中文摘要：

在这份报纸，我们关于素数 andBlum 整数给二条定理和一猜测。我们关于 Blum 整数证明二条定理。把猜测与筛 primitivenon 相结合二次的筛，我们建议了改进的筛得非的二次的筛(INQS ) 。在 INQS， wenot 仅仅减少广场和模 n 的时间，而且暗示另一个重要结论， thatis，我们穿上“当我们在 PNQS 做，发现二个整数的最大的普通除数的 t 需要。由 someexamples，我们把它与原始的筛得非的二次的筛(PNQS ) 作比较。它“对由使用的因素 ainteger 更快的 s 比 theprimitive 改进了筛得非的二次的筛。

英文摘要：

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.