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# carlos157oliveira's solution

## to Nth Prime in the Lua Track

Published at Jan 10 2021 · 0 comments
Instructions
Test suite
Solution

Given a number n, determine what the nth prime is.

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.

If your language provides methods in the standard library to deal with prime numbers, pretend they don't exist and implement them yourself.

## Running the tests

To run the tests, run the command `busted` from within the exercise directory.

## Further information

For more detailed information about the Lua track, including how to get help if you're having trouble, please visit the exercism.io Lua language page.

## Source

A variation on Problem 7 at Project Euler http://projecteuler.net/problem=7

## Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

### nth-prime_spec.lua

``````local nth = require('nth-prime')

describe('nth-prime', function()
local function benchmark(f)
local start = os.clock()
f()
return os.clock() - start
end

it('should give 2 as the first prime', function()
assert.equal(2, nth(1))
end)

it('should give 3 as the second prime', function()
assert.equal(3, nth(2))
end)

it('should be able to calculate the nth prime for small n', function()
assert.equal(13, nth(6))
end)

it('should be able to calculate the nth prime for large n', function()
assert.equal(104743, nth(10001))
end)

it('should be efficient for large n', function()
local execution_time = benchmark(function()
nth(10001)
end)

assert(execution_time < 1, 'should take less than a second to execute')
end)

it('should raise an error for n <= 0', function()
assert.has_error(function()
nth(0)
end)

assert.has_error(function()
nth(-1)
end)
end)
end)``````
``````-- 2 and 3 are included initially because they are exceptions:
-- 2 is the initial prime number and 3 is only one unit ahead of 2
local primes = { 2, 3 }
local last_prime = primes[#primes]

local function is_new_prime(number)

for _, prime in pairs(primes) do
if number % prime == 0 then
return false
end
end

return true
end

return function(n)
assert(n > 0, '\'n\' should be an integer greater than 0!')

local number = last_prime + 2

if n <= #primes then
return primes[n]
end

--for number = last_prime + 2, math.huge, 2 do
while true do
if is_new_prime(number) then
table.insert(primes, number)
if #primes == n then
last_prime = number
return number
end
end
number = number + 2
end
end``````