TryDivide

// Requires .NET Core 3.0

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Runtime.Intrinsics;
using System.Runtime.Intrinsics.X86;

class Program {

    static int TryDivide(int size) {
        var primes = new List<Vector256<float>>() {
            Vector256.Create(16777216f, 16777216f, 16777216f, 16777216f, 16777216f, 16777216f, 3f, 2f)
        };
        int sqr = 2, maxSqr = (int)Math.Sqrt(size);
        int pos = Vector256<float>.Count - 3;
        bool flag = true;
        int fastSize = Math.Min(size, 16777216);
        int current = 5;
        int count = 2;

        for (; current <= fastSize; current += (flag = !flag) ? 4 : 2) {
            var num = Vector256.Create((float)current);
            if (sqr * sqr <= current) {
                ++sqr;
            }

            for (var i = 0; i < primes.Count; ++i) {
                var divisor = primes[i];
                var div = Avx.Divide(num, divisor);
                var temp = Avx.Compare(div, Avx.Floor(div), FloatComparisonMode.OrderedEqualNonSignaling);
                if (!Avx.TestZ(temp, temp)) {
                    break; // not prime
                }
                if ((int)divisor.ToScalar() >= sqr) {
                    // prime number found
                    ++count;
                    if (current <= maxSqr) {
                        // we only stores values <= sqrt(size)
                        primes[primes.Count - 1] = primes[primes.Count - 1].WithElement(pos, current);
                        if (--pos < 0) {
                            primes.Add(Vector256.Create(16777216f));
                            pos = Vector256<float>.Count - 1;
                        }
                    }

                    break;
                }
            }
        }

        while (current <= size) {
            var num = Vector256.Create((double)current);
            if (sqr * sqr <= current) {
                ++sqr;
            }

            for (var i = 0; i < primes.Count; ++i) {
                for (byte j = 1; j != byte.MaxValue; --j) {
                    var divisor = Avx.ConvertToVector256Double(Avx.ExtractVector128(primes[i], j));
                    var div = Avx.Divide(num, divisor);
                    var temp = Avx.Compare(div, Avx.Floor(div), FloatComparisonMode.OrderedEqualNonSignaling);
                    if (!Avx.TestZ(temp, temp)) {
                        goto next; // not prime
                    }
                    if ((int)divisor.ToScalar() >= sqr) {
                        // prime number found
                        ++count;
                        goto next;
                    }
                }
            }

        next:
            current += (flag = !flag) ? 4 : 2;
        }

        return count;
    }

    static void Main() {
        const int size = 10000_0000;
        var watch = Stopwatch.StartNew();
        Console.WriteLine("{0}: {1}", size, TryDivide(size));
        watch.Stop();
        Console.WriteLine(watch.Elapsed);
    }
}