The real problem is your infinite loop. Stop that! I suspect ctrl-c is to blame for the truncation. (After having faithfully reproduced the error as shown) I rewrote the program as follows and got no truncated lines.

@primes = ( 2 );
$testnumber = 3;
open( SAVE, ">primes.dat" );
close SAVE;

while ( 1 ) {
    foreach $placeholder ( @primes ) {
    if ( ( $testnumber / $placeholder ) =~ /^[+-]?\d+$/ ) {
        $testnumber = $testnumber + 2;
        next;
    }
    if ( $placeholder == $primes[-1] ) {
        push ( @primes, $testnumber );
        open ( SAVE, '>>primes.dat' ) or 
        die "Couldn't open primes.dat";
        print SAVE "$testnumber\n";
        close SAVE;
    }
    next;
    }
}
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