摘要
(n,2n)中至少有一个素数,称为伯特兰猜测(华罗庚,1979),其正确性首先为俄国数学家切必雪夫所证明。但一百多年来,此猜测未能再进一步。本文将这一猜测推广为:a>1,n充分大时,(n,an)中至少有一个素数。并由此推出:对任何正整数k,n充分大时,(n,2n)中至少含有k个素数。
There is at least one prime number in （n, 2n）, which is well known as prime number distribution theorem. This paper proves that for any real number a is greater than 1, there exists at least one prime number in （ n, an） , when n is sufficiently large. And for a certain number k, there exist k prime numbers at least in （n, 2n） when n is sufficiently large.
出处
《贵州科学》
2013年第4期1-2,共2页
Guizhou Science
关键词
素数
素数分布
(n
an)中的素数
prime number, distribution of prime numbers, prime number in the interval （n, an）
