MIT Puzzle

Ron Rivest, of MIT, has revealed a puzzle today.
And this puzzle involves some very big numbers.
The biggest number of the bunch is 2^{279685186856218}, which you need to divide by another number and find the remainder.
Yes, 2 to the power of almost 280 trillion.
Google calculator can't handle that.
New scientist tells us it's 74 quadrillion digits long.
What if you wanted to solve the puzzle by hand?
First you'd need to write out this problem.
Let's say you teamed up with everyone else on the planet to write it down.
And you can all write a digit every second.
The number would take 12 and a half days to write down.
And the you have to start with the long division.





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