//
// factor -- Perform prime factorization on one or a range of integers.
//
// 10-Sep-2010 tvb www.LeapSecond.com/tools
//

#include <stdio.h>
#include <stdlib.h>

void factor (long N)
{
    char c;
    long e, f, n, i;

    if (N < 2) return;

    printf("%ld", N);
    c = '=';
    e = 0;
    n = N;
    for (f = 2; f <= n / f; f += i) {
        while ((n % f) == 0) {
            n /= f;
            e += 1;
        }
        if (e != 0) {
            printf(" %c %ld", c, f);
            if (e > 1) {
                printf("^%ld",  e);
            }
            c = '*';
            e = 0;
        }
        i = (f > 2) ? 2 : 1;
    }
    if (n == N) {
        printf(" prime");

    } else if (n != 1) {
        printf(" %c %ld", c, n);
    }
    printf("\n");
}

void main (int argc, char *argv[])
{
    long n, m;

    if (argc < 2 || argc > 3) {
        fprintf(stderr, "Usage: factor number [limit]\n");
        exit(1);
    }

    if (argc >= 2) {
        n = m = atol(argv[1]);
    }
    if (argc >= 3) {
        m = atol(argv[2]);
    }

    for ( ; n <= m; n += 1) {
        factor(n);
    }
}