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###
# 10001st prime
# Problem 7
#
# By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th
# prime is 13.
# What is the 10 001st prime number?
###
using Printf
using Base.Iterators
# Can't use eratosthenes sieve since we don't know when to stop (no predefined list of numbers)
# A algorithm that caches the previous found primes should be faster
function is_prime(n)
if n == 2 || n == 3 || n == 5
return true
end
if n % 2 == 0 || n % 3 == 0 || n % 5 == 0
return false
end
for d in 6:6:ceil(Integer, √n) + 1
if n % (d - 1) == 0 || n % (d + 1) == 0
return false
end
end
true
end
const PRIME_INDEX = 10_001
result = (
Iterators.countfrom(2)
|> x -> Iterators.filter(is_prime, x)
|> x -> Iterators.take(x, PRIME_INDEX)
|> collect
)[end]
println(result)
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