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.
In order to run the tests for this track, you will need to install DUnitX. Please see the installation instructions for more information.
If Delphi is properly installed, and
*.dpr file types have been associated with Delphi, then double clicking the supplied
*.dpr file will start Delphi and load the exercise/project.
control + F9 is the keyboard shortcut to compile the project or pressing
F9 will compile and run the project.
Alternatively you may opt to start Delphi and load your project via. the
File drop down menu.
Note that, when trying to submit an exercise, make sure the exercise file you're submitting is in the
For example, if you're submitting
ubob.pas for the Bob exercise, the submit command would be something like
exercism submit <path_to_exercism_dir>/delphi/bob/ubob.pas.
A variation on Problem 7 at Project Euler http://projecteuler.net/problem=7
It's possible to submit an incomplete solution so you may request help from a mentor.
unit uNthPrimeTests; interface uses DUnitX.TestFramework; const CanonicalVersion = '18.104.22.168'; type [TestFixture] TNthPrimeTest = class(TObject) public [Test] // [Ignore('Comment the "[Ignore]" statement to run the test')] procedure there_is_no_zeroth_prime; [Test] [Ignore] procedure first_prime; [Test] [Ignore] procedure second_prime; [Test] [Ignore] procedure sixth_prime; [Test] [Ignore] procedure big_prime; end; implementation uses System.SysUtils, uNthPrime; procedure TNthPrimeTest.first_prime; begin Assert.AreEqual(2, NthPrime(1)); end; procedure TNthPrimeTest.second_prime; begin Assert.AreEqual(3, NthPrime(2)); end; procedure TNthPrimeTest.sixth_prime; begin Assert.AreEqual(13, NthPrime(6)); end; procedure TNthPrimeTest.big_prime; begin Assert.AreEqual(104743, NthPrime(10001)); end; procedure TNthPrimeTest.there_is_no_zeroth_prime; begin Assert.WillRaiseWithMessage(procedure begin NthPrime(0); end , EArgumentOutOfRangeException, 'there is no zeroth prime'); end; initialization TDUnitX.RegisterTestFixture(TNthPrimeTest); end.
unit uNthPrime; interface uses System.Math, System.SysUtils; type EArgumentOutOfRangeException = class(Exception); function NthPrime(Number: Integer): Integer; implementation function Sieve(Candidate: Integer): Boolean; var Factor: Integer; begin // Since primes are rare, default to non-prime Result := False; // A prime number must be a positive integer greater than one. If the // candidate number doesn't meet this criterion, leave early. if Candidate < 2 then exit; // If Candidate is two, we can short cut here, since two is the first prime, // and is also the only even prime. if Candidate = 2 then begin Result := True; exit; end; // Three is the first odd prime, so we start there Factor := 3; // We only need to check 3..Sqrt(Candidate). As part of this we need to // for Candidate to be a real number for Sqrt(). while Factor <= Trunc(Sqrt(Candidate * 1.0)) do begin // Is this factor a prime factor? if Candidate mod Factor = 0 then // This factor is a factor for Candidate, so Candidate isn't prime. Exit; // Try the next possible factor Inc(Factor, 2); end; // If we got this far, Candidate is prime Result := True; end; function NthPrime(Number: Integer): Integer; var Count: Integer; Current: Integer; begin // The count of primes must be a positive integer. if Number < 1 then raise EArgumentOutOfRangeException.Create('there is no zeroth prime'); // We handle the first prime differently than all others. The first prime is // two, which is also the only even prime. if Number = 1 then begin Result := 2; Exit; end; // We already know the first prime, so we set the count to one. This is done // to simplify the code in the loop. Count := 1; // Set the current candidate to start at one Current := 1; // We need to keep looping until we find the correct prime while Count < Number do begin // Since we know all remaining primes are odd, we move to the // next odd candidate Inc(Current, 2); // Is the current candidate prime? if Sieve(Current) then // Yes - increment the count of primes Inc(Count); end; // We found the correct prime, so return it Result := Current; end; end.
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.