Task: N-smooth numbers



C#: using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;

namespace NSmooth {
    class Program {
        static readonly List<BigInteger> primes = new List<BigInteger>();
        static readonly List<int> smallPrimes = new List<int>();

        static Program() {
            primes.Add(2);
            smallPrimes.Add(2);

            BigInteger i = 3;
            while (i <= 521) {
                if (IsPrime(i)) {
                    primes.Add(i);
                    if (i <= 29) {
                        smallPrimes.Add((int)i);
                    }
                }
                i += 2;
            }
        }

        static bool IsPrime(BigInteger value) {
            if (value < 2) return false;

            if (value % 2 == 0) return value == 2;
            if (value % 3 == 0) return value == 3;

            if (value % 5 == 0) return value == 5;
            if (value % 7 == 0) return value == 7;

            if (value % 11 == 0) return value == 11;
            if (value % 13 == 0) return value == 13;

            if (value % 17 == 0) return value == 17;
            if (value % 19 == 0) return value == 19;

            if (value % 23 == 0) return value == 23;

            BigInteger t = 29;
            while (t * t < value) {
                if (value % t == 0) return false;
                value += 2;

                if (value % t == 0) return false;
                value += 4;
            }

            return true;
        }

        static List<BigInteger> NSmooth(int n, int size) {
            if (n < 2 || n > 521) {
                throw new ArgumentOutOfRangeException("n");
            }
            if (size < 1) {
                throw new ArgumentOutOfRangeException("size");
            }

            BigInteger bn = n;
            bool ok = false;
            foreach (var prime in primes) {
                if (bn == prime) {
                    ok = true;
                    break;
                }
            }
            if (!ok) {
                throw new ArgumentException("must be a prime number", "n");
            }

            BigInteger[] ns = new BigInteger[size];
            ns[0] = 1;
            for (int i = 1; i < size; i++) {
                ns[i] = 0;
            }

            List<BigInteger> next = new List<BigInteger>();
            foreach (var prime in primes) {
                if (prime > bn) {
                    break;
                }
                next.Add(prime);
            }

            int[] indices = new int[next.Count];
            for (int i = 0; i < indices.Length; i++) {
                indices[i] = 0;
            }
            for (int m = 1; m < size; m++) {
                ns[m] = next.Min();
                for (int i = 0; i < indices.Length; i++) {
                    if (ns[m] == next[i]) {
                        indices[i]++;
                        next[i] = primes[i] * ns[indices[i]];
                    }
                }
            }

            return ns.ToList();
        }

        static void Println<T>(IEnumerable<T> nums) {
            Console.Write('[');

            var it = nums.GetEnumerator();
            if (it.MoveNext()) {
                Console.Write(it.Current);
            }
            while (it.MoveNext()) {
                Console.Write(", ");
                Console.Write(it.Current);
            }

            Console.WriteLine(']');
        }

        static void Main() {
            foreach (var i in smallPrimes) {
                Console.WriteLine("The first {0}-smooth numbers are:", i);
                Println(NSmooth(i, 25));
                Console.WriteLine();
            }
            foreach (var i in smallPrimes.Skip(1)) {
                Console.WriteLine("The 3,000 to 3,202 {0}-smooth numbers are:", i);
                Println(NSmooth(i, 3_002).Skip(2_999));
                Console.WriteLine();
            }
            foreach (var i in new int[] { 503, 509, 521 }) {
                Console.WriteLine("The 30,000 to 3,019 {0}-smooth numbers are:", i);
                Println(NSmooth(i, 30_019).Skip(29_999));
                Console.WriteLine();
            }
        }
    }
}





Python: primes = [2, 3, 5, 7, 11, 13, 17, 19, 23]

def isPrime(n):
    if n < 2:
        return False

    for i in primes:
        if n == i:
            return True
        if n % i == 0:
            return False
        if i * i > n:
            return True
    print "Oops,", n, " is too large"

def init():
    s = 24
    while s < 600:
        if isPrime(s - 1) and s - 1 > primes[-1]:
            primes.append(s - 1)
        if isPrime(s + 1) and s + 1 > primes[-1]:
            primes.append(s + 1)
        s += 6

def nsmooth(n, size):
    if n < 2 or n > 521:
        raise Exception("n")
    if size < 1:
        raise Exception("n")

    bn = n
    ok = False
    for prime in primes:
        if bn == prime:
            ok = True
            break
    if not ok:
        raise Exception("must be a prime number: n")

    ns = [0] * size
    ns[0] = 1

    next = []
    for prime in primes:
        if prime > bn:
            break
        next.append(prime)

    indicies = [0] * len(next)
    for m in xrange(1, size):
        ns[m] = min(next)
        for i in xrange(0, len(indicies)):
            if ns[m] == next[i]:
                indicies[i] += 1
                next[i] = primes[i] * ns[indicies[i]]

    return ns

def main():
    init()

    for p in primes:
        if p >= 30:
            break
        print "The first", p, "-smooth numbers are:"
        print nsmooth(p, 25)
        print

    for p in primes[1:]:
        if p >= 30:
            break
        print "The 3000 to 3202", p, "-smooth numbers are:"
        print nsmooth(p, 3002)[2999:]
        print

    for p in [503, 509, 521]:
        print "The 30000 to 3019", p, "-smooth numbers are:"
        print nsmooth(p, 30019)[29999:]
        print

main()