In this paper, we give about prime numbers and Blum two theorems and one guess integers.We prove the two theorems about Blum integers.Combining the guess with the primitive non-sieving quadratic sieve,we proposed a im...In this paper, we give about prime numbers and Blum two theorems and one guess integers.We prove the two theorems about Blum integers.Combining the guess with the primitive non-sieving quadratic sieve,we proposed a improved non-sieving quadratic sieve（INQS）.In INQS,we not only reduce the times of squares and modulo n, but also imply another important conclusion,that is,we don＇t need to find the greatest common divisor of two integers as we do in PNQS.By some examples,we compare it with the primitive non-sieving quadratic sieve（PNQS）. It＇s faster to factor a integer by using improved non-sieving quadratic sieve than the primitive one.展开更多
基金Supported by the National Natural Science Founda-tion of China (60573120)
文摘In this paper, we give about prime numbers and Blum two theorems and one guess integers.We prove the two theorems about Blum integers.Combining the guess with the primitive non-sieving quadratic sieve,we proposed a improved non-sieving quadratic sieve（INQS）.In INQS,we not only reduce the times of squares and modulo n, but also imply another important conclusion,that is,we don＇t need to find the greatest common divisor of two integers as we do in PNQS.By some examples,we compare it with the primitive non-sieving quadratic sieve（PNQS）. It＇s faster to factor a integer by using improved non-sieving quadratic sieve than the primitive one.
