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# Naytoxp's solution

## to Nth Prime in the Lua Track

Published at Jul 08 2020 · 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)``````
``````function GetPrime(s)
local c, n, f = 0, 1, false
repeat
if n == 2 or IsPrime(n) then
if c == s then
f = true return n
end
c = c + 1
end
n = n + 1
until f
end

local sqrt = math.sqrt

function IsPrime(n)
if n % 2 == 0 then return false	end

for i = 3, sqrt(n) + 1, 1 do
if n % i == 0 then return false end
end

return true
end

return function(n)
if n > 0 then
return GetPrime(n)
else return error()
end
end``````