2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Then mark all multiples of 2:
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 x x x x x x x x xMove to the next unmarked number, which in this case is 3, then mark all its multiples:
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 x x x x x x x x x x xContinue in this fashion, marking all multiples of the next unmarked number until there are no new unmarked numbers. The numbers which survive this marking process (the Sieve of Eratosthenses) are primes. (You should complete this marking process yourself).
The new part of the C language that you will have to learn in order to do this program is the array.
PSEUDOPROGRAM: Set up an array of integers z[N]: for i from 0 to N, set z[i] = i. for i from 2 to N, mark all multiples of i by setting them to zero for i from 2 to N, print all unmarked multiples.Your program should be as short and elegant as possible, while still being clearly understandable. Below is an outline for the program
#define N 20 /* use small number for testing */ main(){ int z[N]; /* array of integers, z[0], ... z[N-1] */ for ( i = 0; i < N; i++ ) initialize z[i]; for ( i = 2; i < N; i++ ) mark the multiples of i; /* this marking can be done with one for and one if statement */ for ( i = 2; i < N; i++ ) print the unmarked entries of z; }
p(n) = Number of primes less than n
1/2 + 1/3 + 1/5 + 1/7 + 1/11 + 1/13 + ...constructed by adding the reciprocals of the primes.