Full Prime

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.

You might also enjoy Merge Prime.

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