Generating Table with random Numbers from 1 to 100.000.000 without any doubles in a short amount of time

for a Project do I need to create a Table that stores 100.000.000 Numbers in a random Order without any doubles, which then get saved as .csv File.

void Anonym_Option::GenerateTable(){
    ui->progressBar->setValue(0);
    QList<int> l(100000000);
    std::iota(l.begin(), l.end(), 0);

    QVector<QList<int>::iterator> v(l.size());
    std::iota(v.begin(), v.end(), l.begin());

    ui->progressBar->setValue(10);

    unsigned seed = std::chrono::system_clock::now().time_since_epoch().count();
    auto rng = std::default_random_engine {seed};

    QCoreApplication::processEvents();
    std::shuffle(v.begin(), v.end(), rng);

    QString SortString;
    QString CombinedString;

    ui->progressBar->setValue(30);

    for (auto z: v){
        QCoreApplication::processEvents();
        SortString += QString::number(*z) + "," + "\n";
    }

    ui->progressBar->setValue(70);

    CombinedString = SortString.replace(QString("\n;"), QString("\n"));

    QString Table = "Generated ID; \n" + CombinedString;

    ui->progressBar->setValue(90);

    QString Path = QDir::currentPath();
    QFile file(Path + "/Table.csv");
    if (!file.open(QFile::WriteOnly | QFile::Text)){
        QMessageBox::warning(this, "ACHTUNG","ACHTUNG! Der Anonymisierungs-Table kann nicht generiert werden! Bitte Kontaktieren sie den Support.");
        return;
    }
    else{
        QTextStream stream(&file);
        QCoreApplication::processEvents();
        stream << Table;
        ui->progressBar->setValue(100);
        hide();
        anonymisierung = new Anonymisierung();
        QTimer::singleShot(1500,anonymisierung,SLOT(show()));
    }
}

The purpose of that Table is to replace Numbers in the Customer File, so that it's anonymised. The Problem I have with my Code is that while if I use 10.000.000 Numbers does it take around 8 Min to get done,but when I use 100.000.000 does it seem to take more RAM and Time than it is practical. The Problem could I localize in this Function

    for (auto z: v){
        QCoreApplication::processEvents();
        SortString += QString::number(*z) + "," + "\n";
    }

which whole purpose is to add a "," and "\n" after each Number, so that it does get seperated accordingly and can be used later on. Any Ideas how to fasten up the Progress?

TL;DR I use QT6 in hope for Ranges, sadly not implemented yet, so not an Option I can use!