number-theoretic/primes

/**
 * Upper bound for computing the nth prime number.
 *
 * see http://math.univ-lille1.fr/~ramare/TME-EMT/Articles/Art01.html
 *
 * /!\ n = 1 will work only if loglog(0) returns 0
 *
 */

export function __upperbound__(log, loglog) {
    const upperbound = function (n) {
        if (n < 55) {
            return n * (log(n) + loglog(n)) + 3;
        }

        if (n < 39_018) {
            return n * (log(n) + loglog(n) - 0.5);
        }

        return n * (log(n) + loglog(n) - 0.9484);
    };

    return upperbound;
}