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---
id: 5900f3871000cf542c50fe9a
title: 问题27二次素数
title: 'Problem 27: Quadratic primes'
challengeType: 5
videoUrl: ''
forumTopicId: 301919
dashedName: problem-27-quadratic-primes
---
# --description--
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 = 4040 + 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
Euler discovered the remarkable quadratic formula:
$ 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 $
<div style='margin-left: 4em;'>$n^2 + n + 41$</div>
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。
It turns out that the formula will produce 40 primes for the consecutive integer values $0 \\le n \\le 39$. However, when $n = 40, 40^2 + 40 + 41 = 40(40 + 1) + 41$ is divisible by 41, and certainly when $n = 41, 41^2 + 41 + 41$ is clearly divisible by 41.
The incredible formula $n^2 - 79n + 1601$ was discovered, which produces 80 primes for the consecutive values $0 \\le n \\le 79$. The product of the coefficients, 79 and 1601, is 126479.
Considering quadratics of the form:
<div style='margin-left: 4em;'>
$n^2 + an + b$, where $|a| < range$ and $|b| \le range$<br>
where $|n|$ is the modulus/absolute value of $n$<br>
e.g. $|11| = 11$ and $|-4| = 4$<br>
</div>
Find the product of the coefficients, $a$ and $b$, for the quadratic expression that produces the maximum number of primes for consecutive values of $n$, starting with $n = 0$.
# --hints--
`quadraticPrimes(200)`应返回-4925。
`quadraticPrimes(200)` should return a number.
```js
assert(typeof quadraticPrimes(200) === 'number');
```
`quadraticPrimes(200)` should return -4925.
```js
assert(quadraticPrimes(200) == -4925);
```
`quadraticPrimes(500)`应返回-18901
`quadraticPrimes(500)` should return -18901.
```js
assert(quadraticPrimes(500) == -18901);
```
`quadraticPrimes(800)`应返回-43835
`quadraticPrimes(800)` should return -43835.
```js
assert(quadraticPrimes(800) == -43835);
```
`quadraticPrimes(1000)`应返回-59231
`quadraticPrimes(1000)` should return -59231.
```js
assert(quadraticPrimes(1000) == -59231);