2-3-5-7车轮分解似乎跳过了质数331 [英] 2-3-5-7 wheel factorization seems to skip prime number 331

问题描述

按照用于车轮分解的维基百科上的程序时，我似乎偶然发现了一个问题如果我尝试构建2-3-5-7车轮，则素数331将被视为合成数字.

When following the procedure on wikipedia for wheel factorization, I seem to have stumbled into a problem where the prime number 331 is treated as a composite number if I try to build a 2-3-5-7 wheel.

对于2-3-5-7车轮，2 * 3 * 5 * 7 = 210.因此，我设置了一个具有210个插槽的圆，并顺利完成了步骤1-7.然后，我进入第8步并剔除所有质数倍数的辐条，最终我剔除以121为根的辐条，这是11的倍数，即质数.对于根植于121的辐条，则121 + 210 =331.不幸的是，331是质数.

With 2-3-5-7 wheel, 2*3*5*7=210. So I setup a circle with 210 slots and go through steps 1-7 without any issues. Then I get to step 8 and strike off the spokes of all multiples of prime numbers, I eventually strike off the spoke rooted at 121, which is a multiple of 11, which is a prime. For the spoke rooted at 121, 121 + 210 = 331. Unfortunately, 331 is a prime number.

维基百科上的程序不正确吗?

Is the procedure on Wikipedia incorrect?

还是我误解了程序，应该只剔除2、3、5和7的倍数的辐条，但其他任何质数都不小于210的辐条?

Or did I misunderstand the procedure, and should have only struck out spokes that are multiples of 2, 3, 5, and 7, but not any of the other primes less than 210?

推荐答案

维基百科是正确的.

331在车轮的1根辐条中.辐条未着色，因此331可能是素数.实际上，这是最重要的.

331 is in the 1 spoke of the wheel. The spoke is not shaded, so 331 is potentially prime. And in fact, it is prime.

121也在车轮的1根辐条中，因此121可能是素数.就是说，它并没有被车轮排除在外.但是，它不是素数.

121 is also in the 1 spoke of the wheel, so 121 is potentially prime. That is, it is not eliminated as a prime by the wheel. However, it is not prime.

方向盘不允许您基于121的非素数来推断331的素数.对不起.

The wheel doesn't allow you to make any inference about the primality of 331 based on the non-primality of 121. Sorry.

在我的博客上，我有实施车轮分解的方法，如果您想看看.

I have an implementation of wheel factorization at my blog, if you want to look at it.

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