Let \(S\) be the sum of all 100-digit prime numbers found in consecutive digits of \(\pi\) to the 100,000 decimal places. What is the digit sum of \(S\)?

**Clarification**: The numbers should not have leading zeroes. 00857 is considered as a 3-digit number.

The image is of the Google Billboard Puzzle in 2004 asking for the first 10-digit prime number found in consecutive digits of \(e\). It's been more than 10 years since the puzzle being published in Silicon Valley, and over 800 Brilliant.org users have solved the problem! Now, computers have more computational power and programmers are getting smarter and younger, which inspired this problem.

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