At her weblog Allison Alvarez enthuses that:

Hooray! A new Mersenne prime has been discovered and it’s the largest one yet. The new number, expressed as 213,466,917-1, contains 4,053,946 digits and would take the best part of three weeks to write out longhand. Sweet!

I’m curious to see the derivation of this time estimate. How many weeks would it take to write it out longhand without making a mistake?