Primes

using System;
using System.Linq;
using System.Collections.Generic;


public enum Mode {
    Time,
    Value,
    Count,
    NextByValue,
    NextByCount
}

public class Factor {
    public uint Value { get; set; }
    public uint Count { get; set; }
    public Factor(uint value) {
        Value = value;
        Count = 1;
    }
    public void Increment() {
        Count++;
    }
    public override string ToString() {
        return $"{Value}{(Count > 1 ? $"^{Count}" : "")}";
    }
}
public class Factors {
    List<Factor> List { get; set; } = new List<Factor>();
    public bool IsPrime { get { return List.Count == 1 && List.First().Count == 1; } }
    public uint Value { get; set; }
    
    public void Add(uint value) {
        if(List.Any(f => f.Value == value)) {
            List.Single(f => f.Value == value).Increment();
        }
        else {
            List.Add(new Factor(value));
        }
    }
    public static List<Factors> FactorizeRange(uint min, uint max) {
        var facsList = new List<Factors>();
        var primes = MainClass.GetPrimes(Mode.Value, max);
        for(var i = min; i <= max; i++) {
            facsList.Add(new Factors(i, primes));
        }
        return facsList;
    }
    public Factors(uint value, List<uint> primes = null) {
        this.Value = value;
        if(primes == null) {
            primes = MainClass.GetPrimes(Mode.Value, (uint)Math.Sqrt(value));
        }
        else {
            var max = (uint)Math.Sqrt(value);
            primes = primes.TakeWhile(p => p <= max).ToList();
        }
        
        while(value > 1) {
            uint factor = primes.FirstOrDefault(p => value % p == 0);
            if(factor == 0) {
                factor = value;
            }
            value /= factor;
            Add(factor);
        }
    }
    public override string ToString() {
        return string.Join(" * ", List.Select(f => f.ToString()));
    }
}
public class MainClass {
    public static List<uint> GetPrimes(Mode mode, uint value) 
    {
        var primes = new List<uint>();
        DateTime start = DateTime.Now;
        uint i = 0;
        uint nextCount;
        
        Func<bool> limit;
        switch(mode)
        {
            case Mode.Time:
                limit = () => (DateTime.Now - start).TotalSeconds < value;
                break;
            case Mode.Count:
                limit = () => (uint)primes.Count < value;
                break;
            case Mode.NextByValue:
                nextCount = (uint)GetPrimes(Mode.Value, value).Count + 1;
                limit = () => (uint)primes.Count < nextCount;
                break;
            case Mode.NextByCount:
                nextCount = (uint)GetPrimes(Mode.Count, value).Count + 1;
                limit = () => (uint)primes.Count < nextCount;
                break;
            case Mode.Value:
            default:
                limit = () => i <= value;
                break;
        }
        
        for(i = 2; limit(); i++) {
            var max = Math.Sqrt(i);
            if(!primes.TakeWhile(p => p <= max).Any(p => i % p == 0)) {
                primes.Add(i);
            }
        }
        return primes;
    }
    static List<uint> GetPrimesInRange(uint min, uint max) {
        var primes = GetPrimes(Mode.Value, max);
        return primes.SkipWhile(p => p < min).ToList();
    }
    static void EvalPrimesByCalcTime(uint value) {
        List<uint> primes;
        
        primes = GetPrimes(Mode.Time, value);
        Console.WriteLine($"{value} seconds: {primes.Last()}");
        Console.WriteLine($"...and count: {primes.Count}");
        value = (uint)Math.Pow(primes.Last(),.5);
        Console.WriteLine($"{value} = sqrt({primes.Last()})");
        Console.WriteLine();
        
        primes = GetPrimes(Mode.Value, value);
        Console.WriteLine($"highest prime under {value}: {primes.Last()}");
        Console.WriteLine($"...and count: {primes.Count}");
        Console.WriteLine();
        
        value = primes.Last();
        primes = GetPrimes(Mode.Count, value);
        Console.WriteLine($"{value}th prime = {primes.Last()}");
    }
    static void EvalHighestValueByPrimeFactors(uint count) {
        var primes = GetPrimes(Mode.Count, count);
        Console.WriteLine($"{primes.Count}th prime: {primes.Last()}");
        primes = GetPrimes(Mode.NextByCount, count);
        Console.WriteLine($"{primes.Count}th prime: {primes.Last()}");
        primes = GetPrimes(Mode.Value, (uint)Math.Pow(primes.Last(), 2));
        Console.WriteLine($"Max prime coverage: {primes.Last(p => p != primes.Last())}");
    }
    
    static void Main()
    {
        //var primes = GetPrimes(Mode.Value, (uint)Math.Pow(622,.5));
        //Console.WriteLine($"lowest prime factor for numbers up to 622 ranges from 2 to {primes.Last()}");
        //Factors.FactorizeRange(529, 622).ForEach(value => Console.WriteLine($"{value.Value} = {value}"));
        //EvalHighestValueByPrimeFactors(100);
        EvalPrimesByCalcTime(14);
    }
}