Moores Law in 34th Centruy? What do you want to do with your ships computer core?

Y'all know moores law, "Computational Power roughly doubles every 18 months +/-", so I was wondering how that would apply in the 34th centruy, ie what sort of power would my commanders PC have relative to todays PC to see what he'd be able to do with such computers. So I put it into a spreadsheet, column A1 = 2017 A2 = 2020, fill that pattern down to about row 435, Column B1 = 1, B2 = B1*4, fill that down to B432.

Well ahem, it broke excel.... (4.8048 x 10 ^ 257)

48048 with 263 zeros on the end of it.

480,480,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Like I said - it broke excel, obviously a recurring multiply by four is not going to end in that many zeroes, it would most likely have four or six at the end and seemingly random integers throughout. And remembering that the seed "1" was a unit of current PC power, so obviously we are extremely unlikely to ever end up with that mcuh computational power, such things defy the landauer limit and many other laws of pyhsics.

So assuming that the computer core in your spaceship dates back to the time of the first builds of your ships class or its oldest competitors, it is a couple of hundred years old at the time you are flying it in 3303, its still many many orders of magnitude better than all the computation available to humanity today... What "Apps" would you like to be able to run on it?
 
Quantum Computing. Your ship is a living processor, kept dumb to stop an AI revolution against humanity.

Or something...
 
3304 is 1287 years from now which is 858 x 18 months. 2^858 is 1921924308174003258872616370050369756495810455948672905389542244035233680030523317234537010836564833497229828911284598430510768810573374275010933992099815720970170092183271059798176857571621225553914820586983072295508566795439261982531741155133337002515103744
and I need to buy a new pencil.
 
What "Apps" would you like to be able to run on it?

My main concern is that while the computer seems fast enough, it is woefully short on storage. I'd like to be able to store any information that I personally have come across while travelling the galaxy (trade data, etc.) rather than have to resort to other means...

Though I guess Angry Birds 3003 could while away that Hutton run. :D
 
Hopefully by then the ship computer will have enough power to finally play Battle Chess without loading times

5uK1gCn.jpg
 
You might think that docking computer is just playing a recording of The Blue Danube, but actually it simulates Johann Strauss conducting an orchestra with one guy using an xbox controller to dock your ship in the middle of it with accuracy down at the sub atomic level. Due to the anachronism and Johann Strauss being only an approximation sometimes it glitches and you smack into the control tower.
 
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