#!/usr/bin/perl -slw
use strict;
use Math::GMPz qw(:mpz);

my @crt = qw( 68083089690 131417981310  36415643880  51194848320
106157886450  30083217780 154569039240  55922110860  18269362650
 12688113900 108608348310   2163950250 195808561410  89629478400
 35610139950 164950347870 104015130450 198396537570   4751926410
 91952139510 187872373920 182291125170 144638376960 149365639500
 45991448580  94402601370 142813754160  69142506510 132477398130
164144843940 );

my $beg = shift || 91960283;
my $end = shift || 300000000;
my $fact = 2*3*5*7*11*13*17*19*23*29*31;
my $target = 650;

open FH, '>', 'prime_dump.txt' or die "could not open file: $!\n";
for my $i ($beg .. $end) {
    for (@crt) {
        my $num = $fact*$i+$_;
        my $start = Rmpz_init(); my_prev_prime_p($start,$num);
        my $end   = Rmpz_init(); Rmpz_nextprime($end, Math::GMPz->new($num));
        my $gap   = Rmpz_init(); Rmpz_sub($gap, $end, $start);
        print FH "$i $_ $gap ",$gap/log($num) if $gap > $target;
    }
}
close FH;
# ----------------------------------------------------------------
# Find probable prime that precedes param2 via Rmpz_probab_prime_p
# ----------------------------------------------------------------
sub my_prev_prime_p {
    my ($rop,$num) = (shift,shift); my $i = $num;
    Rmpz_set_d($rop,2); # default param1 to 2 (the smallest prime)
    while ($i > 2) {
        $i--; next unless $i % 2; # evaluate odd numbers only
        Rmpz_set_str($rop,$i,10) || return if Rmpz_probab_prime_p(Math::GMPz->new($i),10);
    }
    return;
}
__END__