I can't answer your question directly, but it seems as though you have either uncovered a bug or you have exceeded some not-so-obviously specified limit of the bfac function of Math::BigFloat. It seems the maximum value for this function is between 2**23 and 2**24. This does not generate the error:

use strict;
use warnings;
use diagnostics;
use Math::BigFloat;

my $x = Math::BigFloat->new(2**23);
print "x=$x\n";

my $product = $x->copy();
$product->bfac();
print "p=$product\n";
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You could submit a bug report on CPAN. But, before doing so, you could use Super Search to see if anyone has encountered similar issues with this module.

I tried Math::BigInt as well, but I get the same results.