Find the first 10-digit prime number that is found in consecutive digits of \(e\).

Background: The tech giant Google is known to have setup such billboards in the heart of Silicon Valley, and later in Cambridge, Massachusetts; Seattle, Washington; and Austin, Texas. It read

"

{first 10-digit prime found in consecutive digits of e}.com".

Solving this problem and visiting the website led to an even more difficult problem to solve, which in turn led to Google Labs where the visitor was invited to submit a resume. Unfortunately, that website has been taken down.

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