One question had been solved very early on.
很早以前，其中一个问题被解决了，
Euclid had been able to show that there were infinitely many prime numbers, so that although in 1937 the number 2127 – 1 = 170141183460469231731687303715884105727 was the largest known prime, it was also known that they continued for ever.
也就是欧几里德证明了素数有无限多个。所以，虽然在1937年人们已知的最大素数是（图）2^127 - 1 = 170141183460469231731687303715884105727，但是人们知道永远还有更大的。
But another property that was easy to guess, but very hard to prove, was that the primes would always thin out,
然而，素数还有另一个性质，虽然很容易看出来，但却很难证明，那就是它的分布越来越稀疏。
at first almost every other number being prime, but near 100 only one in four, near 1000 only one in seven, and near 10,000,000,000 only one in 23.
一开始几乎每个数都是素数，100以内则只有1/4的数是素数，1000以内只有1/7，而到了10, 000, 000, 000以内，就只有1/23了。
There had to be a reason for it.
人们需要知道这是为什么。
In about 1793, the fifteen-year-old Gauss noticed that there was a regular pattern to the thinning-out.
大约在1793年，15岁的高斯注意到，这个稀释的过程是有规律的。
The spacing of the primes near a number n was proportional to the number of digits in the number n;
n以内的的素数的间距，与n的大小有关，
more precisely, it increased as the natural logarithm of n.
准确地说，它与n的自然对数成正比。
Throughout his life Gauss, who apparently liked doing this sort of thing, gave idle leisure hours to identifying all the primes less than three million, verifying his observation as far as he could go.
高斯在他的余生中，只要有空就去验证这个猜想，他很喜欢做这样的事。他检查了3, 000, 000以内的所有素数，死而后已。