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[讨论]某数内相邻素数的最大间距的公式及推导

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 楼主| 发表于 2020-8-6 22:14 | 显示全部楼层
本帖最后由 ysr 于 2020-8-6 14:16 编辑

1与10000之间有1228个素数:(不包括2的)
/3/5/7/11/13/17/19/23/29/31/37/41/43/47/53/59/61/67/71/73/79/83/89/97/101/103/107/109/113/127/131/137/139/149/151/157/163/167/173/179/181/191/193/197/199/211/223/227/229/233/239/241/251/257/263/269/271/277/281/283/293/307/311/313/317/331/337/347/349/353/359/367/373/379/383/389/397/401/409/419/421/431/433/439/443/449/457/461/463/467/479/487/491/499/503/509/521/523/541/547/557/563/569/571/577/587/593/599/601/607/613/617/619/631/641/643/647/653/659/661/673/677/683/691/701/709/719/727/733/739/743/751/757/761/769/773/787/797/809/811/821/823/827/829/839/853/857/859/863/877/881/883/887/907/911/919/929/937/941/947/953/967/971/977/983/991/997/1009/1013/1019/1021/1031/1033/1039/1049/1051/1061/1063/1069/1087/1091/1093/1097/1103/1109/1117/1123/1129/1151/1153/1163/1171/1181/1187/1193/1201/1213/1217/1223/1229/1231/1237/1249/1259/1277/1279/1283/1289/1291/1297/1301/1303/1307/1319/1321/1327/1361/1367/1373/1381/1399/1409/1423/1427/1429/1433/1439/1447/1451/1453/1459/1471/1481/1483/1487/1489/1493/1499/1511/1523/1531/1543/1549/1553/1559/1567/1571/1579/1583/1597/1601/1607/1609/1613/1619/1621/1627/1637/1657/1663/1667/1669/1693/1697/1699/1709/1721/1723/1733/1741/1747/1753/1759/1777/1783/1787/1789/1801/1811/1823/1831/1847/1861/1867/1871/1873/1877/1879/1889/1901/1907/1913/1931/1933/1949/1951/1973/1979/1987/1993/1997/1999/2003/2011/2017/2027/2029/2039/2053/2063/2069/2081/2083/2087/2089/2099/2111/2113/2129/2131/2137/2141/2143/2153/2161/2179/2203/2207/2213/2221/2237/2239/2243/2251/2267/2269/2273/2281/2287/2293/2297/2309/2311/2333/2339/2341/2347/2351/2357/2371/2377/2381/2383/2389/2393/2399/2411/2417/2423/2437/2441/2447/2459/2467/2473/2477/2503/2521/2531/2539/2543/2549/2551/2557/2579/2591/2593/2609/2617/2621/2633/2647/2657/2659/2663/2671/2677/2683/2687/2689/2693/2699/2707/2711/2713/2719/2729/2731/2741/2749/2753/2767/2777/2789/2791/2797/2801/2803/2819/2833/2837/2843/2851/2857/2861/2879/2887/2897/2903/2909/2917/2927/2939/2953/2957/2963/2969/2971/2999/3001/3011/3019/3023/3037/3041/3049/3061/3067/3079/3083/3089/3109/3119/3121/3137/3163/3167/3169/3181/3187/3191/3203/3209/3217/3221/3229/3251/3253/3257/3259/3271/3299/3301/3307/3313/3319/3323/3329/3331/3343/3347/3359/3361/3371/3373/3389/3391/3407/3413/3433/3449/3457/3461/3463/3467/3469/3491/3499/3511/3517/3527/3529/3533/3539/3541/3547/3557/3559/3571/3581/3583/3593/3607/3613/3617/3623/3631/3637/3643/3659/3671/3673/3677/3691/3697/3701/3709/3719/3727/3733/3739/3761/3767/3769/3779/3793/3797/3803/3821/3823/3833/3847/3851/3853/3863/3877/3881/3889/3907/3911/3917/3919/3923/3929/3931/3943/3947/3967/3989/4001/4003/4007/4013/4019/4021/4027/4049/4051/4057/4073/4079/4091/4093/4099/4111/4127/4129/4133/4139/4153/4157/4159/4177/4201/4211/4217/4219/4229/4231/4241/4243/4253/4259/4261/4271/4273/4283/4289/4297/4327/4337/4339/4349/4357/4363/4373/4391/4397/4409/4421/4423/4441/4447/4451/4457/4463/4481/4483/4493/4507/4513/4517/4519/4523/4547/4549/4561/4567/4583/4591/4597/4603/4621/4637/4639/4643/4649/4651/4657/4663/4673/4679/4691/4703/4721/4723/4729/4733/4751/4759/4783/4787/4789/4793/4799/4801/4813/4817/4831/4861/4871/4877/4889/4903/4909/4919/4931/4933/4937/4943/4951/4957/4967/4969/4973/4987/4993/4999/5003/5009/5011/5021/5023/5039/5051/5059/5077/5081/5087/5099/5101/5107/5113/5119/5147/5153/5167/5171/5179/5189/5197/5209/5227/5231/5233/5237/5261/5273/5279/5281/5297/5303/5309/5323/5333/5347/5351/5381/5387/5393/5399/5407/5413/5417/5419/5431/5437/5441/5443/5449/5471/5477/5479/5483/5501/5503/5507/5519/5521/5527/5531/5557/5563/5569/5573/5581/5591/5623/5639/5641/5647/5651/5653/5657/5659/5669/5683/5689/5693/5701/5711/5717/5737/5741/5743/5749/5779/5783/5791/5801/5807/5813/5821/5827/5839/5843/5849/5851/5857/5861/5867/5869/5879/5881/5897/5903/5923/5927/5939/5953/5981/5987/6007/6011/6029/6037/6043/6047/6053/6067/6073/6079/6089/6091/6101/6113/6121/6131/6133/6143/6151/6163/6173/6197/6199/6203/6211/6217/6221/6229/6247/6257/6263/6269/6271/6277/6287/6299/6301/6311/6317/6323/6329/6337/6343/6353/6359/6361/6367/6373/6379/6389/6397/6421/6427/6449/6451/6469/6473/6481/6491/6521/6529/6547/6551/6553/6563/6569/6571/6577/6581/6599/6607/6619/6637/6653/6659/6661/6673/6679/6689/6691/6701/6703/6709/6719/6733/6737/6761/6763/6779/6781/6791/6793/6803/6823/6827/6829/6833/6841/6857/6863/6869/6871/6883/6899/6907/6911/6917/6947/6949/6959/6961/6967/6971/6977/6983/6991/6997/7001/7013/7019/7027/7039/7043/7057/7069/7079/7103/7109/7121/7127/7129/7151/7159/7177/7187/7193/7207/7211/7213/7219/7229/7237/7243/7247/7253/7283/7297/7307/7309/7321/7331/7333/7349/7351/7369/7393/7411/7417/7433/7451/7457/7459/7477/7481/7487/7489/7499/7507/7517/7523/7529/7537/7541/7547/7549/7559/7561/7573/7577/7583/7589/7591/7603/7607/7621/7639/7643/7649/7669/7673/7681/7687/7691/7699/7703/7717/7723/7727/7741/7753/7757/7759/7789/7793/7817/7823/7829/7841/7853/7867/7873/7877/7879/7883/7901/7907/7919/7927/7933/7937/7949/7951/7963/7993/8009/8011/8017/8039/8053/8059/8069/8081/8087/8089/8093/8101/8111/8117/8123/8147/8161/8167/8171/8179/8191/8209/8219/8221/8231/8233/8237/8243/8263/8269/8273/8287/8291/8293/8297/8311/8317/8329/8353/8363/8369/8377/8387/8389/8419/8423/8429/8431/8443/8447/8461/8467/8501/8513/8521/8527/8537/8539/8543/8563/8573/8581/8597/8599/8609/8623/8627/8629/8641/8647/8663/8669/8677/8681/8689/8693/8699/8707/8713/8719/8731/8737/8741/8747/8753/8761/8779/8783/8803/8807/8819/8821/8831/8837/8839/8849/8861/8863/8867/8887/8893/8923/8929/8933/8941/8951/8963/8969/8971/8999/9001/9007/9011/9013/9029/9041/9043/9049/9059/9067/9091/9103/9109/9127/9133/9137/9151/9157/9161/9173/9181/9187/9199/9203/9209/9221/9227/9239/9241/9257/9277/9281/9283/9293/9311/9319/9323/9337/9341/9343/9349/9371/9377/9391/9397/9403/9413/9419/9421/9431/9433/9437/9439/9461/9463/9467/9473/9479/9491/9497/9511/9521/9533/9539/9547/9551/9587/9601/9613/9619/9623/9629/9631/9643/9649/9661/9677/9679/9689/9697/9719/9721/9733/9739/9743/9749/9767/9769/9781/9787/9791/9803/9811/9817/9829/9833/9839/9851/9857/9859/9871/9883/9887/9901/9907/9923/9929/9931/9941/9949/9967/9973其中最大的素数是9973.
1~10000内的素数间隔2/4/6/8/10/12/14/16/18/20/22/24/26/28/30/32/34/36/差2=205 差4=202 差6=299 差8的=101 差10的=119 差12=105 差14=54 差16=33 差18=40 差20=15 差22=16 差24=15 差34的=2最大的是9587-9551=36.

这个最大的差值符合前面的定理,而远远低于克莱姆猜想,因为(ln10000)^2=84.  可见把(lnx)^2当某数内的最大素数间距是错误的,而某些人就是不尊重真理,拿外国人信口雌黄的猜想,拿稀牛屎,抹黑真理篡改真理,把已经证明是错误的东西奉为经典,压制排挤中国爱好者,一副汉奸卖国贼嘴脸,打倒汉奸叛徒卖国贼!
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发表于 2020-8-9 01:51 | 显示全部楼层
这里有一个用集合做的素数分布规律,也就是可得到整个素数集。
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发表于 2020-8-9 01:53 | 显示全部楼层

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 楼主| 发表于 2020-8-14 08:08 | 显示全部楼层
此法比常规法快吗?和艾拉托尼筛法相似?艾拉托尼筛法虽然快但用到数组太占内存,不能算的太大否则内存溢出,一般电脑才能算到20亿内,才9位数或10位数。
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 楼主| 发表于 2021-1-15 00:41 | 显示全部楼层
自己顶一下,备查阅!感谢各位老师和朋友长期支持和鼓励!
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