[原创]k生素数群的数量公式

白新岭

这里有点缺失（或者遗憾），并不是6n的数都有孪生素数对中项的解，在整个6n类中有十几个是无解的，它们的值也较小，其中一个就是偶数6，第一个6n类数，12是有解的，它12=6+6，（6是孪生素数对（5，7）的孪中数），18也有解，18=6+12，12为孪生素数对（11，13）的孪中数。有兴趣的可以找完所有没有孪中数解的6n类数，很少，且值较小，不用望而生畏。

白新岭

二生素数L4（P,P+4）的中项合成，与孪生素数对中项的合成基本类似，就有一点不同的是，系数乘∏[（P-3）/(p-4)],对应这P的余数是±4.  P>3的素数。

白新岭

偶数        统计
6        0
96        0
402        0
516        0
786        0
906        0
1116        0
1146        0
1266        0
1356        0
3246        0
4206        0
就这12个6n类数无孪中解。如果这12正好不是孪中数，那么波浪的孪中猜想成立。他首先排除了6，他是说大于等于12的孪中数都是两个孪中的和。而这12个6n类数，除了第三个以外，减1的数个位是5，显然除了第一个素数5以外，别的都是合数（即含有5的因子），而第三个402±1，所得数不是孪生素数对。所以李明波的孪中猜想正确。

白新岭

如果用孪生素数对中的素数代替孪中，则除了上述12组（每组涉及3个偶数），其余偶数都有孪生素数解。偶数2不能划分到任何组（6n-2，6n，6n+2连续三个偶数为一组），所以总共有1+12*3=37个偶数无孪生素数解。最主要的是最大的一组是4206，所以大于4208的偶数都有孪生素数解，即在x+y=2n中，x，y属于孪生素数对中的素数。2n>4208,即n>2104.

ysr

那12个数除了6以外的确不是孪中数：
1与20000之间有342对p,p+2素数对:（只发孪中数）
/4
/6
/12
/18
/30
/42
/60
/72
/102
/108
/138
/150
/180
/192
/198
/228
/240
/270
/282
/312
/348
/420
/432
/462
/522
/570
/600
/618
/642
/660
/810
/822
/828
/858
/882
/1020
/1032
/1050
/1062
/1092
/1152
/1230
/1278
/1290
/1302
/1320
/1428
/1452
/1482
/1488
/1608
/1620
/1668
/1698
/1722
/1788
/1872
/1878
/1932
/1950
/1998
/2028
/2082
/2088
/2112
/2130
/2142
/2238
/2268
/2310
/2340
/2382
/2550
/2592
/2658
/2688
/2712
/2730
/2790
/2802
/2970
/3000
/3120
/3168
/3252
/3258
/3300
/3330
/3360
/3372
/3390
/3462
/3468
/3528
/3540
/3558
/3582
/3672
/3768
/3822
/3852
/3918
/3930
/4002
/4020
/4050
/4092
/4128
/4158
/4218
/4230
/4242
/4260
/4272
/4338
/4422
/4482
/4518
/4548
/4638
/4650
/4722
/4788
/4800
/4932
/4968
/5010
/5022
/5100
/5232
/5280
/5418
/5442
/5478
/5502
/5520
/5640
/5652
/5658
/5742
/5850
/5868
/5880
/6090
/6132
/6198
/6270
/6300
/6360
/6450
/6552
/6570
/6660
/6690
/6702
/6762
/6780
/6792
/6828
/6870
/6948
/6960
/7128
/7212
/7308
/7332
/7350
/7458
/7488
/7548
/7560
/7590
/7758
/7878
/7950
/8010
/8088
/8220
/8232
/8292
/8388
/8430
/8538
/8598
/8628
/8820
/8838
/8862
/8970
/9000
/9012
/9042
/9240
/9282
/9342
/9420
/9432
/9438
/9462
/9630
/9678
/9720
/9768
/9858
/9930
/10008
/10038
/10068
/10092
/10140
/10272
/10302
/10332
/10428
/10458
/10500
/10530
/10710
/10860
/10890
/10938
/11058
/11070
/11118
/11160
/11172
/11352
/11490
/11550
/11700
/11718
/11778
/11832
/11940
/11970
/12042
/12072
/12108
/12162
/12240
/12252
/12378
/12540
/12612
/12822
/12918
/13002
/13008
/13218
/13338
/13398
/13680
/13692
/13710
/13722
/13758
/13830
/13878
/13902
/13932
/13998
/14010
/14082
/14250
/14322
/14388
/14448
/14550
/14562
/14592
/14628
/14868
/15138
/15270
/15288
/15330
/15360
/15582
/15642
/15648
/15732
/15738
/15888
/15972
/16062
/16068
/16140
/16188
/16230
/16362
/16452
/16632
/16650
/16692
/16830
/16902
/16980
/17028
/17190
/17208
/17292
/17388
/17418
/17490
/17580
/17598
/17658
/17682
/17748
/17790
/17838
/17910
/17922
/17958
/17988
/18042
/18048
/18060
/18120
/18132
/18252
/18288
/18312
/18522
/18540
/18912
/18918
/19080
/19140
/19182
/19212
/19380
/19422
/19428
/19470
/19542
/19698
/19752
/19842
/19890
/19962
/19992

ysr

先发一下程序结果：
1与10000之间有205对p,p+2素数对:（只显示孪中数）
/4
/6
/12
/18
/30
/42
/60
/72
/102
/108
/138
/150
/180
/192
/198
/228
/240
/270
/282
/312
/348
/420
/432
/462
/522
/570
/600
/618
/642
/660
/810
/822
/828
/858
/882
/1020
/1032
/1050
/1062
/1092
/1152
/1230
/1278
/1290
/1302
/1320
/1428
/1452
/1482
/1488
/1608
/1620
/1668
/1698
/1722
/1788
/1872
/1878
/1932
/1950
/1998
/2028
/2082
/2088
/2112
/2130
/2142
/2238
/2268
/2310
/2340
/2382
/2550
/2592
/2658
/2688
/2712
/2730
/2790
/2802
/2970
/3000
/3120
/3168
/3252
/3258
/3300
/3330
/3360
/3372
/3390
/3462
/3468
/3528
/3540
/3558
/3582
/3672
/3768
/3822
/3852
/3918
/3930
/4002
/4020
/4050
/4092
/4128
/4158
/4218
/4230
/4242
/4260
/4272
/4338
/4422
/4482
/4518
/4548
/4638
/4650
/4722
/4788
/4800
/4932
/4968
/5010
/5022
/5100
/5232
/5280
/5418
/5442
/5478
/5502
/5520
/5640
/5652
/5658
/5742
/5850
/5868
/5880
/6090
/6132
/6198
/6270
/6300
/6360
/6450
/6552
/6570
/6660
/6690
/6702
/6762
/6780
/6792
/6828
/6870
/6948
/6960
/7128
/7212
/7308
/7332
/7350
/7458
/7488
/7548
/7560
/7590
/7758
/7878
/7950
/8010
/8088
/8220
/8232
/8292
/8388
/8430
/8538
/8598
/8628
/8820
/8838
/8862
/8970
/9000
/9012
/9042
/9240
/9282
/9342
/9420
/9432
/9438
/9462
/9630
/9678
/9720
/9768
/9858
/9930

ysr

10000内的孪中两两相加排序：
12/18/24/30/36/42/48/54/60/66/72/78/84/90/102/108/114/120/126/132/
138/144/150/156/162/168/174/180/186/192/198/204/210/216/222/228/234/240/246/252/
258/264/270/276/282/288/294/300/306/312/318/324/330/336/342/348/354/360/366/372/
378/384/390/396/408/414/420/426/432/438/444/450/456/462/468/474/480/486/492/498/
504/510/522/528/534/540/546/552/558/564/570/576/582/588/594/600/606/612/618/624/
630/636/642/648/654/660/666/672/678/684/690/696/702/708/714/720/726/732/738/744/
750/756/762/768/774/780/792/798/804/810/816/822/828/834/840/846/852/858/864/870/
876/882/888/894/900/912/918/924/930/936/942/948/954/960/966/972/978/984/990/996/
1002/1008/1014/1020/1026/1032/1038/1044/1050/1056/1062/1068/1074/1080/1086/1092/1098/1104/1110/1122/
1128/1134/1140/1152/1158/1164/1170/1176/1182/1188/1194/1200/1206/1212/1218/1224/1230/1236/1242/1248/
1254/1260/1272/1278/1284/1290/1296/1302/1308/1314/1320/1326/1332/1338/1344/1350/1362/1368/1374/1380/
1386/1392/1398/1404/1410/1416/1422/1428/1434/1440/1446/1452/1458/1464/1470/1476/1482/1488/1494/1500/
1506/1512/1518/1524/1530/1536/1542/1548/1554/1560/1566/1572/1578/1584/1590/1596/1602/1608/1614/1620/
1626/1632/1638/1644/1650/1656/1662/1668/1674/1680/1686/1692/1698/1704/1710/1716/1722/1728/1734/1740/

ysr

接续：
1746/1752/1758/1764/1770/1776/1782/1788/1794/1800/1806/1812/1818/1824/1830/1836/1842/1848/1854/1860/
1866/1872/1878/1884/1890/1896/1902/1908/1914/1920/1926/1932/1938/1944/1950/1956/1962/1968/1974/1980/
1986/1992/1998/2004/2010/2016/2022/2028/2034/2040/2046/2052/2058/2064/2070/2076/2082/2088/2094/2100/
2106/2112/2118/2124/2130/2136/2142/2148/2154/2160/2166/2172/2178/2184/2190/2196/2202/2208/2214/2220/
2226/2232/2238/2244/2250/2256/2262/2268/2274/2280/2286/2292/2298/2304/2310/2316/2322/2328/2334/2340/
2346/2352/2358/2364/2370/2376/2382/2388/2394/2400/2406/2412/2418/2424/2430/2436/2442/2448/2454/2460/
2466/2472/2478/2484/2490/2496/2502/2508/2514/2520/2526/2532/2538/2544/2550/2556/2562/2568/2574/2580/
2586/2592/2598/2604/2610/2616/2622/2628/2634/2640/2646/2652/2658/2664/2670/2676/2682/2688/2694/2700/
2706/2712/2718/2724/2730/2736/2742/2748/2754/2760/2766/2772/2778/2784/2790/2796/2802/2808/2814/2820/
2826/2832/2838/2844/2850/2856/2862/2868/2874/2880/2886/2892/2898/2904/2910/2916/2922/2928/2934/2940/
2946/2952/2958/2964/2970/2976/2982/2988/2994/3000/3006/3012/3018/3024/3030/3036/3042/3048/3054/3060/
3066/3072/3078/3084/3090/3096/3102/3108/3114/3120/3126/3132/3138/3144/3150/3156/3162/3168/3174/3180/

ysr

接续：
3186/3192/3198/3204/3210/3216/3222/3228/3234/3240/3252/3258/3264/3270/3276/3282/3288/3294/3300/3306/
3312/3318/3324/3330/3336/3342/3348/3354/3360/3366/3372/3378/3384/3390/3396/3402/3408/3414/3420/3426/
3432/3438/3444/3450/3456/3462/3468/3474/3480/3486/3492/3498/3504/3510/3516/3522/3528/3534/3540/3546/
3552/3558/3564/3570/3576/3582/3588/3594/3600/3606/3612/3618/3624/3630/3636/3642/3648/3654/3660/3666/
3672/3678/3684/3690/3696/3702/3708/3714/3720/3726/3732/3738/3744/3750/3756/3762/3768/3774/3780/3786/
3792/3798/3804/3810/3816/3822/3828/3834/3840/3846/3852/3858/3864/3870/3876/3882/3888/3894/3900/3906/
3912/3918/3924/3930/3936/3942/3948/3954/3960/3966/3972/3978/3984/3990/3996/4002/4008/4014/4020/4026/
4032/4038/4044/4050/4056/4062/4068/4074/4080/4086/4092/4098/4104/4110/4116/4122/4128/4134/4140/4146/
4152/4158/4164/4170/4176/4182/4188/4194/4200/4212/4218/4224/4230/4236/4242/4248/4254/4260/4266/4272/
4278/4284/4290/4296/4302/4308/4314/4320/4326/4332/4338/4344/4350/4356/4362/4368/4374/4380/4386/4392/

ysr

接续：
4398/4404/4410/4416/4422/4428/4434/4440/4446/4452/4458/4464/4470/4476/4482/4488/4494/4500/4506/4512/
4518/4524/4530/4536/4542/4548/4554/4560/4566/4572/4578/4584/4590/4596/4602/4608/4614/4620/4626/4632/
4638/4644/4650/4656/4662/4668/4674/4680/4686/4692/4698/4704/4710/4716/4722/4728/4734/4740/4746/4752/
4758/4764/4770/4776/4782/4788/4794/4800/4806/4812/4818/4824/4830/4836/4842/4848/4854/4860/4866/4872/
4878/4884/4890/4896/4902/4908/4914/4920/4926/4932/4938/4944/4950/4956/4962/4968/4974/4980/4986/4992/
4998/5004/5010/5016/5022/5028/5034/5040/5046/5052/5058/5064/5070/5076/5082/5088/5094/5100/5106/5112/
5118/5124/5130/5136/5142/5148/5154/5160/5166/5172/5178/5184/5190/5196/5202/5208/5214/5220/5226/5232/
5238/5244/5250/5256/5262/5268/5274/5280/5286/5292/5298/5304/5310/5316/5322/5328/5334/5340/5346/5352/
5358/5364/5370/5376/5382/5388/5394/5400/5406/5412/5418/5424/5430/5436/5442/5448/5454/5460/5466/5472/
5478/5484/5490/5496/5502/5508/5514/5520/5526/5532/5538/5544/5550/5556/5562/5568/5574/5580/5586/5592/
5598/5604/5610/5616/5622/5628/5634/5640/5646/5652/5658/5664/5670/5676/5682/5688/5694/5700/5706/5712/
5718/5724/5730/5736/5742/5748/5754/5760/5766/5772/5778/5784/5790/5796/5802/5808/5814/5820/5826/5832/
5838/5844/5850/5856/5862/5868/5874/5880/5886/5892/5898/5904/5910/5916/5922/5928/5934/5940/5946/5952/
5958/5964/5970/5976/5982/5988/5994/6000/6006/6012/6018/6024/6030/6036/6042/6048/6054/6060/6066/6072/
6078/6084/6090/6096/6102/6108/6114/6120/6126/6132/6138/6144/6150/6156/6162/6168/6174/6180/6186/6192/
6198/6204/6210/6216/6222/6228/6234/6240/6246/6252/6258/6264/6270/6276/6282/6288/6294/6300/6306/6312/
6318/6324/6330/6336/6342/6348/6354/6360/6366/6372/6378/6384/6390/6396/6402/6408/6414/6420/6426/6432/
6438/6444/6450/6456/6462/6468/6474/6480/6486/6492/6498/6504/6510/6516/6522/6528/6534/6540/6546/6552/
6558/6564/6570/6576/6582/6588/6594/6600/6606/6612/6618/6624/6630/6636/6642/6648/6654/6660/6666/6672/
6678/6684/6690/6696/6702/6708/6714/6720/6726/6732/6738/6744/6750/6756/6762/6768/6774/6780/6786/6792/
6798/6804/6810/6816/6822/6828/6834/6840/6846/6852/6858/6864/6870/6876/6882/6888/6894/6900/6906/6912/
6918/6924/6930/6936/6942/6948/6954/6960/6966/6972/6978/6984/6990/6996/7002/7008/7014/7020/7026/7032/
7038/7044/7050/7056/7062/7068/7074/7080/7086/7092/7098/7104/7110/7116/7122/7128/7134/7140/7146/7152/
7158/7164/7170/7176/7182/7188/7194/7200/7206/7212/7218/7224/7230/7236/7242/7248/7254/7260/7266/7272/
7278/7284/7290/7296/7302/7308/7314/7320/7326/7332/7338/7344/7350/7356/7362/7368/7374/7380/7386/7392/
7398/7404/7410/7416/7422/7428/7434/7440/7446/7452/7458/7464/7470/7476/7482/7488/7494/7500/7506/7512/
7518/7524/7530/7536/7542/7548/7554/7560/7566/7572/7578/7584/7590/7596/7602/7608/7614/7620/7626/7632/
7638/7644/7650/7656/7662/7668/7674/7680/7686/7692/7698/7704/7710/7716/7722/7728/7734/7740/7746/7752/
7758/7764/7770/7776/7782/7788/7794/7800/7806/7812/7818/7824/7830/7836/7842/7848/7854/7860/7866/7872/
7878/7884/7890/7896/7902/7908/7914/7920/7926/7932/7938/7944/7950/7956/7962/7968/7974/7980/7986/7992/
7998/8004/8010/8016/8022/8028/8034/8040/8046/8052/8058/8064/8070/8076/8082/8088/8094/8100/8106/8112/
8118/8124/8130/8136/8142/8148/8154/8160/8166/8172/8178/8184/8190/8196/8202/8208/8214/8220/8226/8232/
8238/8244/8250/8256/8262/8268/8274/8280/8286/8292/8298/8304/8310/8316/8322/8328/8334/8340/8346/8352/
8358/8364/8370/8376/8382/8388/8394/8400/8406/8412/8418/8424/8430/8436/8442/8448/8454/8460/8466/8472/
8478/8484/8490/8496/8502/8508/8514/8520/8526/8532/8538/8544/8550/8556/8562/8568/8574/8580/8586/8592/
8598/8604/8610/8616/8622/8628/8634/8640/8646/8652/8658/8664/8670/8676/8682/8688/8694/8700/8706/8712/
8718/8724/8730/8736/8742/8748/8754/8760/8766/8772/8778/8784/8790/8796/8802/8808/8814/8820/8826/8832/
8838/8844/8850/8856/8862/8868/8874/8880/8886/8892/8898/8904/8910/8916/8922/8928/8934/8940/8946/8952/
8958/8964/8970/8976/8982/8988/8994/9000/9006/9012/9018/9024/9030/9036/9042/9048/9054/9060/9066/9072/
9078/9084/9090/9096/9102/9108/9114/9120/9126/9132/9138/9144/9150/9156/9162/9168/9174/9180/9186/9192/
9198/9204/9210/9216/9222/9228/9234/9240/9246/9252/9258/9264/9270/9276/9282/9288/9294/9300/9306/9312/
9318/9324/9330/9336/9342/9348/9354/9360/9366/9372/9378/9384/9390/9396/9402/9408/9414/9420/9426/9432/
9438/9444/9450/9456/9462/9468/9474/9480/9486/9492/9498/9504/9510/9516/9522/9528/9534/9540/9546/9552/
9558/9564/9570/9576/9582/9588/9594/9600/9606/9612/9618/9624/9630/9636/9642/9648/9654/9660/9666/9672/
9678/9684/9690/9696/9702/9708/9714/9720/9726/9732/9738/9744/9750/9756/9762/9768/9774/9780/9786/9792/
9798/9804/9810/9816/9822/9828/9834/9840/9846/9852/9858/9864/9870/9876/9882/9888/9894/9900/9906/9912/
9918/9924/9930/9936/9942/9948/9954/9960/9966/9972/9978/9984/9990/9996/10002/10008/10014/10020/10026/10032/
10038/10044/10050/10056/10062/10068/10074/10080/10086/10092/10098/10104/10110/10116/10122/10128/10134/10140/10146/10152/
10158/10164/10170/10176/10182/10188/10194/10200/10206/10212/10218/10224/10230/10236/10242/10248/10254/10260/10266/10272/
后面的不发了。