What is the value of this infinite continued fraction?

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What is the value of the simple continued fraction [1;2,3,5,7,11,13,...,nth prime] as n goes to infinity?
 
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You can compute it to as many decimals as you like. There is absolutely no reason to think this constant can be written in any simpler way.
 
g_edgar said:
You can compute it to as many decimals as you like. There is absolutely no reason to think this constant can be written in any simpler way.

...but if you find a pattern, you'd better run it by my before telling anyone else! :cool:
 

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