even-perfect-numbers-scanner/PerfectNumbers.Core.Tests/PrimesGeneratorTests.cs

using FluentAssertions;
using Xunit;

namespace PerfectNumbers.Core.Tests;

public class PrimesGeneratorTests
{
    [Fact]
    [Trait("Category", "Fast")]
    public void Small_primes_and_squares_match()
    {
        var primes = PrimesGenerator.SmallPrimes;
        var squares = PrimesGenerator.SmallPrimesPow2;

        primes[..5].Should().Equal([2, 3, 5, 7, 11]);
        squares[..5].Should().Equal([4UL, 9UL, 25UL, 49UL, 121UL]);

        for (int i = 0; i < 5; i++)
        {
            squares[i].Should().Be(primes[i] * primes[i]);
        }

        primes.Length.Should().Be((int)PerfectNumberConstants.PrimesLimit);
        squares.Length.Should().Be((int)PerfectNumberConstants.PrimesLimit);
    }

    [Fact]
    [Trait("Category", "Fast")]
    public void Residue_prime_tables_follow_digit_rules()
    {
        var lastOne = PrimesGenerator.SmallPrimesLastOne;
        var lastOnePow2 = PrimesGenerator.SmallPrimesPow2LastOne;
        var lastSeven = PrimesGenerator.SmallPrimesLastSeven;
        var lastSevenPow2 = PrimesGenerator.SmallPrimesPow2LastSeven;
        var lastThree = DivisorGenerator.SmallPrimesLastThree;
        var lastThreePow2 = DivisorGenerator.SmallPrimesPow2LastThree;
        var lastNine = DivisorGenerator.SmallPrimesLastNine;
        var lastNinePow2 = DivisorGenerator.SmallPrimesPow2LastNine;
        var lastOneWithoutThree = DivisorGenerator.SmallPrimesLastOneWithoutLastThree;
        var lastOneWithoutThreePow2 = DivisorGenerator.SmallPrimesPow2LastOneWithoutLastThree;
        var lastSevenWithoutThree = DivisorGenerator.SmallPrimesLastSevenWithoutLastThree;
        var lastSevenWithoutThreePow2 = DivisorGenerator.SmallPrimesPow2LastSevenWithoutLastThree;
        var lastNineWithoutThree = DivisorGenerator.SmallPrimesLastNineWithoutLastThree;
        var lastNineWithoutThreePow2 = DivisorGenerator.SmallPrimesPow2LastNineWithoutLastThree;

        lastOne.Length.Should().Be((int)PerfectNumberConstants.PrimesLimit);
        lastSeven.Length.Should().Be((int)PerfectNumberConstants.PrimesLimit);
        lastThree.Length.Should().Be((int)PerfectNumberConstants.PrimesLimit);
        lastNine.Length.Should().Be((int)PerfectNumberConstants.PrimesLimit);
        lastOneWithoutThree.Length.Should().BeGreaterThan(0);
        lastSevenWithoutThree.Length.Should().BeGreaterThan(0);
        lastNineWithoutThree.Length.Should().BeGreaterThan(0);
        lastOneWithoutThree.Length.Should().BeLessThan(lastOne.Length);
        lastSevenWithoutThree.Length.Should().BeLessThan(lastSeven.Length);
        lastNineWithoutThree.Length.Should().BeLessThan(lastNine.Length);
        lastOnePow2.Length.Should().Be(lastOne.Length);
        lastSevenPow2.Length.Should().Be(lastSeven.Length);
        lastThreePow2.Length.Should().Be(lastThree.Length);
        lastNinePow2.Length.Should().Be(lastNine.Length);
        lastOneWithoutThreePow2.Length.Should().Be(lastOneWithoutThree.Length);
        lastSevenWithoutThreePow2.Length.Should().Be(lastSevenWithoutThree.Length);
        lastNineWithoutThreePow2.Length.Should().Be(lastNineWithoutThree.Length);

        lastOne[..5].Should().Equal([3U, 7U, 11U, 13U, 19U]);
        lastSeven[..5].Should().Equal([3U, 7U, 11U, 13U, 17U]);
        lastThree[..6].Should().Equal([3U, 7U, 11U, 13U, 17U, 19U]);
        lastNine[..6].Should().Equal([3U, 7U, 11U, 13U, 17U, 19U]);

        for (int i = 0; i < lastOne.Length; i++)
        {
            uint prime = lastOne[i];
            uint mod10 = prime % 10U;
            (mod10 == 1U || mod10 == 3U || mod10 == 9U || prime == 7U || prime == 11U)
                .Should().BeTrue();
            lastOnePow2[i].Should().Be(prime * (ulong)prime);
        }

        for (int i = 0; i < lastSeven.Length; i++)
        {
            uint prime = lastSeven[i];
            uint mod10 = prime % 10U;
            (mod10 == 3U || mod10 == 7U || mod10 == 9U || prime == 11U)
                .Should().BeTrue();
            lastSevenPow2[i].Should().Be(prime * (ulong)prime);
        }

        for (int i = 0; i < lastThree.Length; i++)
        {
            uint prime = lastThree[i];
            uint mod10 = prime % 10U;
            (mod10 == 3U || mod10 == 7U || prime == 11U || prime == 19U)
                .Should().BeTrue();
            lastThreePow2[i].Should().Be(prime * (ulong)prime);
        }


        lastOneWithoutThree.Should().NotBeEmpty();
        lastSevenWithoutThree.Should().NotBeEmpty();
        lastNineWithoutThree.Should().NotBeEmpty();

        for (int i = 0; i < lastOneWithoutThree.Length; i++)
        {
            uint prime = lastOneWithoutThree[i];
            (prime % 10U != 3U).Should().BeTrue();
            if (i > 0)
            {
                prime.Should().BeGreaterThan(lastOneWithoutThree[i - 1]);
            }

            lastOneWithoutThreePow2[i].Should().Be(prime * (ulong)prime);
        }

        for (int i = 0; i < lastSevenWithoutThree.Length; i++)
        {
            uint prime = lastSevenWithoutThree[i];
            (prime % 10U != 3U).Should().BeTrue();
            if (i > 0)
            {
                prime.Should().BeGreaterThan(lastSevenWithoutThree[i - 1]);
            }

            lastSevenWithoutThreePow2[i].Should().Be(prime * (ulong)prime);
        }

        for (int i = 0; i < lastNineWithoutThree.Length; i++)
        {
            uint prime = lastNineWithoutThree[i];
            (prime % 10U != 3U).Should().BeTrue();
            if (i > 0)
            {
                prime.Should().BeGreaterThan(lastNineWithoutThree[i - 1]);
            }

            lastNineWithoutThreePow2[i].Should().Be(prime * (ulong)prime);
        }

        for (int i = 0; i < lastNine.Length; i++)
        {
            uint prime = lastNine[i];
            uint mod10 = prime % 10U;
            (mod10 == 3U || mod10 == 7U || mod10 == 9U || prime == 11U)
                .Should().BeTrue();
            lastNinePow2[i].Should().Be(prime * (ulong)prime);
        }
    }
}