GeneratePrimesData.cs

/*
    https://byteterrace.blob.core.windows.net/temp/Gödels.dat
    https://byteterrace.blob.core.windows.net/temp/Primes.dat
*/

var buffer = new byte[10];
var cacheSize = 4096;
var numbersCache = new byte[cacheSize][];
var primeIndex = 0;
var recordSeparator = ((byte)Convert.ToChar(value: 30));

using var primesFileStream = new FileStream(
    options: new FileStreamOptions {
        Access = FileAccess.Write,
        Mode = FileMode.CreateNew,
        Options = FileOptions.SequentialScan,
        Share = FileShare.Read,
    },
    path: args[0]
);

BitConverter.GetBytes(value: 2U).CopyTo(array: buffer, index: 0);
buffer[4] = ((byte)2U.DigitalRoot());
BitConverter.GetBytes(value: 0U).CopyTo(array: buffer, index: 5);
buffer[^1] = recordSeparator;
numbersCache[primeIndex++] = buffer;

for (var i = 1U; (i < (uint.MaxValue - 2U)); i += 2U) {
    var isPrime = i.IsPrime();

    if (isPrime) {
        buffer = new byte[10];
        BitConverter.GetBytes(value: i).CopyTo(array: buffer, index: 0);
        buffer[4] = ((byte)i.DigitalRoot());
        BitConverter.GetBytes(value: i.ModularInverse()).CopyTo(array: buffer, index: 5);
        buffer[^1] = recordSeparator;
        numbersCache[primeIndex++] = buffer;

        if (0 == (primeIndex % cacheSize)) {
            for (var j = 0; (j < cacheSize); ++j) {
                primesFileStream.Write(numbersCache[j]);
            }

            primeIndex = 0;
        }
    }
}

for (var j = 0; (j < primeIndex); ++j) {
    primesFileStream.Write(numbersCache[j]);
}

Console.WriteLine("Complete.");