This code calculated the remainder if we divide 5 into 11, which is one.

这段代码计算是11除以5，结果是1。

And then the remainder, 358, I'll just say the remainder.

然，358，我就说。

And of course, the other residue classes mod 710 also form these nearly straight lines.

当然，模710其他类也形成了这些近乎直线线。

When you divide them by two, there's nothing left over.

当你把它们除以时，没有。

There's no " remainder, " we would say.

我们不会说“”。

If there's no remainder, then okay, two is a factor.

如果没有，那么就是一个因。

Finally, how many times does 4 go into the remainder?

最，中 4 除以多少？

76 is 6 twelves, remainder 4, and there's 1 four in the remainder.

76 是 6 个十，为 4，中有 1 个四。

So too, at the present time there is a remnant chosen by grace.

如今也是这样，照着拣选恩典，还有所留。

The hard part is figuring out the exponent given only the result and the base.

重点是，如果只给和基，很难得知指是多少。

Remainder. The next word is remainder.

。 下一个词是。

'69 is 5 twelves, remainder 9, which is 2 fours.

'69 为 5 个 12， 9，即 2 个 4。

" 10 divided by 4" gives you 2 with a remainder of 2, so: " 2 remainder 2" .

所以：“10 除以 4” 得到 2，为 2， 所以：“2 2” 。

Again as time goes on we see an even spread between the 20 different allowable residue classes.

随着时间推移，我们看到20个不同允许类之间分布得更加均匀。

Which is simply that each of these residue classes that MIGHT have infinitely many primes DOES have infinitely many.

这 simplemente 意味着每个可能包含无限多个素类确实都包含无限多个素。

Everything whose last digit is 0 is a residue class, everything whose last digit is 1 is another residue class and so on.

所有个位是0构成一个类，所有个位是1构成另一个类，依此类推。

The second is that many of these residue classes contain zero prime numbers or sometimes just one so they won't show up.

第个原因是，许多这样类包含零个素，或者有时只有一个素，所以它们不会显示出来。

This means taking one number, the base, to the power of another number, the exponent, and taking the remainder when dividing by a third number, the modulus.

这意味着将一个（底）乘以自身另一个（指）次，然除以第三个（模）取。

And this isn't just antiquated technology either Understanding the distribution of primes in residue classes like this Continues to be relevant in modern research too!

而这不仅仅是过时技术，理解素在类中分布，在现代研究中仍然具有相关性！

Each one of these sequences where you're counting up by 6 is fancifully called a " residue class mod 6" .

每当你按6递增计这些序列都被形象地称为“模6类”。