Project Euler/27

Problem Statement

Euler discovered a quadratic formula that would generate primes:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle n^2 + n + 41 }

for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 0 \leq n \leq 39}

Another formula, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle n^2 - 79n + 1601} , was discovered, that produces 80 primes for consecutive values $0\leq n\leq 79$

Now consider equadratics of the form

$n^{2}+an+b$

where $|a|\leq 1000$, $|b|\leq 1000$

Find product of coefficients a, b for the quadratic expression producing the maximum number of primes for consecutive values of n, starting with n = 0

Solution

Solution: https://git.charlesreid1.com/cs/euler/src/branch/master/java/Problem027.java

Implemented 2 nested for loops to search for parameter values by brute force. Keep running track of consecutive number of primes generated, and best a/b. Return them at the end.

This algorithm did not have any trickness, or require any special optimization. Used a standard prime number sieve, nothing special.