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problem_27.rb
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problem_27.rb
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# Euler discovered the remarkable quadratic formula:
# n² + n + 41
# 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.
# 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.
# 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.
require 'prime'
require 'pry'
def formula(n:, a:, b:)
( n ** 2 ) + ( a * n ) + b
end
array = (-999..999).to_a
combinations = []
highest_combo = {a: '', b: '', count: 0}
array.each do |a|
array.each do |b|
combinations << [a, b]
end
end
combinations.each do |a, b|
count = 0
(0..1000).to_a.each do |n|
number = formula(n: n, a: a, b: b)
if number.prime?
count += 1
else
break
end
end
if count > highest_combo[:count]
highest_combo[:a] = a
highest_combo[:b] = b
highest_combo[:count] = count
p "a: #{a}, b: #{b}, count: #{count}"
end
end
p highest_combo