Created
January 17, 2019 17:03
-
-
Save imtiaz-emu/f36feafbfa79ba5272406c93e5af4ab6 to your computer and use it in GitHub Desktop.
Finology challenge: Sum of primes below 2 million and sum of consecutive prime below 1 million to be a prime.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
''' | |
Problem 1 | |
The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17 | |
Find the sum of all the primes below 2 million. | |
Problem 2 | |
Which prime, below one million, can be written as the sum of the | |
most consecutive primes? | |
''' | |
class GenerateSolution | |
def sieve_of_eratosthenes(n) | |
primes = (0..n).to_a | |
primes[0] = primes[1] = nil | |
primes.each do |p| | |
next unless p | |
break if p * p > n | |
(p*p).step(n, p) { |m| primes[m] = nil } | |
end | |
primes.compact | |
end | |
def prime?(number) | |
return false if (number <= 1) | |
return true if (number <= 3) | |
return false if (number % 2 == 0 || number % 3 == 0) | |
i = 5 | |
while (i*i < number) | |
return false if (number % i == 0 || number % (i+2) == 0) | |
i += 6 | |
end | |
return true | |
end | |
def consecutive_prime_sum(primes, max_range) | |
max_sum = 0 | |
max_no_of_primes = 0 | |
for i in (0...primes.count) | |
for j in (i...primes.count) | |
sum, counter = primes[i..j].reduce(:+), j - i + 1 | |
break if sum > max_range | |
if (prime?(sum)) && (max_no_of_primes < counter) | |
max_sum = sum | |
max_no_of_primes = counter | |
end | |
end | |
end | |
return max_sum | |
end | |
end | |
test1_max_range = 2000000 | |
test2_max_range = 1000000 | |
solution = GenerateSolution.new | |
start = Time.now | |
primes = solution.sieve_of_eratosthenes(test1_max_range) | |
puts "Sum of primes below #{test1_max_range} = #{primes.reduce(:+)}" | |
puts "The prime number below #{test2_max_range}, can be written as the sum of the most consecutive primes = #{solution.consecutive_prime_sum(primes, test2_max_range)}" | |
finish = Time.now | |
puts "Program excecution time = #{finish - start}" |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment