Here's something you can do without thinking, assuming you've had the same realisation I've just had:
Write down a multiple of 2¹⁰⁰
This is Mur 
@mur2501 I should have specified: write down a number as a sequence of digits
@christianp My first thought was \( 2^{101} \), my second thought was probably what you're thinking. An interested starting place to create a possibly interesting puzzle.
CC: @mur2501
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@ColinTheMathmo @christianp
Also show me what you two are thinking 
