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/*
Copyright (C) 2010 Fredrik Johansson
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "ulong_extras.h"
ulong n_nth_prime(ulong n)
{
if (n == 0)
{
flint_throw(FLINT_ERROR, "Exception (n_nth_prime). n_nth_prime(0) is undefined.\n");
}
return n_primes_arr_readonly(n)[n-1];
}
void n_nth_prime_bounds(ulong *lo, ulong *hi, ulong n)
{
int bits, ll;
double llo, lhi;
/* Lower and upper bounds for ln(n) */
bits = FLINT_BIT_COUNT(n);
llo = (bits-1) * 0.6931471;
lhi = bits * 0.6931472;
/* Lower bound for ln(ln(n)) */
if (n < 16) ll = 0;
else if (n < 1619) ll = 1;
else if (n < 528491312) ll = 2;
else ll = 3;
*lo = (ulong) (n * (llo + ll - 1));
*hi = (ulong) (n * (lhi + (ll+1) - (n >= 15985 ? 0.9427 : 0.0)));
}