质数的奇妙分布

• 出 处: 四川教育
• 发表日期: 2004年期
• 关键词: 自然数列 公元前三世纪 自然对数 发砚

质数在自然数列中的分布很奇妙,从公元前三世纪以来,许多数学家一直想找出这个分布的规律来,可是至今仍然没有彻底解决。但从一张大的质数表中,可以看出一些有趣的规律。如表的开头部分,质数分布得比后面的要稠密得多,越与1距离得远,质数的分布就越稀。从1到10之间就有4个质数2,3,5,7,90到100之间却只有1个质数97,再往后看质数分布就更稀少了。我们再看在给定的范围内质数所占的百分比,在100之内有26个质数,占26%;在1000之内有168个质数,占16.8%;

The distribution of prime numbers in natural series is fantastic. Since the third century BC, many mathematicians have been trying to find out the law of this distribution, but so far they have not yet been completely solved. But from a large table of prime numbers, you can see some interesting rules. As the beginning of the table, the prime numbers are much denser than the back ones, and the more distant one is, the thinner the distribution of prime numbers. There are 4 prime numbers from 1 to 10, but there is only one prime number between 2, 3, 5, 7, 90 and 100, 97, and the distribution of prime numbers is even more sparse. Let us look at the percentage of primes within a given range, with 26 primes within 100, accounting for 26%; 168 primes within 1000, accounting for 16.8%;