What is the largest prime number printed by a computer?
As of February 10, 2021, the largest known prime is
2^{82589933}-1
And here it is, printed in its full glory.
Yes, right there.
There, right above. Three lines ago.
Yup, this is it. It’s printed. On your screen. Or phone. Or watch, or whatever you Quora on.
What’s that? You want to know the digits? Oh, ok. Here they are, in base 2 for your convenience:
11111111111111111111111111111…1111
To save space I’ve suppressed the rest but, you know, they’re all the same so why bother, amirite? There’s exactly 82,589,933 of those 1’s in there. Pretty boring if you ask me, but hey, whatever chops your suey.
You want it printed? Sure, just get reams of paper and a few extra toner cartridges for your printer. Oh actually, I’m just being silly, why bother with a printer? Print a single page with 2,000 “1”s on it, and just photocopy it 41,294 times. Photocopying machines are wicked fast, but you’ll still need those reams of paper.
Just remember to erase the last 67 1’s on the last page, otherwise – the horror! The number printed on your 41,295 pages is no longer prime! We can’t have that. We must ensure that those reams of paper actually carry a prime number, represented in base 2.
The good news: you can mess up the order of the pages. Doesn’t matter.
What’s that? Base 10? You really insist on decimals, eh? Ok, time to get those toner cartridges. You’ll need to print 24,862,048 digits, which would probably fit on 13,813 pages or so. That’s not too bad, it’s less than half of the Encyclopedia Britannica, if someone still remembers what that is.
I don’t expect anyone actually bothered to do that, wasting 13,000 pages on such a useless list of digits, but if you wanted to, there’s nothing to it. The computation of the sequence of digits would take like a few minutes with a reasonable computer, and printing it… well, however fast your printer is. A few hours, at 40ppm. Sounds reasonable.
This time, though, do not mess up the order of the pages. Otherwise… I shudder at the thought.