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.

Make sure you have read the C page on the Exercism site. This covers the basic information on setting up the development environment expected by the exercises.

Get the first test compiling, linking and passing by following the three rules of test-driven development.

The included makefile can be used to create and run the tests using the `test`

task.

```
make test
```

Create just the functions you need to satisfy any compiler errors and get the test to fail. Then write just enough code to get the test to pass. Once you've done that, move onto the next test.

As you progress through the tests, take the time to refactor your implementation for readability and expressiveness and then go on to the next test.

Try to use standard C99 facilities in preference to writing your own low-level algorithms or facilities by hand.

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.

```
#include "vendor/unity.h"
#include "../src/nth_prime.h"
void setUp(void)
{
}
void tearDown(void)
{
}
void test_first_prime(void)
{
TEST_ASSERT_EQUAL_UINT32(2, nth(1));
}
void test_second_prime(void)
{
TEST_IGNORE(); // delete this line to run test
TEST_ASSERT_EQUAL_UINT32(3, nth(2));
}
void test_sixth_prime(void)
{
TEST_IGNORE();
TEST_ASSERT_EQUAL_UINT32(13, nth(6));
}
void test_large_prime(void)
{
TEST_IGNORE();
TEST_ASSERT_EQUAL_UINT32(104743, nth(10001));
}
void test_weird_case(void)
{
TEST_IGNORE();
TEST_ASSERT_EQUAL_UINT32(0, nth(0));
}
int main(void)
{
UnityBegin("test/test_nth_prime.c");
RUN_TEST(test_first_prime);
RUN_TEST(test_second_prime);
RUN_TEST(test_sixth_prime);
RUN_TEST(test_large_prime);
RUN_TEST(test_weird_case);
UnityEnd();
return 0;
}
```

```
CFLAGS = -std=c99
CFLAGS += -g
CFLAGS += -Wall
CFLAGS += -Wextra
CFLAGS += -pedantic
CFLAGS += -Werror
VFLAGS = --quiet
VFLAGS += --tool=memcheck
VFLAGS += --leak-check=full
VFLAGS += --error-exitcode=1
test: tests.out
@./tests.out
memcheck: tests.out
@valgrind $(VFLAGS) ./tests.out
@echo "Memory check passed"
clean:
rm -rf *.o *.out *.out.dSYM
tests.out: test/test_nth_prime.c src/nth_prime.c src/nth_prime.h
@echo Compiling $@
@cc $(CFLAGS) src/nth_prime.c test/vendor/unity.c test/test_nth_prime.c -o tests.out -lm
```

```
#include "nth_prime.h"
#include <stdlib.h>
#include <stdint.h>
#include <math.h>
uint32_t nth(const uint32_t n)
{
if (!n)
return 0;
/* https://en.wikipedia.org/wiki/Prime_number_theorem\
#Approximations_for_the_nth_prime_number */
uint32_t limit =
(uint32_t) (n * log(n) + n * log(log(n)));
if (limit < 6)
limit = 6;
int *sieve = (int*) malloc(sizeof(int) * (limit + 1));
if (sieve == NULL)
return 0;
uint32_t i, j, upto;
for (i = 2; i <= limit; i++)
sieve[i] = 1;
upto = (uint32_t) sqrt(limit);
for (i = 2; i <= upto; i++)
if (sieve[i] == 1)
for (j = i*i; j <= limit; j += i)
sieve[j] = 0;
i = 0;
for (j = 2; j <= limit; j++)
if (sieve[j] == 1)
if (++i == n) {
free(sieve);
return j;
}
free(sieve);
return 0;
}
```

```
#ifndef NTH_PRIME_H
#define NTH_PRIME_H
#include <stdint.h>
uint32_t nth(const uint32_t n);
#endif
```

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.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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