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

这段代码计算11以5余数，结果1。

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

然后余数，358，我就说余数。

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

当然，模710其他余数类也形成了这些近乎直线线。

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

当你把它们以时，没有余数。

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

我们不会说“余数”。

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

如果没有余数，那么就一个因数。

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

最后，余数中 4 以多少？

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

76 6 个十，余数为 4，余数中有 1 个四。

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

如今也这样，照着拣选恩典，还有所留余数。

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

重点，如果只给余数和基数，很指数多少。

Remainder. The next word is remainder.

余。 下一个词余数。

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

'69 为 5 个 12，余数 9，即 2 个 4。

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

所以：“10 以 4” 到 2，余数为 2， 所以：“2 余数 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个不同允许余数类之间分布更加均匀。

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数余数类确实都包含无限多个素数。

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

所有个位数0数构成一个余数类，所有个位数1数构成另一个余数类，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，许多这样余数类包含零个素数，或者有时只有一个素数，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.

这意味着将一个数（底数）乘以自身另一个数（指数）次，然后以第三个数（模数）取余数。

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!

而这不仅仅过时技术，理解素数在余数类中分布，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递增计数这些序列都被形象地称为“模6余数类”。