What are the last digits of Moser's number?

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How can I find the terminating digits of Moser's number, which is 2 in a "mega"-gon in Steinhaus-Moser notation (a mega being 2 in a pentagon)?

I was able to calculate the last 6 digits by analyzing the last digits of much smaller numbers in the 2 in a polygon sequence (2 in a hexagon, 2 in a heptagon, etc.), but is it possible to calculate, say, the last 10 digits?

How many terminating digits of the Moser can be practically calculated?