数论问题巅峰对决

ysr

额，我刚才下班，好的，等会儿给你结果。

ysr

先验证1~10000内的p,p+6数对：
1与10000之间有411对孪生（6）素数对:（仅显示孪中）
/8/10/14/16/20/26/34/40/44/50/56/64/70/76/86/100/104/106/110/134/154/160/170/176/194/196/226/230/236/254/260/266/274/280/310/314/334/350/356/370/376/386/436/446/460/464/506/544/560/566/574/590/596/604/610/616/644/650/656/680/730/736/754/824/826/856/860/880/884/944/950/974/980/994/1016/1036/1066/1090/1094/1100/1106/1120/1126/1184/1190/1220/1226/1234/1280/1286/1294/1300/1304/1324/1364/1370/1426/1430/1436/1450/1456/1484/1486/1490/1496/1546/1556/1604/1610/1616/1624/1660/1666/1696/1744/1750/1756/1780/1786/1864/1870/1874/1876/1904/1910/1976/1990/1996/2000/2014/2066/2084/2086/2134/2140/2210/2240/2270/2284/2290/2336/2344/2354/2374/2380/2386/2396/2414/2420/2444/2470/2546/2554/2660/2674/2680/2686/2690/2696/2710/2716/2794/2800/2840/2854/2900/2906/2960/2966/3064/3086/3166/3184/3206/3254/3256/3304/3310/3316/3326/3410/3460/3464/3466/3514/3530/3536/3544/3610/3620/3634/3640/3674/3694/3730/3736/3764/3800/3850/3914/3920/3926/4004/4010/4016/4024/4054/4076/4096/4130/4136/4156/4214/4256/4286/4360/4394/4444/4454/4460/4510/4516/4520/4564/4594/4600/4640/4646/4654/4660/4676/4726/4786/4790/4796/4874/4906/4934/4940/4954/4970/4990/4996/5006/5084/5104/5110/5116/5150/5230/5234/5276/5300/5306/5384/5390/5396/5410/5416/5434/5440/5446/5474/5480/5504/5524/5560/5566/5644/5650/5654/5656/5686/5714/5740/5746/5804/5810/5824/5846/5854/5864/5900/5984/6040/6050/6070/6076/6200/6214/6260/6266/6274/6314/6320/6326/6340/6356/6364/6370/6376/6424/6550/6566/6574/6656/6676/6706/6826/6830/6860/6866/6914/6964/6974/6980/6994/7016/7106/7124/7190/7210/7216/7240/7250/7414/7454/7484/7520/7526/7544/7580/7586/7646/7684/7720/7756/7820/7826/7870/7876/7880/7904/7930/8014/8056/8084/8090/8114/8120/8164/8234/8240/8266/8290/8294/8314/8366/8426/8464/8524/8540/8626/8644/8666/8696/8710/8716/8734/8744/8750/8834/8864/8890/8926/8966/9004/9010/9046/9106/9130/9154/9184/9206/9224/9280/9340/9346/9374/9394/9400/9416/9434/9436/9464/9470/9476/9494/9536/9616/9626/9646/9736/9746/9784/9814/9836/9854/9904/9926/9970。

ysr

16/18/20/22/24/26/28/30/32/34/36/40/42/44/46/48/50/52/54/56/
58/60/64/66/68/70/72/74/76/78/80/82/84/86/88/90/92/94/96/98/
100/102/104/106/108/110/112/114/116/118/120/122/124/126/128/130/132/134/136/138/
140/142/144/146/148/150/152/154/156/160/162/164/166/168/170/172/174/176/178/180/
182/184/186/188/190/192/194/196/198/200/202/204/206/208/210/212/214/216/218/220/
222/224/226/228/230/232/234/236/238/240/242/244/246/250/252/254/256/258/260/262/
264/266/268/270/272/274/276/280/282/284/286/288/290/292/294/296/298/300/302/304/
306/308/310/312/314/316/318/320/322/324/326/328/330/332/334/336/338/340/342/344/
346/348/350/352/354/356/358/360/364/366/368/370/372/374/376/378/380/382/384/386/
388/390/392/394/396/398/400/402/404/406/408/410/412/414/416/418/420/422/424/426/
428/430/432/434/436/438/440/442/444/446/448/450/452/454/456/460/462/464/466/468/
470/472/474/476/478/480/482/484/486/488/490/492/494/496/498/500/502/504/506/508/
510/512/514/516/520/522/524/526/528/530/532/534/536/540/542/544/546/548/550/552/
554/556/558/560/562/564/566/568/570/572/574/576/578/580/582/584/586/588/590/592/
594/596/598/600/602/604/606/608/610/612/614/616/618/620/622/624/626/628/630/632/
634/636/638/640/642/644/646/648/650/652/654/656/658/660/662/664/666/668/670/672/
674/676/678/680/682/684/686/688/690/692/694/696/698/700/702/704/706/708/710/712/
714/716/718/720/722/724/726/728/730/732/734/736/738/740/742/744/746/748/750/752/
754/756/758/760/762/764/766/768/770/772/774/776/778/780/784/786/788/790/792/794/
796/798/800/802/804/806/810/812/814/816/818/820/822/824/826/828/830/832/834/836/
838/840/842/844/846/848/850/852/854/856/858/860/862/864/866/868/870/872/874/876/
878/880/882/884/886/888/890/892/894/896/898/900/902/904/906/908/910/912/914/916/
918/920/922/924/926/928/930/932/934/936/938/940/942/944/946/948/950/952/954/956/
958/960/962/964/966/970/972/974/976/978/980/982/984/986/988/990/992/994/996/1000/
1002/1004/1006/1008/1010/1012/1014/1016/1018/1020/1022/1024/1026/1028/1030/1032/1034/1036/1038/1040/
1042/1044/1046/1048/1050/1052/1054/1056/1058/1060/1062/1064/1066/1068/1070/1072/1074/1076/1078/1080/
1082/1084/1086/1088/1090/1092/1094/1096/1098/1100/1102/1104/1106/1108/1110/1112/1114/1116/1118/1120/
1122/1124/1126/1128/1130/1132/1134/1136/1138/1140/1142/1144/1146/1148/1150/1152/1154/1156/1158/1160/
1162/1164/1166/1168/1170/1172/1174/1176/1178/1180/1182/1184/1186/1188/1190/1192/1194/1196/1198/1200/
1202/1204/1206/1208/1210/1212/1214/1216/1218/1220/1222/1224/1226/1228/1230/1232/1234/1236/1240/1242/
1244/1246/1248/1250/1252/1254/1256/1258/1260/1262/1264/1266/1268/1270/1272/1274/1276/1278/1280/1282/
1284/1286/1288/1290/1292/1294/1296/1298/1300/1302/1304/1306/1308/1310/1312/1314/1316/1318/1320/1322/
1324/1326/1328/1330/1332/1334/1336/1338/1340/1342/1344/1346/1348/1350/1352/1354/1356/1358/1360/1362/
1364/1366/1368/1370/1372/1374/1376/1378/1380/1384/1386/1388/1390/1392/1394/1396/1398/1400/1402/1404/
1406/1408/1410/1412/1414/1416/1420/1422/1424/1426/1428/1430/1434/1436/1438/1440/1442/1444/1446/1448/
1450/1452/1454/1456/1458/1460/1462/1464/1466/1468/1470/1472/1474/1476/1478/1480/1482/1484/1486/1488/
1490/1492/1494/1496/1498/1500/1502/1504/1506/1508/1510/1512/1514/1516/1518/1520/1522/1524/1526/1528/
1530/1532/1534/1536/1538/1540/1542/1544/1546/1548/1550/1552/1554/1556/1558/1560/1562/1564/1566/1568/
1570/1572/1574/1576/1578/1580/1582/1584/1586/1588/1590/1592/1594/1596/1598/1600/1602/1604/1606/1608/
1610/1612/1614/1616/1618/1620/1622/1624/1626/1628/1630/1632/1634/1636/1638/1640/1642/1644/1646/1648/
1650/1652/1654/1656/1658/1660/1662/1664/1666/1668/1670/1672/1674/1676/1678/1680/1682/1684/1686/1688/
1690/1692/1694/1696/1698/1700/1702/1704/1706/1708/1710/1712/1714/1716/1720/1722/1724/1726/1728/1730/
1732/1734/1736/1738/1740/1742/1744/1746/1748/1750/1752/1754/1756/1758/1760/1762/1764/1766/1768/1770/
1772/1774/1776/1778/1780/1782/1784/1786/1788/1790/1792/1794/1796/1798/1800/1802/1804/1806/1808/1810/
1812/1814/1816/1818/1820/1822/1824/1826/1828/1830/1832/1834/1836/1838/1840/1842/1844/1846/1848/1850/
1852/1854/1856/1858/1860/1862/1864/1866/1868/1870/1872/1874/1876/1878/1880/1882/1884/1886/1888/1890/
1892/1894/1896/1898/1900/1902/1904/1906/1908/1910/1912/1914/1916/1918/1920/1922/1924/1926/1928/1930/
1932/1934/1936/1938/1940/1942/1944/1946/1948/1950/1952/1954/1956/1958/1960/1962/1964/1966/1968/1970/
1972/1974/1976/1978/1980/1982/1984/1986/1988/1990/1992/1994/1996/1998/2000/2002/2004/2006/2008/2010/
2012/2014/2016/2018/2020/2022/2024/2026/2028/2030/2032/2034/2036/2038/2040/2042/2044/2046/2048/2050/
2052/2054/2056/2058/2060/2062/2064/2066/2068/2070/2072/2074/2076/2078/2080/2082/2084/2086/2088/2090/
2092/2094/2096/2098/2100/2102/2104/2106/2110/2112/2114/2116/2118/2120/2122/2124/2126/2128/2130/2132/
2134/2136/2138/2140/2142/2144/2146/2148/2150/2152/2154/2156/2158/2160/2162/2164/2166/2168/2170/2172/
2174/2176/2178/2180/2182/2184/2186/2188/2190/2192/2194/2196/2198/2200/2202/2204/2206/2208/2210/2212/
2214/2216/2218/2220/2222/2224/2226/2228/2230/2232/2234/2236/2238/2240/2242/2244/2246/2248/2250/2252/
2254/2256/2260/2262/2264/2266/2268/2270/2272/2274/2276/2278/2280/2282/2284/2286/2288/2290/2292/2294/
2296/2298/2300/2302/2304/2306/2308/2310/2312/2314/2316/2318/2320/2322/2324/2326/2328/2330/2332/2334/
2336/2338/2340/2342/2344/2346/2348/2350/2352/2354/2356/2358/2360/2362/2364/2366/2368/2370/2372/2374/
2376/2378/2380/2382/2384/2386/2388/2390/2392/2394/2396/2398/2400/2402/2404/2406/2408/2410/2412/2414/
2416/2418/2420/2422/2424/2426/2428/2430/2432/2434/2436/2438/2440/2442/2444/2446/2448/2450/2452/2454/
2456/2458/2460/2462/2464/2466/2468/2470/2472/2474/2476/2478/2480/2482/2484/2486/2488/2490/2492/2494/
2496/2498/2500/2502/2504/2506/2508/2510/2512/2514/2516/2518/2520/2522/2524/2526/2528/2530/2532/2534/
2536/2538/2540/2542/2544/2546/2548/2550/2552/2554/2556/2558/2560/2562/2564/2566/2568/2570/2572/2574/
2576/2578/2580/2582/2584/2586/2588/2590/2592/2594/2596/2598/2600/2602/2604/2606/2608/2610/2612/2614/
2616/2618/2620/2622/2624/2626/2628/2630/2632/2634/2636/2638/2640/2642/2644/2646/2648/2650/2652/2654/
2656/2658/2660/2662/2664/2666/2668/2670/2672/2674/2676/2678/2680/2682/2684/2686/2688/2690/2692/2694/
2696/2698/2700/2702/2704/2706/2708/2710/2712/2714/2716/2718/2720/2722/2724/2726/2728/2730/2732/2734/
2736/2738/2740/2742/2744/2746/2748/2750/2752/2754/2756/2758/2760/2762/2764/2766/2768/2770/2772/2774/
2776/2778/2780/2782/2784/2786/2788/2790/2792/2794/2796/2800/2802/2804/2806/2808/2810/2812/2814/2816/
2818/2820/2822/2824/2826/2828/2830/2832/2834/2836/2838/2840/2842/2844/2846/2848/2850/2852/2854/2856/
2858/2860/2862/2864/2866/2868/2870/2872/2874/2876/2878/2880/2882/2884/2886/2888/2890/2892/2894/2896/
2898/2900/2902/2904/2906/2908/2910/2912/2914/2916/2918/2920/2922/2924/2926/2928/2930/2932/2934/2936/
2940/2942/2944/2946/2948/2950/2952/2954/2956/2958/2960/2962/2964/2966/2968/2970/2972/2974/2976/2978/
2980/2982/2984/2986/2988/2990/2992/2994/2996/2998/3000/3002/3004/3006/3008/3010/3012/3014/3016/3018/
3020/3022/3024/3026/3028/3030/3032/3034/3036/3038/3040/3042/3044/3046/3048/3050/3052/3054/3056/3058/
3060/3062/3064/3066/3068/3070/3072/3074/3076/3078/3080/3082/3084/3086/3088/3090/3092/3094/3096/3098/
3100/3102/3104/3106/3108/3110/3112/3114/3116/3120/3122/3124/3126/3128/3130/3132/3134/3136/3138/3140/
3142/3144/3146/3150/3152/3154/3156/3158/3160/3162/3164/3166/3168/3170/3172/3174/3176/3178/3180/3182/
3184/3186/3188/3190/3192/3194/3196/3198/3200/3202/3204/3206/3208/3210/3212/3214/3216/3218/3220/3222/
3224/3226/3228/3230/3232/3234/3236/3238/3240/3242/3244/3246/3248/3250/3252/3254/3256/3258/3260/3262/
3264/3266/3268/3270/3272/3274/3276/3278/3280/3282/3284/3286/3288/3290/3292/3294/3296/3298/3300/3302/
3304/3306/3308/3310/3312/3314/3316/3318/3320/3322/3324/3326/3328/3330/3332/3334/3336/3338/3340/3342/
3344/3346/3348/3350/3352/3354/3356/3358/3360/3362/3364/3366/3368/3370/3372/3374/3376/3378/3380/3382/
3384/3386/3388/3390/3392/3394/3396/3398/3400/3402/3404/3406/3408/3410/3412/3414/3416/3418/3420/3422/
3424/3426/3428/3430/3432/3434/3436/3438/3440/3442/3444/3446/3448/3450/3452/3454/3456/3458/3460/3462/
3464/3466/3468/3470/3472/3474/3476/3478/3480/3482/3484/3486/3488/3490/3492/3494/3496/3498/3500/3502/
3504/3506/3508/3510/3512/3514/3516/3518/3520/3522/3524/3526/3528/3530/3532/3534/3536/3538/3540/3542/
3544/3546/3548/3550/3552/3554/3556/3558/3560/3562/3564/3566/3568/3570/3572/3574/3576/3578/3580/3582/
3584/3586/3588/3590/3592/3594/3596/3598/3600/3602/3604/3606/3608/3610/3612/3614/3616/3618/3620/3622/
3624/3626/3628/3630/3632/3634/3636/3638/3640/3642/3644/3646/3648/3650/3652/3654/3656/3658/3660/3662/
3664/3666/3668/3670/3672/3674/3676/3678/3680/3682/3684/3686/3688/3690/3692/3694/3696/3698/3700/3702/
3704/3706/3708/3710/3712/3714/3716/3718/3720/3722/3724/3726/3728/3730/3732/3734/3736/3738/3740/3742/
3744/3746/3748/3750/3752/3754/3756/3758/3760/3762/3764/3766/3768/3770/3772/3774/3776/3778/3780/3782/
3784/3786/3788/3790/3792/3794/3796/3798/3800/3802/3804/3806/3808/3810/3812/3814/3816/3818/3820/3822/
3824/3826/3828/3830/3832/3834/3836/3838/3840/3842/3844/3846/3848/3850/3852/3854/3856/3858/3860/3862/
3864/3866/3868/3870/3872/3874/3876/3878/3880/3882/3884/3886/3888/3890/3892/3894/3896/3898/3900/3902/
3904/3906/3908/3910/3912/3914/3916/3918/3920/3922/3924/3926/3928/3930/3932/3934/3936/3938/3940/3942/
3944/3946/3948/3950/3952/3954/3956/3958/3960/3962/3964/3966/3968/3970/3972/3974/3976/3978/3980/3982/
3984/3986/3988/3990/3992/3994/3996/3998/4000/4002/4004/4006/4008/4010/4012/4014/4016/4018/4020/4022/
4024/4026/4028/4030/4032/4034/4036/4038/4040/4042/4044/4046/4048/4050/4052/4054/4056/4058/4060/4062/
4064/4066/4068/4070/4072/4074/4076/4078/4080/4082/4084/4086/4088/4090/4092/4094/4096/4098/4100/4102/
4104/4106/4108/4110/4112/4114/4116/4118/4120/4122/4124/4126/4128/4130/4132/4134/4136/4138/4140/4142/
4144/4146/4148/4150/4152/4154/4156/4158/4160/4162/4164/4166/4168/4170/4172/4174/4176/4178/4180/4182/
4184/4186/4188/4190/4192/4194/4196/4198/4200/4202/4204/4206/4208/4210/4212/4214/4216/4218/4220/4222/
4224/4226/4228/4230/4232/4234/4236/4238/4240/4242/4244/4246/4248/4250/4252/4254/4256/4258/4260/4262/
4264/4266/4268/4270/4272/4274/4276/4278/4280/4282/4284/4286/4288/4290/4292/4294/4296/4298/4300/4302/
4304/4306/4308/4310/4312/4314/4316/4318/4320/4322/4324/4326/4328/4330/4332/4334/4336/4338/4340/4342/
4344/4346/4348/4350/4352/4354/4356/4358/4360/4362/4364/4366/4368/4370/4372/4374/4376/4378/4380/4382/
4384/4386/4388/4390/4392/4394/4396/4398/4400/4402/4404/4406/4408/4410/4412/4414/4416/4418/4420/4422/
4424/4426/4428/4430/4432/4434/4436/4438/4440/4442/4444/4446/4448/4450/4452/4454/4456/4458/4460/4462/
4464/4466/4468/4470/4472/4474/4476/4478/4480/4482/4484/4486/4488/4490/4492/4494/4496/4498/4500/4502/
4504/4506/4508/4510/4512/4514/4516/4518/4520/4522/4524/4526/4528/4530/4532/4534/4536/4538/4540/4542/
4544/4546/4548/4550/4552/4554/4556/4558/4560/4562/4564/4566/4568/4570/4572/4574/4576/4578/4580/4582/
4584/4586/4588/4590/4592/4594/4596/4598/4600/4602/4604/4606/4608/4610/4612/4614/4616/4618/4620/4622/
4624/4626/4628/4630/4632/4634/4636/4638/4640/4642/4644/4646/4648/4650/4652/4654/4656/4658/4660/4662/
4664/4666/4668/4670/4672/4674/4676/4678/4680/4682/4684/4686/4688/4690/4692/4694/4696/4698/4700/4702/
4704/4706/4708/4710/4712/4714/4716/4718/4720/4722/4724/4726/4728/4730/4732/4734/4736/4738/4740/4742/
4744/4746/4748/4750/4752/4754/4756/4758/4760/4762/4764/4766/4768/4770/4772/4774/4776/4778/4780/4782/
4784/4786/4788/4790/4792/4794/4796/4798/4800/4802/4804/4806/4808/4810/4812/4814/4816/4818/4820/4822/
4824/4826/4828/4830/4832/4834/4836/4838/4840/4842/4844/4846/4848/4850/4852/4854/4856/4858/4860/4862/
4864/4866/4868/4870/4872/4874/4876/4878/4880/4882/4884/4886/4888/4890/4892/4894/4896/4898/4900/4902/
4904/4906/4908/4910/4912/4914/4916/4918/4920/4922/4924/4926/4928/4930/4932/4934/4936/4938/4940/4942/
4944/4946/4948/4950/4952/4954/4956/4958/4960/4962/4964/4966/4968/4970/4972/4974/4976/4978/4980/4982/
4984/4986/4988/4990/4992/4994/4996/4998/5000/5002/5004/5006/5008/5010/5012/5014/5016/5018/5020/5022/

ysr

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9948/9950/9952/9954/9956/9958/9960/9962/9964/9966/9968/9970/9972/9974/9976/9978/9980/9982/9984/9986/
9988/9990/9992/9994/9996/9998/10000/10002/10004/10006/10008/10010/10012/10014/10016/10018/10020/10022/10024/10026/
10028/10030/10032/10034/10036/10038/10040/10042/10044/10046/10048/10050/10052/10054/10056/10058/10060/10062/10064/10066/
10068/10070/10072/10074/10076/10078/10080/10082/10084/10086/10088/10090/10092/10094/10096/10098/10100/10102/10104/10106/
10108/10110/10112/10114/10116/10118/10120/10122/10124/10126/10128/10130/10132/10134/10136/10138/10140/10142/10144/10146/
10148/10150/10152/10154/10156/10158/10160/10162/10164/10166/10168/10170/10172/10174/10176/10178/10180/10182/10184/10186/
10188/10190/10192/10194/10196/10198/10200/10202/10204/10206/10208/10210/10212/10214/10216/10218/10220/10222/10224/10226/
10228/10230/10232/10234/10236/10238/10240/10242/10244/10246/10248/10250/10252/10254/10256/10258/10260/10262/10264/10266/
（后面的太长已被删掉）
经过观察16~10026（除了8，10，14）没有缺少的p+3项，命题成立。

ysr

8026~10026之间没有缺少的项，而前面缺少的项如38，62等，不是孪中p+3项，所以，至少在8028以上是成立的，而前面缺少的项是有限的几个，找全以后在看看，是否有孪中p+3项，就可以确定了。

ysr

这个和值太多，最大值到了19940，16~10026之间的偶数基本全了，缺少的是很少几个，正在统计。

ysr

对，中项56是有的。缺少38，62等，还在统计。

ysr

统计出来了，缺少24个，分别是：
38， 62， 158，248，278，
362，458，518，538，782，
808，968，998，1238，1382，
1718，2108，2258，2798，2938，
3118，3148，5458，8012.

ysr

和前面的孪中比较，没有一个是孪中，最接近的是8014（孪中），而8012不是乱中，所以，命题成立，除了8，10，14，其他都可以。

ysr

下面对p,p+14在1~10000内验证：
1与10000之间有245对孪生（p,p+14）素数对:
/10/12/24/30/36/54/60/66/90/96/120/144/156/174/186/204/234/264/270/276/300/324/360/366/390/426/450/456/516/564/570/594/600/606/624/654/666/684/726/750/780/804/816/846/870/960/984/990/1026/1056/1110/1116/1194/1224/1230/1284/1290/1296/1314/1374/1416/1440/1446/1560/1590/1614/1620/1716/1740/1794/1854/1980/1986/2004/2010/2046/2076/2106/2136/2214/2244/2274/2280/2304/2340/2364/2430/2466/2550/2586/2640/2664/2670/2700/2706/2760/2784/2796/2826/2844/2850/2910/2946/2964/3030/3174/3210/3264/3306/3336/3354/3366/3456/3534/3540/3564/3600/3624/3630/3666/3684/3726/3786/3840/3870/3924/3936/3996/4014/4020/4086/4146/4224/4236/4266/4290/4356/4416/4500/4554/4590/4644/4650/4656/4794/4806/4824/4896/4926/4944/4950/4980/5016/5094/5106/5160/5316/5340/5400/5406/5424/5514/5646/5676/5814/5820/5850/5874/5946/6036/6060/6204/6210/6264/6270/6294/6330/6336/6360/6366/6570/6666/6696/6726/6786/6834/6864/6876/6954/6984/6990/7020/7050/7200/7236/7290/7314/7530/7554/7566/7584/7596/7614/7680/7710/7734/7860/7926/7944/7956/8046/8094/8154/8226/8280/8304/8370/8436/8454/8520/8616/8634/8670/8700/8706/8754/8814/8856/9006/9036/9144/9180/9234/9330/9384/9426/9504/9540/9594/9636/9726/9774/9810/9864/9894