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problem 27 · 11 lines

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<p>Euler discovered the remarkable quadratic formula:</p>
<p class="center">$n^2 + n + 41$</p>
<p>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 $41$.</p>
<p>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 $-126479$.</p>
<p>Considering quadratics of the form:</p>
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$n^2 + an + b$, where $|a| &lt; 1000$ and $|b| \le 1000$<br/><br/><div>where $|n|$ is the modulus/absolute value of $n$<br/>e.g. $|11| = 11$ and $|-4| = 4$</div>
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<p>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 $n = 0$.</p>
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