Project Euler #10 in Ruby. Three ways to sum primes below 2 million

Question:


Add all prime numbers smaller than 2,000,000.

The first method is done by deriving own is_prime? method:

# First Method
def is_prime(n)
    if n  1
    elsif (n % 2 == 0 || n % 3 == 0)
        return false
    else
        (5..Math.sqrt(n).ceil).step(6) do |i|
            if (n % i == 0 || n % (i+2) == 0)
                return false
            end
        end
        return true
    end
end

start_time = Time.now
range = 2000000
array_of_primes = []

(1..range).each do |n|
    if is_prime(n)
        array_of_primes << n
    end
end

answer = array_of_primes.inject(:+)
duration = Time.now - start_time

puts "Sum of primes below #{range} is #{answer}. Took #{duration} s to calculate using my first method."

Second Method is using Ruby's Prime.is_prime?(n) method:

# Second Method
require 'prime'
array_of_primes = []
start_time = Time.now
(1..range).each do |n|
    if Prime.prime?(n)
        array_of_primes << n
    end
end

answer = array_of_primes.inject(:+)
duration = Time.now - start_time

puts "Sum of primes below #{range} is #{answer}. Took #{duration} s to calculate using my Ruby's Prime.prime? method."

Third method is the simplest form - by using Ruby's Prime.each(2000000) method

# Third Method - Prime.each
start_time = Time.now
answer = Prime.each(range).inject(:+)
duration = Time.now - start_time

puts "Sum of primes below #{range} is #{answer}. Took #{duration} s to calculate using my Ruby's Prime.each method."

All methods gave the correct answer, but the interesting findings is they have drastically different performance, as shown below are the outputs of duration for the computation from each method.

`Sum of primes below 2000000 is 142913828922. Took 3.694159 s to calculate using my first method.
Sum of primes below 2000000 is 142913828922. Took 39.370195 s to calculate using my Ruby's Prime.prime? method.
Sum of primes below 2000000 is 142913828922. Took 0.300214 s to calculate using my Ruby's Prime.e

You should use implicit looping (filtering):

def primes_below(limit)
    (1..limit).select{|i| Prime.prime?(i)}
end

You should use the built-in profiler:

require 'benchmark'
puts Benchmark.measure{primes_below(limit).inject(:+)}

StackExchange Code Review Q#85812, answer score: 2