# Additive primes: primes whose sum of digits is also prime
# Check if a number is prime
def prime?(n)
return false if n < 2
return n == 2 if n.even?
return n == 3 if n % 3 == 0
i = 5
while i * i <= n
return false if n % i == 0
i += 2
return false if n % i == 0
i += 4
end
true
end
# Compute the sum of digits of a number
def sum_digits(n)
sum = 0
while n > 0
sum += n % 10
n /= 10
end
sum
end
# Check if a number is an additive prime
def additive_prime?(n)
prime?(n) && prime?(sum_digits(n))
end
TOP = 500
count = 0
line = ""
(1...TOP).each do |n|
if additive_prime?(n)
line << n.to_s.rjust(3) + " "
count += 1
if count % 10 == 0
puts line.rstrip
line = ""
end
end
end
puts line.rstrip unless line.empty?
puts
puts "Total additive primes = #{count}"
=begin
run:
2 3 5 7 11 23 29 41 43 47
61 67 83 89 101 113 131 137 139 151
157 173 179 191 193 197 199 223 227 229
241 263 269 281 283 311 313 317 331 337
353 359 373 379 397 401 409 421 443 449
461 463 467 487
Total additive primes = 54
=end
