Task: N-smooth numbers
C: #include <stdbool.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <gmp.h>

void* xmalloc(size_t n) {
    void* ptr = malloc(n);
    if (ptr == NULL) {
        fprintf(stderr, "Out of memory\n");
        exit(1);
    }
    return ptr;
}

void* xrealloc(void* p, size_t n) {
    void* ptr = realloc(p, n);
    if (ptr == NULL) {
        fprintf(stderr, "Out of memory\n");
        exit(1);
    }
    return ptr;
}

bool is_prime(uint32_t n) {
    if (n == 2)
        return true;
    if (n < 2 || n % 2 == 0)
        return false;
    for (uint32_t p = 3; p * p <= n; p += 2) {
        if (n % p == 0)
            return false;
    }
    return true;
}



uint32_t find_primes(uint32_t from, uint32_t to, uint32_t** primes) {
    uint32_t count = 0, buffer_length = 16;
    uint32_t* buffer = xmalloc(sizeof(uint32_t) * buffer_length);
    for (uint32_t p = from; p <= to; ++p) {
        if (is_prime(p)) {
            if (count >= buffer_length) {
                uint32_t new_length = buffer_length * 2;
                if (new_length < count + 1)
                    new_length = count + 1;
                buffer = xrealloc(buffer, sizeof(uint32_t) * new_length);
                buffer_length = new_length;
            }
            buffer[count++] = p;
        }
    }
    *primes = buffer;
    return count;
}

void free_numbers(mpz_t* numbers, size_t count) {
    for (size_t i = 0; i < count; ++i)
        mpz_clear(numbers[i]);
    free(numbers);
}


mpz_t* find_nsmooth_numbers(uint32_t n, uint32_t count) {
    uint32_t* primes = NULL;
    uint32_t num_primes = find_primes(2, n, &primes);
    mpz_t* numbers = xmalloc(sizeof(mpz_t) * count);
    mpz_t* queue = xmalloc(sizeof(mpz_t) * num_primes);
    uint32_t* index = xmalloc(sizeof(uint32_t) * num_primes);
    for (uint32_t i = 0; i < num_primes; ++i) {
        index[i] = 0;
        mpz_init_set_ui(queue[i], primes[i]);
    }
    for (uint32_t i = 0; i < count; ++i)
        mpz_init(numbers[i]);
    mpz_set_ui(numbers[0], 1);
    for (uint32_t i = 1; i < count; ++i) {
        for (uint32_t p = 0; p < num_primes; ++p) {
            if (mpz_cmp(queue[p], numbers[i - 1]) == 0)
                mpz_mul_ui(queue[p], numbers[++index[p]], primes[p]);
        }
        uint32_t min_index = 0;
        for (uint32_t p = 1; p < num_primes; ++p) {
            if (mpz_cmp(queue[min_index], queue[p]) > 0)
                min_index = p;
        }
        mpz_set(numbers[i], queue[min_index]);
    }
    free_numbers(queue, num_primes);
    free(primes);
    free(index);
    return numbers;
}

void print_nsmooth_numbers(uint32_t n, uint32_t begin, uint32_t count) {
    uint32_t num = begin + count;
    mpz_t* numbers = find_nsmooth_numbers(n, num);
    printf("%u: ", n);
    mpz_out_str(stdout, 10, numbers[begin]);
    for (uint32_t i = 1; i < count; ++i) {
        printf(", ");
        mpz_out_str(stdout, 10, numbers[begin + i]);
    }
    printf("\n");
    free_numbers(numbers, num);
}

int main() {
    printf("First 25 n-smooth numbers for n = 2 -> 29:\n");
    for (uint32_t n = 2; n <= 29; ++n) {
        if (is_prime(n))
            print_nsmooth_numbers(n, 0, 25);
    }
    printf("\n3 n-smooth numbers starting from 3000th for n = 3 -> 29:\n");
    for (uint32_t n = 3; n <= 29; ++n) {
        if (is_prime(n))
            print_nsmooth_numbers(n, 2999, 3);
    }
    printf("\n20 n-smooth numbers starting from 30,000th for n = 503 -> 521:\n");
    for (uint32_t n = 503; n <= 521; ++n) {
        if (is_prime(n))
            print_nsmooth_numbers(n, 29999, 20);
    }
    return 0;
}

Java: import java.math.BigInteger;
import java.util.ArrayList;
import java.util.List;

public class NSmoothNumbers {

    public static void main(String[] args) {
        System.out.printf("show the first 25 n-smooth numbers for n = 2 through n = 29%n");
        int max = 25;
        List<BigInteger> primes = new ArrayList<>();
        for ( int n = 2 ; n <= 29 ; n++ ) {
            if ( isPrime(n) ) {
                primes.add(BigInteger.valueOf(n));
                System.out.printf("The first %d %d-smooth numbers:%n", max, n);
                BigInteger[] humble = nSmooth(max, primes.toArray(new BigInteger[0]));
                for ( int i = 0 ; i < max ; i++ ) {
                    System.out.printf("%s ", humble[i]);
                }
                System.out.printf("%n%n");
            }
        }
        
        System.out.printf("show three numbers starting with 3,000 for n-smooth numbers for n = 3 through n = 29%n");
        int count = 3;
        max = 3000 + count - 1;
        primes = new ArrayList<>();
        primes.add(BigInteger.valueOf(2));
        for ( int n = 3 ; n <= 29 ; n++ ) {
            if ( isPrime(n) ) {
                primes.add(BigInteger.valueOf(n));
                System.out.printf("The %d through %d %d-smooth numbers:%n", max-count+1, max, n);
                BigInteger[] nSmooth = nSmooth(max, primes.toArray(new BigInteger[0]));
                for ( int i = max-count ; i < max ; i++ ) {
                    System.out.printf("%s ", nSmooth[i]);
                }
                System.out.printf("%n%n");
            }
        }
        
        System.out.printf("Show twenty numbers starting with 30,000 n-smooth numbers for n=503 through n=521%n");
        count = 20;
        max = 30000 + count - 1;
        primes = new ArrayList<>();
        for ( int n = 2 ; n <= 521 ; n++ ) {
            if ( isPrime(n) ) {
                primes.add(BigInteger.valueOf(n));
                if ( n >= 503 && n <= 521 ) {
                    System.out.printf("The %d through %d %d-smooth numbers:%n", max-count+1, max, n);
                    BigInteger[] nSmooth = nSmooth(max, primes.toArray(new BigInteger[0]));
                    for ( int i = max-count ; i < max ; i++ ) {
                        System.out.printf("%s ", nSmooth[i]);
                    }
                    System.out.printf("%n%n");
                }
            }
        }

    }

    private static final boolean isPrime(long test) {
        if ( test == 2 ) {
            return true;
        }
        if ( test % 2 == 0 ) return false;
        for ( long i = 3 ; i <= Math.sqrt(test) ; i += 2 ) {
            if ( test % i == 0 ) {
                return false;
            }
        }
        return true;
    }

    private static BigInteger[] nSmooth(int n, BigInteger[] primes) {
        int size = primes.length;
        BigInteger[] test = new BigInteger[size];
        for ( int i = 0 ; i < size ; i++ ) {
            test[i] = primes[i];
        }
        BigInteger[] results = new BigInteger[n];
        results[0] = BigInteger.ONE;
        
        int[] indexes = new int[size];
        for ( int i = 0 ; i < size ; i++ ) {
            indexes[i] = 0;
        }
        
        for ( int index = 1 ; index < n ; index++ ) {
            BigInteger min = test[0];
            for ( int i = 1 ; i < size ; i++ ) {
                min = min.min(test[i]);
            }
            results[index] = min;
            
            for ( int i = 0 ; i < size ; i++ ) {
                if ( results[index].compareTo(test[i]) == 0 ) {
                    indexes[i] = indexes[i] + 1;
                    test[i] = primes[i].multiply(results[indexes[i]]);
                }
            }
        }
        return results;
    }

}