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.
To run the tests, run the command
busted from within the exercise directory.
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.
A variation on Problem 7 at Project Euler http://projecteuler.net/problem=7
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
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)
local function isPrime(n) if n <= 3 then return n > 1 end if n % 2 == 0 or n % 3 == 0 then return false end for i = 5, math.sqrt(n), 6 do if n % i == 0 or n % (i + 2) == 0 then return false end end return true end local function nth(n) assert(n > 0) if n < 3 then return n + 1 end local prime local i, j, k = 2, 5, 1 repeat local p = k%2 == 0 and j+2 or j if isPrime(p) then i = i + 1 prime = p end j = j + (k%2 == 0 and 6 or 0) k = k + 1 until i == n return prime end return nth
A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.
Here are some questions to help you reflect on this solution and learn the most from it.