(n^2,(n+1)~2)中至少有一个素数的证明

The proof of at least one of the prime numbers in(n^2,(n+1)~2)

证明(n^2,(n+1)~2)中至少有一个素数,是一个众所周知的数论难题(华罗庚1979,(美)阿尔伯特·H·贝勒1998)。本文用筛法先证明一个叫做筛不完原理的定理,使用筛不完原理证明了(n^2,(n+1)~2)中至少有一个素数。还给出素数在自然数中的概率为0的一个新的证法。

In this paper, a well known problem that at least one of the prime numbers is in （ n2, （ n＋ 1 ） 2 ） （ Hua Luo-geng 1979, [ America ] Albert H Belier 1998）has been proved. At first, the proof of the endless sieve theorem on the basis of sieve method was completed. And second,it proves that at least one of the prime numbers is in（ n2, （n＋ 1 ） 2） on the basis of the endless sieve theorem. Then, a new proof method was given, in which the probability of prime number in natural number is 0.