Integer factorisation in C#

By Oct 23, 2016

Description:

Integer factorization in CSharp

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Factoring an integer is to write it as a product of prime factors.
We will factor only long unsigned integers.
The method consists in dividing the integer as many times as possible, primarily by prime numbers of a table, less or equal than its square root, and then optionally by integers not divisible by 2, 3, 5, 7, 11 and 13, less or equal than its square root.
To generate the table of primes, we use the method of primality test program.
The other table allows to browse all integers not divisible by 2, 3, 5, 7, 11, 13.
We noticed that there is a periodicity of 2x3x5x7x11x13 length in the divisibility by 2, 3, 5, 7, 11 and 13.
If  an integer d divides the given integer, then d is prime since the integer is not divisible by any integer greater than 2 and less than d.
The first number that divides the integer is prime, if not, a lower integer would divide it, which is impossible because the integer has already been divided by it.
The integer is divided as possible by this divider, replacing the number by the quotient.
Then continue with the next integers.

using System;
using System.Collections.Generic;
using System.Text;
 
namespace IntegerFactorization
{
    class Program
    {
 
     static ulong[] Factor(ulong n)
        {
            int[] primeTable ={
                2,3,5,7,11,13,17,19,23,29,31,37,41,43,
                47,53,59,61,67,71,73,79,83,89,
                97,101,103,107,109,113,127,131,137,139,
                149,151,157,163,167,173,179,181,191,193,
                197,199,211,223,227,229,233,239,241,251,
                257,263,269,271,277,281,283,293,307,311,
                313,317,331,337,347,349,353,359,367,373,
                379,383,389,397,401,409,419,421,431,433,
                439,443,449,457,461,463,467,479,487,491,
                499,503,509,521,523,541,547,557,563,569,
                571,577,587,593,599,601,607,613,617,619,
                631,641,643,647,653,659,661,673,677,683,
                691,701,709,719,727,733,739,743,751,757,
                761,769,773,787,797,809,811,821,823,827,
                829,839,853,857,859,863,877,881,883,887,
                907,911,919,929,937,941,947,953,967,971,
                977,983,991,997,1009,1013,1019,1021,1031,1033,
                1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,
                1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,
                1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,
                1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,
                1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,
                1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,
                1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,
                1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,
                1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,
                1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,
                1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,
                1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,
                1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,
                2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,
                2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,
                2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,
                2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,
                2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,
                2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,
                2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,
                2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,
                2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,
                2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,
                2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,
                2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,
                2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,
                3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,
                3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,
                3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,
                3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,
                3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,
                3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,
                3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,
                3613
            };
            // GenerateDivisibilityTable(13*11 * 7 * 5 * 3 * 2, 3613);
            // 3613 is successor of 3607
            byte[] dep ={
               0,4,6,6,2,6,6,6,10,8,4,2,4,6,8,
                6,4,8,4,6,2,6,6,4,2,4,6,12,2,4,
                2,10,2,10,2,4,2,4,8,10,2,4,6,8,6,
                4,2,6,4,6,8,4,8,4,8,6,4,6,2,4,
                6,2,6,6,4,6,6,2,6,6,4,2,10,12,2,
                4,2,4,6,2,6,4,2,16,2,6,4,2,10,6,
                8,4,2,4,2,12,6,10,2,4,6,2,12,4,2,
                4,8,6,4,2,4,2,12,10,6,2,4,6,2,6,
                4,2,4,6,6,2,6,4,2,10,6,8,10,2,4,
                8,6,4,6,2,4,6,2,6,6,6,4,6,8,4,
                2,4,2,10,12,2,4,2,10,2,6,4,2,4,6,
                6,2,10,2,6,4,14,6,4,2,4,8,10,6,2,
                4,6,2,6,6,4,2,4,8,6,4,2,4,12,2,
                12,4,2,4,6,2,6,4,2,10,6,2,6,4,8,
                4,6,8,4,2,4,2,4,14,4,6,2,10,8,6,
                4,2,4,6,2,10,2,4,2,12,10,2,4,6,6,
                2,6,4,6,6,6,2,6,6,6,4,6,12,2,4,
                6,8,6,10,2,4,8,6,6,4,2,4,6,2,6,
                4,2,6,10,2,10,2,6,4,6,8,4,6,12,2,
                6,4,2,6,4,6,12,2,4,2,4,14,4,6,2,
                4,6,2,6,10,2,10,2,6,4,2,4,12,2,10,
                2,4,6,6,2,6,6,4,6,6,2,10,2,6,4,
                6,8,4,2,6,4,8,6,4,6,2,4,6,8,6,
                4,2,10,2,6,4,2,6,10,2,10,6,2,4,8,
                6,4,2,4,6,6,2,6,4,8,4,6,8,4,2,
                4,2,4,8,6,4,6,12,2,6,6,4,6,6,2,
                6,4,2,4,2,10,2,12,6,4,6,2,10,2,4,
                6,6,8,4,2,6,18,4,2,4,2,4,8,10,6,
                2,4,8,6,6,6,4,6,2,6,4,6,2,10,2,
                10,2,4,2,4,6,2,6,4,2,4,6,6,8,6,
                6,4,6,8,4,2,4,2,12,6,4,12,6,2,6,
                6,4,2,4,6,8,6,4,2,10,2,10,2,4,2,
                4,6,2,10,2,4,6,8,6,4,2,6,4,6,8,
                4,6,2,4,8,6,4,8,4,6,2,6,10,6,6,
                2,6,6,4,2,10,2,10,2,4,2,4,6,8,4,
                2,10,6,2,6,4,2,6,10,8,4,2,4,14,6,
                4,6,2,4,6,2,12,4,2,4,8,10,2,4,2,
                10,2,10,6,2,4,8,6,4,2,4,6,6,2,6,
                4,2,10,6,8,6,6,4,8,6,4,6,2,4,6,
                2,6,6,6,4,6,2,6,4,2,4,2,10,12,2,
                4,2,10,2,6,4,2,4,12,2,10,2,10,14,4,
                2,4,2,4,8,6,10,2,4,6,2,12,4,2,4,
                6,2,6,4,2,4,14,12,4,2,4,6,2,6,4,
                2,4,6,6,2,6,4,2,6,4,6,8,4,6,2,
                4,14,4,6,2,10,2,6,6,4,2,4,6,12,2,
                4,2,12,10,2,4,2,10,2,6,4,6,6,6,2,
                6,4,2,6,4,6,8,6,4,6,8,16,2,4,6,
                2,6,6,4,2,4,8,6,4,2,6,10,2,10,2,
                4,2,4,6,8,4,2,16,2,6,4,8,4,6,12,
                2,4,2,4,8,6,4,6,2,4,6,8,10,2,4,
                6,2,6,4,2,4,2,10,2,10,2,4,6,6,2,
                6,6,4,6,6,2,6,6,6,4,6,12,2,6,4,
                8,6,4,6,2,4,14,6,4,2,10,2,6,4,2,
                4,2,10,2,10,2,6,4,8,6,4,6,6,6,2,
                6,4,8,4,6,8,4,2,4,2,4,14,4,6,6,
                6,2,6,6,4,2,10,2,6,4,2,4,12,2,10,
                2,6,4,6,2,6,6,4,6,6,12,2,6,10,8,
                4,2,4,2,4,8,10,6,2,4,8,6,6,4,2,
                4,6,2,6,4,8,10,2,10,6,2,4,6,2,6,
                4,2,4,6,6,2,6,6,6,4,6,8,4,2,4,
                2,4,8,6,4,8,10,2,6,6,4,6,6,8,4,
                2,4,2,10,2,12,4,2,4,6,2,10,2,4,6,
                8,6,4,2,6,4,14,4,6,2,4,8,6,4,6,
                2,4,6,2,6,6,10,6,2,6,10,2,10,2,10,
                2,4,2,4,6,2,6,4,2,10,6,8,4,2,6,
                4,6,8,4,2,4,2,12,6,4,6,6,6,2,12,
                4,2,4,8,6,6,4,2,10,2,10,6,2,4,6,
                2,6,4,2,4,6,8,6,4,2,10,6,8,6,4,
                2,4,8,6,4,8,4,6,2,6,12,4,6,2,6,
                4,2,4,2,10,12,2,4,2,10,8,4,2,4,6,
                6,2,10,2,6,18,4,2,4,6,8,6,4,6,2,
                4,6,2,6,6,4,2,4,6,2,10,2,4,12,2,
                12,4,2,4,8,6,4,2,4,6,6,2,6,4,2,
                6,4,6,8,4,2,6,4,14,4,6,2,10,2,6,
                6,4,2,4,6,2,10,2,4,2,22,2,4,2,4,
                6,2,6,4,6,12,2,6,4,2,10,6,8,4,2,
                4,6,8,6,10,2,4,6,2,12,4,2,4,6,2,
                6,4,2,6,12,10,2,4,2,4,6,8,4,2,4,
                12,2,6,4,2,6,4,6,12,6,2,4,8,6,4,
                6,2,4,6,2,6,10,2,4,6,8,4,2,4,2,
                10,2,10,2,4,12,2,6,6,4,6,6,2,6,4,
                2,6,4,6,8,6,6,4,8,10,6,2,4,6,8,
                6,4,2,12,6,4,2,4,2,10,2,10,2,4,2,
                4,8,6,4,2,10,6,2,6,4,8,4,6,8,4,
                2,4,2,4,8,6,4,6,6,6,8,6,4,2,4,
                6,2,6,4,2,4,2,10,2,10,2,10,6,2,6,
                4,2,4,6,6,8,6,6,10,12,2,4,2,4,8,
                10,6,2,4,8,6,6,4,2,4,6,2,6,4,6,
                2,10,2,10,2,6,4,6,2,6,4,6,6,6,2,
                6,6,6,4,6,8,4,2,4,2,4,14,4,8,4,
                6,2,6,6,4,2,10,8,4,2,4,12,2,10,2,
                4,2,4,6,2,12,4,6,8,10,2,6,4,6,8,
                4,6,2,4,8,6,4,6,2,4,6,2,6,6,4,
                6,6,2,6,6,6,10,2,10,6,2,4,6,2,6,
                4,2,10,6,2,6,4,2,6,4,6,8,4,2,4,
                2,12,6,4,6,2,10,2,12,4,6,8,6,4,2,
                4,2,10,2,16,2,4,6,2,10,2,4,6,6,2,
                6,4,2,10,14,6,4,2,4,8,6,4,6,2,4,
                6,2,6,6,6,4,6,2,6,4,6,2,10,12,2,
                4,2,10,2,6,4,2,4,6,6,12,2,6,4,14,
                4,2,4,2,12,6,4,6,6,6,2,6,6,4,2,
                4,6,2,6,6,4,12,2,12,4,2,4,6,2,6,
                4,2,4,6,8,6,4,2,6,4,6,8,4,2,4,
                2,4,14,4,8,10,2,6,10,2,4,6,2,10,2,
                4,2,12,10,2,4,2,4,6,8,4,6,6,6,2,
                6,4,2,6,10,8,4,2,4,6,8,6,10,2,4,
                6,2,6,6,4,2,4,6,2,10,2,6,10,2,10,
                2,4,2,4,14,4,2,4,12,2,6,4,2,6,4,
                6,12,2,6,4,8,6,4,6,2,4,6,2,6,10,
                2,4,6,2,6,4,2,4,2,10,12,2,4,6,6,
                2,6,6,4,12,2,6,4,2,10,6,8,4,2,6,
                4,8,6,10,2,4,6,14,4,2,10,2,6,4,2,
                4,2,12,10,2,4,2,4,8,6,4,2,4,6,6,
                2,6,4,8,4,6,8,4,6,2,4,8,6,4,6,
                6,6,2,6,6,4,2,4,6,8,4,2,4,2,10,
                2,10,2,6,10,2,6,4,2,4,6,6,8,4,2,
                6,10,8,6,4,2,4,8,10,6,2,4,8,6,6,
                4,2,4,8,6,4,6,2,10,2,10,2,4,2,4,
                6,2,6,4,2,10,6,2,6,12,4,6,8,4,2,
                4,2,4,8,6,4,8,4,6,8,6,4,2,4,6,
                8,4,2,4,2,10,2,10,2,4,6,6,2,10,2,
                4,6,8,6,6,6,4,6,12,6,2,4,8,6,4,
                6,2,4,8,6,6,4,6,6,2,6,6,4,2,10,
                2,10,2,6,4,6,2,6,4,12,6,2,6,4,2,
                6,4,6,8,4,2,4,2,18,4,6,2,4,6,2,
                12,4,2,12,6,4,2,4,12,2,10,6,2,4,6,
                2,6,6,4,6,6,2,10,2,10,6,8,6,4,2,
                4,8,6,4,6,2,4,6,2,6,6,6,4,6,2,
                6,4,2,6,10,12,6,2,10,2,6,4,2,4,6,
                6,2,10,2,6,4,14,4,2,4,2,4,8,6,4,
                6,2,10,2,6,6,4,6,6,2,6,4,2,4,12,
                2,12,4,2,4,6,2,10,2,4,6,6,2,6,4,
                2,6,4,14,4,2,4,2,4,14,4,6,2,10,2,
                6,6,6,4,6,2,10,6,2,12,10,2,4,2,4,
                6,2,6,4,6,6,6,8,4,2,6,4,6,8,4,
                2,4,14,6,10,6,6,2,6,6,4,2,4,6,2,
                6,6,6,10,2,10,2,4,2,4,6,8,4,2,4,
                14,6,4,2,6,4,6,12,2,4,2,4,8,6,4,
                8,4,6,2,6,10,2,4,6,2,6,4,2,4,2,
                10,2,10,2,4,6,6,8,6,4,6,6,2,6,4,
                2,6,10,8,4,2,10,8,6,4,6,2,4,6,8,
                6,4,2,10,2,10,2,4,2,10,2,10,2,4,2,
                4,8,6,4,2,4,6,6,2,6,4,8,4,6,8,
                4,2,6,4,8,6,4,6,6,6,2,6,6,4,2,
                4,6,2,6,4,2,4,2,10,12,2,6,4,6,2,
                6,4,2,4,12,8,4,2,16,8,4,2,4,2,4,
                8,16,2,4,8,12,4,2,4,6,2,6,4,6,2,
                12,10,2,4,2,4,6,2,6,4,2,4,6,6,2,
                6,6,6,4,6,8,4,6,2,4,8,6,4,8,4,
                6,2,6,6,4,2,4,6,8,4,2,4,2,10,2,
                10,2,4,2,10,2,10,2,4,6,8,6,4,2,6,
                4,6,8,10,2,4,8,10,6,2,4,6,2,6,6,
                4,6,8,6,6,4,2,10,2,10,2,4,2,4,6,
                2,6,4,2,10,6,2,6,4,8,4,6,8,4,2,
                4,2,12,6,4,6,2,4,6,14,4,2,4,8,6,
                4,2,4,2,10,2,10,6,6,6,2,6,4,2,4,
                6,6,2,6,6,10,6,14,4,2,4,8,6,4,6,
                2,4,8,6,6,6,4,6,2,6,4,2,4,2,10,
                12,2,6,10,2,6,4,6,6,6,2,10,2,6,4,
                14,4,2,4,2,4,14,4,6,2,4,6,2,6,6,
                4,2,10,2,6,4,2,4,12,2,12,4,2,4,6,
                2,6,6,4,6,6,2,10,2,6,4,6,8,4,2,
                4,2,4,14,4,6,2,10,2,6,6,4,2,4,6,
                2,10,2,6,12,10,6,2,4,6,2,6,4,6,6,
                6,2,6,4,2,6,4,6,8,4,2,4,6,8,6,
                10,2,10,2,6,6,4,6,6,2,6,4,2,6,10,
                2,12,4,2,4,6,12,2,4,12,2,6,4,2,6,
                4,18,2,4,2,4,8,6,4,6,2,4,6,2,6,
                12,4,6,2,6,4,6,2,10,2,10,2,4,6,6,
                2,6,6,4,6,6,8,4,2,6,4,6,8,4,2,
                6,12,6,4,6,6,6,8,6,4,2,10,2,6,6,
                4,2,10,2,10,2,4,2,4,8,6,4,2,4,6,
                8,6,4,8,4,6,8,4,2,4,2,4,8,6,4,
                12,6,2,6,10,2,4,6,2,6,4,2,4,2,10,
                2,10,2,6,4,6,8,4,2,4,6,6,8,4,2,
                6,10,8,4,2,4,6,8,10,6,2,4,8,6,6,
                4,2,4,6,2,10,6,2,10,2,10,2,4,2,4,
                8,6,4,2,4,6,6,2,6,6,6,4,6,8,4,
                2,6,4,8,6,4,8,4,6,2,6,6,4,2,4,
                6,8,4,2,4,2,10,12,2,4,2,4,6,2,10,
                2,4,14,6,4,2,10,6,8,4,6,2,4,8,6,
                10,2,4,6,2,12,4,6,6,2,6,6,4,2,12,
                10,2,4,2,4,6,2,6,4,2,10,6,2,6,4,
                2,6,4,6,8,4,6,2,12,6,4,6,2,4,6,
                2,12,4,2,4,14,4,2,4,2,10,2,10,6,2,
                10,2,6,4,2,4,6,6,2,6,4,2,10,6,8,
                6,4,2,4,8,10,6,2,4,6,2,6,6,6,4,
                8,6,4,2,4,2,10,12,2,4,2,10,2,6,4,
                2,10,6,2,10,8,4,14,4,2,4,2,4,8,6,
                4,6,2,4,6,8,6,4,2,4,6,2,6,4,2,
                4,12,2,12,4,6,6,2,6,4,2,4,6,6,2,
                6,6,6,4,6,12,2,4,2,4,14,4,6,2,12,
                6,6,4,2,4,6,2,10,2,4,2,12,10,2,6,
                4,6,2,6,4,6,6,6,2,6,4,2,6,4,6,
                8,4,2,4,6,14,10,2,4,6,2,6,6,4,2,
                10,2,6,4,2,16,2,10,2,4,2,4,6,8,6,
                4,12,2,10,2,6,4,6,12,2,4,2,4,8,6,
                4,6,2,4,6,2,6,10,2,4,6,2,6,4,2,
                6,10,2,10,6,6,6,2,6,6,4,6,6,2,6,
                4,2,6,4,6,8,4,2,6,4,8,6,4,6,2,
                10,8,6,4,12,2,6,4,2,4,2,10,2,12,4,
                2,4,8,10,2,4,6,6,2,6,4,8,4,14,4,
                2,4,2,4,8,6,4,6,6,6,2,6,6,6,4,
                6,2,6,4,6,2,10,2,10,2,6,4,6,2,6,
                4,2,4,6,6,8,4,2,6,10,8,4,2,4,2,
                12,10,6,6,8,6,6,4,2,4,6,2,6,10,2,
                10,2,10,2,4,2,4,6,2,6,4,2,4,6,8,
                6,6,6,4,6,8,4,2,4,2,4,8,6,4,8,
                4,6,2,6,10,2,4,6,8,4,2,4,2,10,2,
                10,2,4,2,4,6,12,2,4,6,8,6,4,2,6,
                10,8,4,6,6,8,6,4,6,2,4,6,2,6,6,
                4,6,6,2,12,4,2,10,2,10,2,4,2,4,8,
                6,4,2,10,6,2,6,4,2,6,4,6,8,4,2,
                6,12,6,4,6,2,4,6,2,12,4,2,4,8,6,
                4,2,4,2,10,12,6,2,4,6,2,6,4,2,4,
                12,2,6,4,2,10,6,8,6,4,2,4,8,6,10,
                2,4,6,2,12,6,4,6,2,6,4,2,4,2,22,
                2,4,2,10,2,6,4,2,4,6,6,2,10,2,6,
                4,14,4,6,2,4,8,6,4,6,2,4,6,2,6,
                6,4,2,4,6,8,4,2,4,12,2,12,4,2,10,
                2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,
                6,4,2,4,18,6,2,10,2,6,6,4,2,4,8,
                10,2,4,2,12,10,2,4,2,4,6,2,6,4,12,
                6,2,6,4,8,4,6,8,4,2,4,6,8,6,10,
                2,4,6,8,6,4,2,4,6,2,6,4,2,6,10,
                2,10,2,4,6,6,8,4,2,4,12,2,6,6,6,
                4,6,12,2,4,2,4,8,6,4,6,2,4,8,6,
                10,2,4,6,2,6,4,2,4,2,10,2,10,2,10,
                6,2,6,10,6,6,2,6,4,2,6,4,6,8,4,
                2,6,4,14,4,6,2,4,6,8,6,4,2,10,2,
                6,4,2,4,12,2,10,2,4,2,4,8,6,6,4,
                6,6,2,10,8,4,6,8,4,2,4,2,4,8,6,
                4,6,6,6,2,6,6,4,2,4,6,2,6,4,2,
                6,10,2,10,8,4,6,2,6,4,2,4,6,6,8,
                4,2,6,10,8,4,2,4,2,4,8,10,6,2,12,
                6,6,4,6,6,2,6,4,6,2,10,2,12,4,2,
                4,6,2,10,2,4,6,6,2,6,6,6,4,14,4,
                2,4,2,4,8,6,4,8,4,6,2,6,6,6,4,
                6,8,4,6,2,10,2,10,2,4,2,4,6,2,10,
                2,4,6,14,4,2,6,4,6,8,4,6,2,12,6,
                4,6,6,6,2,6,6,4,6,6,2,6,6,4,2,
                10,2,10,2,4,2,4,6,2,6,4,2,10,8,6,
                4,2,6,4,6,8,4,2,4,2,12,6,4,8,4,
                6,2,16,2,4,8,6,4,2,4,2,10,2,10,6,
                2,4,6,8,4,2,4,6,6,2,6,4,2,16,8,
                6,4,6,8,6,4,6,2,4,6,2,6,6,6,4,
                6,2,10,2,4,2,10,12,2,4,2,12,6,4,2,
                4,6,6,2,10,2,6,4,14,4,2,6,4,8,6,
                4,6,2,4,6,2,6,6,4,2,4,6,2,6,4,
                2,4,12,14,4,2,4,6,2,6,4,2,4,12,2,
                6,4,2,10,6,8,4,2,4,2,4,14,10,2,10,
                2,12,4,2,4,6,2,10,2,4,2,12,10,2,4,
                2,4,6,2,6,4,6,6,6,2,6,4,2,6,4,
                6,8,4,6,6,8,6,10,2,4,6,2,6,6,4,
                2,4,6,8,4,2,6,10,2,10,2,4,2,10,8,
                4,2,4,12,2,6,4,2,6,4,6,14,4,2,4,
                8,10,6,2,4,6,2,6,10,2,4,8,6,4,2,
                4,2,10,2,10,2,4,6,6,2,6,6,10,6,2,
                6,4,8,4,6,8,4,2,6,4,8,6,4,6,2,
                4,6,8,6,4,2,10,2,6,4,2,4,2,10,2,
                10,2,4,6,8,6,4,2,4,6,6,2,6,12,4,
                6,12,2,4,2,4,8,6,4,6,6,8,6,6,4,
                2,4,6,2,6,4,2,4,2,10,2,10,2,6,4,
                6,2,6,4,6,6,6,8,4,2,6,10,8,4,2,
                4,2,4,18,6,2,4,8,6,6,4,2,10,2,6,
                4,6,12,2,10,2,4,2,4,6,2,6,6,4,6,
                6,2,12,6,4,6,8,4,2,4,2,4,8,6,4,
                8,4,6,2,6,6,4,2,4,6,8,4,2,6,10,
                2,10,6,2,4,6,2,10,2,4,6,8,6,4,2,
                6,4,6,8,4,6,2,4,8,6,4,6,2,10,2,
                6,6,4,6,6,2,6,6,4,2,10,2,12,4,2,
                4,6,2,10,2,10,6,2,6,4,2,6,4,14,4,
                2,4,2,12,6,4,6,2,4,6,2,12,6,4,8,
                6,4,6,2,10,2,10,6,2,4,6,2,6,4,2,
                4,6,6,8,4,2,10,6,8,6,4,2,12,6,4,
                6,6,6,2,6,6,6,4,6,2,6,6,4,2,10,
                12,2,4,2,10,2,6,4,2,4,6,8,10,2,6,
                4,14,4,2,4,2,4,8,6,4,8,4,6,2,6,
                10,2,4,6,2,6,4,2,4,12,2,12,4,2,4,
                6,8,4,2,4,6,6,2,6,4,2,6,10,8,4,
                2,4,6,14,4,6,2,10,2,6,6,4,2,4,6,
                2,10,2,4,2,12,10,2,4,2,4,8,6,4,6,
                6,6,2,6,4,2,6,4,6,8,4,2,10,8,6,
                10,2,4,6,2,6,6,4,2,4,6,2,6,4,2,
                6,10,12,2,4,2,4,6,8,4,2,4,12,2,6,
                4,2,10,6,12,2,4,2,4,8,6,10,2,4,6,
                2,16,2,4,6,2,6,4,2,4,2,12,10,2,4,
                6,6,2,6,6,4,6,6,2,6,4,2,6,4,6,
                8,4,8,4,8,6,4,6,2,4,6,8,6,4,2,
                10,8,4,2,4,2,10,2,10,2,4,2,12,6,4,
                2,4,6,6,2,6,4,8,4,6,8,6,4,2,4,
                8,10,6,6,6,2,6,6,4,2,4,8,6,4,2,
                4,2,10,2,10,2,6,4,6,2,6,4,2,10,6,
                8,4,8,10,8,4,2,4,2,4,8,10,6,2,4,
                14,6,4,2,4,6,2,6,4,6,2,10,2,10,2,
                4,6,6,2,6,4,2,4,6,6,2,6,6,6,4,
                6,12,2,4,2,4,8,6,4,8,4,8,6,6,4,
                2,4,6,8,4,2,4,2,10,2,10,2,6,4,6,
                2,10,6,6,8,6,4,2,6,4,6,8,4,6,2,
                4,14,4,6,2,4,6,2,6,6,4,12,2,6,6,
                4,12,2,10,2,4,2,4,6,2,6,6,10,6,2,
                10,2,6,4,6,8,4,2,4,2,12,6,4,6,2,
                4,6,2,12,4,2,4,8,6,4,2,6,10,2,10,
                6,2,4,6,2,6,4,2,4,6,6,2,6,4,2,
                10,6,8,6,4,2,4,8,6,4,6,2,10,2,6,
                6,10,6,2,6,4,2,4,2,10,14,4,2,10,2,
                10,2,4,6,6,2,10,2,6,4,14,4,2,4,2,
                4,8,6,4,6,2,4,6,2,6,6,6,4,6,2,
                6,4,6,12,2,12,4,2,4,6,2,6,4,2,4,
                6,6,8,4,2,6,4,6,8,4,2,4,2,18,4,
                6,12,2,6,6,4,2,4,6,2,12,4,2,12,10,
                2,4,2,4,6,2,6,4,6,6,8,6,4,2,6,
                4,6,8,4,2,4,6,8,6,12,4,6,2,6,10,
                2,4,6,2,6,4,2,6,10,2,10,2,4,2,4,
                6,8,4,2,4,12,2,6,4,2,6,10,12,2,4,
                6,8,6,4,6,2,4,6,2,6,10,2,4,6,2,
                10,2,4,2,10,2,10,2,4,6,8,6,6,4,6,
                6,2,6,4,2,6,4,6,8,4,2,6,4,8,6,
                4,6,2,4,6,8,6,4,2,10,2,6,4,2,4,
                2,10,12,2,4,2,4,8,6,4,2,4,12,2,6,
                4,12,6,8,4,2,4,2,4,8,6,10,6,6,2,
                12,4,2,4,6,2,6,4,2,4,2,12,10,2,6,
                4,6,2,6,4,2,4,6,6,8,4,2,6,10,8,
                4,6,2,4,8,10,6,2,4,8,6,6,4,2,4,
                6,8,4,6,2,10,2,10,2,4,2,10,2,6,4,
                2,4,6,6,2,6,6,6,4,6,8,6,4,2,4,
                8,10,8,4,6,2,6,6,4,2,4,14,4,2,4,
                2,10,2,10,2,4,2,4,6,2,10,2,10,8,6,
                4,8,4,6,8,4,6,2,4,8,6,4,6,2,4,
                6,8,6,4,6,6,2,6,6,4,2,10,2,10,2,
                4,6,6,2,6,4,2,10,6,2,6,6,6,4,6,
                12,2,4,2,12,6,4,6,2,4,8,12,4,2,4,
                8,6,4,2,4,2,10,2,10,8,4,6,2,6,4,
                6,6,6,2,6,4,2,10,6,8,6,4,2,4,14,
                4,6,2,4,6,2,6,6,6,10,2,6,4,2,4,
                12,12,2,4,2,10,2,6,6,4,6,6,2,10,2,
                6,4,14,4,2,4,2,4,8,6,4,6,2,4,6,
                2,6,6,4,2,4,6,2,6,4,2,16,2,16,2,
                4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,
                6,8,4,2,4,2,4,14,4,6,2,10,2,6,6,
                4,6,6,2,10,2,4,2,12,12,4,2,4,6,2,
                10,6,6,6,2,6,4,2,6,4,14,4,2,4,6,
                8,6,10,2,4,6,2,6,6,6,4,6,2,6,4,
                8,10,2,10,2,4,2,4,6,8,4,2,4,12,8,
                4,2,6,4,6,12,2,4,2,12,6,4,6,6,6,
                2,6,10,2,4,6,2,6,6,4,2,10,2,10,2,
                4,6,6,2,6,6,4,6,8,6,4,2,6,4,6,
                8,4,2,6,4,8,6,4,8,4,6,8,10,2,10,
                2,6,4,2,4,2,10,2,10,2,4,2,4,14,4,
                2,4,6,6,2,6,4,8,10,8,4,2,4,6,8,
                6,4,6,6,6,2,6,6,4,2,4,6,2,10,2,
                4,2,10,2,10,2,6,4,8,6,4,2,4,6,6,
                8,4,2,6,10,8,4,2,6,4,8,10,6,2,4,
                8,6,6,4,2,4,6,2,6,4,6,2,10,12,2,
                4,2,4,6,2,6,4,2,4,12,2,6,6,10,6,
                8,4,2,4,2,4,8,6,12,4,6,2,12,4,2,
                4,6,8,4,2,4,2,12,10,2,4,2,4,6,2,
                10,2,4,6,8,6,4,2,6,4,6,8,4,6,2,
                4,8,6,4,6,2,4,6,2,6,6,4,6,6,8,
                6,4,2,10,2,10,2,4,2,10,2,6,4,2,10,
                6,2,6,4,2,6,4,6,8,6,4,2,12,10,6,
                2,4,6,2,12,4,2,4,8,6,4,2,4,2,10,
                2,10,6,2,4,6,2,6,4,2,10,6,2,6,4,
                12,6,8,6,4,2,4,8,6,4,6,2,4,6,8,
                6,6,4,6,2,6,4,2,4,2,10,12,2,4,12,
                2,6,4,2,4,6,6,2,12,6,4,18,2,4,2,
                4,8,6,4,6,2,4,8,6,6,4,2,4,6,2,
                6,4,2,4,12,2,12,6,4,6,2,6,4,6,6,
                6,2,6,4,2,6,4,6,8,4,2,4,2,4,14,
                4,6,2,10,2,6,6,4,2,10,2,10,2,4,14,
                10,2,4,2,4,6,2,6,10,6,6,2,10,2,6,
                4,6,8,4,2,4,6,8,6,10,2,4,6,2,6,
                6,4,2,4,6,2,6,4,2,6,10,2,10,6,2,
                4,6,8,4,2,4,12,2,6,4,2,6,4,6,12,
                2,4,2,4,8,6,4,6,2,10,2,6,10,6,6,
                2,6,4,2,4,2,10,2,12,4,6,6,2,12,4,
                6,6,2,6,4,2,6,4,14,4,2,6,4,8,6,
                4,6,2,4,6,8,6,6,10,2,6,4,6,2,10,
                2,10,2,4,2,4,8,6,4,2,4,6,6,8,4,
                8,4,6,8,4,2,4,2,12,6,4,6,6,6,2,
                6,6,4,2,4,6,2,6,6,4,2,10,2,10,2,
                6,4,6,2,6,4,2,4,6,14,4,2,6,10,8,
                4,2,4,2,4,8,10,8,4,8,6,10,2,4,6,
                2,6,4,6,2,10,2,10,2,4,2,4,6,8,4,
                2
};
            List<ulong> factor_list = new List<ulong>();
            ulong i = (ulong)primeTable[0];
            int j = 0;
            ulong m = n;
            while (i * i <= m && j < 504)
            {
                while (m % i == 0)
                {
                    factor_list.Add(i);
                    m /= i;
                }
                i = (ulong)primeTable[++j];
            }
            if (i * i > m && m > 1)
            {
                factor_list.Add(m);
                m = 1;
            }
            i = 3613;
            j = 0;
            while (i * i <= m)
            {
                while (m % i == 0)
                {
                    factor_list.Add(i);
                    m /= i;
                }
                i = i + dep[j];
                j = ++j % 5761; //5761 is dep.Length
            }
            if (i * i > m && m > 1)
            {
                factor_list.Add(m);
            }
            return factor_list.ToArray();
        }
 
 
 
        static void Main(string[] args)
        {
            //GeneratePrimeTable(504);
            //GenerateDivisibilityTable(13, 3613);
            /*
            for (ulong u =2; u < 40; u++)
            {
                ulong[] factors = Factorise(u);
                ulong res = 1;
                Console.Write(u + " = ");
                int l = 0;
                for (l = 0; l < factors.Length - 1; l++)
                {
                    Console.Write(factors[l] + " * ");
                    res *= factors[l];
                }
                res *= factors[l];
                Console.WriteLine(factors[l]);
                if (u != res)
                {
                    Console.WriteLine(res + " <> " + u);
                }
            }
            */
            //Test
            for (ulong u = ulong.MaxValue-10000; u < ulong.MaxValue; u++)
            {
                ulong[] factors = Factor(u);
                ulong res = 1;
                for (int l = 0; l < factors.Length; l++)
                {
                    res *= factors[l];
                }
                if (u != res)
                {
                    Console.WriteLine(res + " <> " + u);
                }
            }
            Console.WriteLine("ok");
            Console.ReadLine();
        }
    }
}

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