We define a *full prime* as a prime number such that every suffix is also a prime.

Some examples of full primes are:

- 2113 because all 2113, 113, 13 and 3 are all primes.
- 6997 because all 6997, 997, 97 and 7 are all primes

Let \(S\) be the sum of all full primes. What are the last three digits of \(S\)?

**Clarification**: 2, 3, 5 and 7 are considered as full prime.

**Hint**: Every suffix of a *full prime* is a full prime.

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