Prime Crime 2

Computer Science Level 4

How many primes \(p\) less than \(10^{5}\) exist such that:

\(p\bmod {10^4},p\bmod {10^3},p\bmod {10^2}\) and \(p\bmod {10}\) are also prime?

As an explicit example, 2017 is one of them since 2017,17 and 7 are all prime.

Hint: The answer is a perfect square.

this problem is a part of set Prime Crimes via Computer Science

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