Reconnecting computer to a running Arduino program

i want to test a sketch over a long time (days?) for overflow etc., but not have my computer tied to it via USB, and on, and unavailable for other use, all that time.
Is there a way to disable and disconnect the USB connection while the sketch is running (on a battery connection of course), use the computer for other things, or turn it off, and then later reconnect and resume monitoring the sketch output of, say, a timing count. I know how to disable and reenable the USB port at the computer.
I know i need to pay attention to my data sizes and i see some at least one (somewhat confusing to me) forum suggestion of how to handle the overflow issues, but I want to test the results. I don't need microsecond precision or accuracy, seconds will be fine.

if you have Ethernet or WiFi why not run a web server on the arduino?
when you switch on your PC you connect to the web server to collect data, e.g.

Normally when an Arduino is connected to a PC with the USB cable and a PC program opens the Serial connection the Arduino will reset.

If you don't want that to happen the simplest way is probably to use a USB-TTL cable to connect directly to the Arduino's Rx. Tx and GND connections. Then the PC can receive data from the Arduino, or send data to it, without interrupting the running Arduino program.

...R

Yet another example of the x-y problem.

If you are confused and concerned about overflow, please explain what kind of overflow you're confused about. I suspect it's the classic millis() overflow/wrap issue which can be clairified in about thirty seconds. We're happy to explain things and demystify your mysteries. Going off on a tangent about monitoring a program in the future isn't the real problem.

Anytime you connect the serial monitor to an Arduino via the USB port, the program will be reset which sets the millis() count back to zero, effectively making it impossible to troubleshoot a what is a only a perceived problem. Write the code correctly, from a position of understanding how it works and stop trying to solve a problem that needs no solution.