chore(i8n,learn): processed translations
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Mrugesh Mohapatra
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---
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id: 5900f3871000cf542c50fe9a
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title: 问题27:二次素数
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title: 'Problem 27: Quadratic primes'
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challengeType: 5
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videoUrl: ''
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forumTopicId: 301919
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dashedName: problem-27-quadratic-primes
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---
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# --description--
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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 $产生80个素数。系数-79和1601的乘积是-126479。考虑形式的二次方:
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Euler discovered the remarkable quadratic formula:
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$ 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 $
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<div style='margin-left: 4em;'>$n^2 + n + 41$</div>
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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。
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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.
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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.
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Considering quadratics of the form:
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<div style='margin-left: 4em;'>
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$n^2 + an + b$, where $|a| < range$ and $|b| \le range$<br>
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where $|n|$ is the modulus/absolute value of $n$<br>
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e.g. $|11| = 11$ and $|-4| = 4$<br>
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</div>
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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 $n = 0$.
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# --hints--
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`quadraticPrimes(200)`应返回-4925。
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`quadraticPrimes(200)` should return a number.
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```js
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assert(typeof quadraticPrimes(200) === 'number');
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```
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`quadraticPrimes(200)` should return -4925.
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```js
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assert(quadraticPrimes(200) == -4925);
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```
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`quadraticPrimes(500)`应返回-18901。
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`quadraticPrimes(500)` should return -18901.
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```js
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assert(quadraticPrimes(500) == -18901);
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```
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`quadraticPrimes(800)`应返回-43835。
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`quadraticPrimes(800)` should return -43835.
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```js
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assert(quadraticPrimes(800) == -43835);
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```
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`quadraticPrimes(1000)`应返回-59231。
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`quadraticPrimes(1000)` should return -59231.
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```js
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assert(quadraticPrimes(1000) == -59231);
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