Reddit reviews AmazonBasics Multipurpose Copy Printer Paper - White, 8.5 x 11 Inches, 5 Ream Case (2,500 Sheets)
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5 reams of 8.5 x 11 inch multipurpose copy paper (2,500 sheets total)Works with laser/inkjet printers, copiers and fax machinesHigh-quality 20-pound weight for economical printing and resistance to paper jamsBright white for better contrast; 92 GE brightness (104 Euro)Acid-free paper
One GB of text takes 677.963 pages on average^1. This is probably a conservative estimate, given that RimWorld logs contain quite a lot of whitespace.
You'll need 73.897.967 sheets of paper, assuming double sided printing. That's 147.796 reams of paper, or 29.560 boxes of 5 reams. At $24,99 per box^2 (currently on discount!), you'll pay about $738.704 and 40 cents. The good news is that you'll have 4 reams of paper leftover, which should last you a good while if you stop printing output logs.
Each box weighs about 25,2 pounds^2 (or 11,43 kg in units that make sense). That comes down to 337,9 metric tonnes of paper, or 10 semi-trucks loaded to the US maximum weight limit^3. You'd have to contact Amazon to see whether this qualifies for free Prime delivery.
Sadly, I don't have the time to calculate what you'll spend on ink (or toner, and the replacement printers you'll need), but you can probably add another cool half a million.
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^(edit; normalized punctuation and decimal points. Clarified metric tonnes.)