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027.js
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027.js
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/*
Quadratic primes
Problem 27
Euler discovered the remarkable quadratic formula:
n2+n+41
It turns out that the formula will produce 40 primes for the consecutive
integer values 0≤n≤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.
The incredible formula n2−79n+1601 was discovered, which produces 80
primes for the consecutive values 0≤n≤79. The product of the coefficients,
−79 and 1601, is −126479.
Considering quadratics of the form:
n2+an+b, where |a|<1000 and |b|≤1000
where |n| is the modulus/absolute value of n
e.g. |11|=11 and |−4|=4
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.
*/
const isPrime = require('./util/is-prime');
let max = 0, a = 0, b = 0;
// for each million algorithms
for (let i = -999; i <= 1000; i++) {
for (let j = -1000; j <= 1000; j++) {
let n = -1;
let result;
do {
n++;
result = formula(n, i, j);
} while (isPrime(result));
// keep going
if (n > max) {
a = i;
b = j;
max = n;
}
}
}
const product = a * b;
console.log(`The product of the 2 coefficients that create the longest consecutive primes is ${product.toLocaleString()}. n^2 + ${a}n + ${b}`);
function formula(n, a, b) {
return (n * n) + (a * n) + b;
}