21 lines
846 B
Markdown
21 lines
846 B
Markdown
Euler discovered the remarkable quadratic formula:
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~~~
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n^2 + n + 41
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~~~
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It turns out that the formula will produce 40 primes for the consecutive values n = 0 to 39.
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However, when `n = 40`, `402 + 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 n = 0 to 79. The product of the coefficients, -79 and 1601, is -126479.
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Considering quadratics of the form:
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~~~
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n^2 + an + b, where |a| < 1000 and |b| < 1000
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~~~
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where `|n|` is the modulus/absolute value of n
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e.g. `|11| = 11` and `|-4| = 4`
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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`. |