2018-10-10 22:03:03 +00:00
|
|
|
|
---
|
|
|
|
|
id: 5900f3871000cf542c50fe9a
|
2020-12-16 07:37:30 +00:00
|
|
|
|
title: 问题27:二次素数
|
2018-10-10 22:03:03 +00:00
|
|
|
|
challengeType: 5
|
|
|
|
|
videoUrl: ''
|
|
|
|
|
---
|
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
# --description--
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
欧拉发现了显着的二次公式:$ n ^ 2 + n + 41 $事实证明,公式将为连续的整数值$ 0 \\ le n \\ le 39 $产生40个素数。但是,当$ n = 40时,40 ^ 2 + 40 + 41 = 40(40 + 1)+ 41 $可被41整除,当然$ n = 41时,41 ^ 2 + 41 + 41 $显然可以被整除41.发现了令人难以置信的公式$ n ^ 2 - 79n + 1601 $,它为连续值$ 0 \\ le n \\ le 79 $产生80个素数。系数-79和1601的乘积是-126479。考虑形式的二次方:
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
$ n ^ 2 + an + b $,其中$ | a | <range $和$ | b | \\ le $ $其中$ | n | $是$ n $的模数/绝对值,例如$ | 11 | = 11 $和$ | -4 | = 4 $
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
找到系数的乘积,$ a $和$ b $,用于生成连续值$ n $的最大素数数的二次表达式,从$ n = 0 $开始。
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
# --hints--
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
`quadraticPrimes(200)`应返回-4925。
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
|
|
|
|
```js
|
2020-12-16 07:37:30 +00:00
|
|
|
|
assert(quadraticPrimes(200) == -4925);
|
2018-10-10 22:03:03 +00:00
|
|
|
|
```
|
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
`quadraticPrimes(500)`应返回-18901。
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
```js
|
|
|
|
|
assert(quadraticPrimes(500) == -18901);
|
|
|
|
|
```
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
`quadraticPrimes(800)`应返回-43835。
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
```js
|
|
|
|
|
assert(quadraticPrimes(800) == -43835);
|
|
|
|
|
```
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
`quadraticPrimes(1000)`应返回-59231。
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
|
|
|
|
```js
|
2020-12-16 07:37:30 +00:00
|
|
|
|
assert(quadraticPrimes(1000) == -59231);
|
2018-10-10 22:03:03 +00:00
|
|
|
|
```
|
2020-08-13 15:24:35 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
# --solutions--
|
|
|
|
|
|