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project_euler_37.rb
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project_euler_37.rb
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# Truncatable primes
# Problem 37
# The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.
#
# Find the sum of the only eleven primes that are both truncatable from left to right and right to left.
#
# NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
def prime?(num)
return false if num < 2
(2..(Math.sqrt(num).to_i)).each do |n|
return false if num % n == 0
end
true
end
def truncatable_prime?(n)
return false if n < 10
if prime?(n)
n = n.to_s
(n.length - 1).times do |i|
if !prime?(n[0..i].to_i) || !prime?(n[i + 1..-1].to_i)
return false
end
end
true
else
false
end
end
truncatable_primes = []
loop.each_with_index do |_, i|
truncatable_primes << i if truncatable_prime?(i)
break if truncatable_primes.size == 11
end
puts truncatable_primes.inject(:+)