9386,9392,9413,9422,9433,9459,9491,9547,9555,9557,9578,9589,9602,9606,9672,9687,9692,9694,9725,9734,9760,9840,9865,9914,9916,9933,9947,9960,9973,9989,9991,9996} |