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#!/usr/bin/env perl
use warnings;
use strict;
use v5.16;
use ntheory ":all";
my $small_nth = 1e7;
my $small_rnth = 1e6;
my $rp_inc = 1e9;
print "Verifying nth prime bounds up to $small_nth\n";
{
my $n = 1;
forprimes {
my $p = $_;
my($l,$u) = (nth_prime_lower($n),nth_prime_upper($n));
die "$n: $l $p $u" unless $l <= $p && $u >= $p;
$n++;
} $small_nth;
}
print "Verifying nth Ramanujan prime bounds to $small_rnth\n";
{
my $r = ramanujan_primes($small_rnth);
for (0 .. $#$r) {
my $n = $_+1;
my $rn = $r->[$_];
my($l,$u) = (nth_ramanujan_prime_lower($n),nth_ramanujan_prime_upper($n));
die "$n: $l $rn $u" unless $l <= $rn && $u >= $rn;
}
}
print "Verifying nth Ramanujan prime bounds:\n";
{
my $s = 0;
my $n = 1;
while ($s < 1e12) {
my $r = ramanujan_primes($s, $s + $rp_inc - 1);
for (0 .. $#$r) {
my $rn = $r->[$_];
my($l,$u) = (nth_ramanujan_prime_lower($n),nth_ramanujan_prime_upper($n));
die "$n: $l $rn $u" unless $l <= $rn && $u >= $rn;
#die "$n: $rn" unless $rn == nth_ramanujan_prime($n);
$n++;
}
print " $s + $rp_inc\n";
$s += $rp_inc;
}
}
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