speckxVoyager 1 runs on 69 KB of memory and an 8-track tape recorder
Voyager 1 & 2 is one of my favourite human science achievements, not even so much from technology standpoint, as it's relatively simple compared to what we have now (although that's one of the charms), but just the fact that it's so far away, it still more or less works long after the scheduled mission end time, we can communicate with it and despite all the modern technology progress, it would take decades to catch up. Absolutely amazing and inspiring!
Voyager 1 and 2 are 25 and 21 billion kilometres away, respectively.
Even if we built a rocket just designed to get stuff as far away as quickly away as possible, it would take decades to catch up to where they are now.
Could we even catch up to them at all with the current propulsion technology? Not only did they have decades of head start but they took advantage of a unique planetary alignment that I don't think will come back around anytime soon.
Yes, easily. The alignment doesn't really matter for that. Almost all your speed gain comes from just Jupiter. Saturn is 30% the mass and 2/3 of the orbital velocity, so your gain from Saturn is only 20% of what you can get from Jupiter (and also your potential gain is limited by a minimum approach distance greater than the rings, or you'd hit them.) And the ice giants are slower and smaller yet; Voyager barely gained from Uranus and actually slowed from Neptune since it wasn't routed to gain speed there.
New Horizons achieved 80% of Voyager's velocity with just Jupiter, and it wasn't really trying to optimize for speed, it approached Jupiter only to 10 million km (over 100x greater than the planet's radius.) A probe dedicated to a fast slingshot past Jupiter could easily overtake Voyager. We haven't had any need to try, unless one of the missions to specifically study the heliopause-interstellar area happens. It would still take a while to catch up to Voyager's head start, but it's doable.