21 lines
1017 B
YAML
21 lines
1017 B
YAML
title: Quadratic primes
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url: http://projecteuler.net/problem=27
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desc: |
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Euler discovered the remarkable quadratic formula:
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n² + n + 41
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It turns out that the formula will produce 40 primes for the consecutive values n = 0 to 39. However, when n = 40, 402 + 40 + 41 = 40(40 + 1) + 41 is divisible by 41, and certainly when n = 41, 41² + 41 + 41 is clearly divisible by 41.
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The incredible formula n² - 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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n² + an + b, where |a| < 1000 and |b| < 1000
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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
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solution: Bruteforce
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solutions:
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solve.php:
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desc: Basic Solution - needs BCMath
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language: php
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