Primes reciprocated

Find the sum of all primes \(P\) such that the decimal expansion of \(\frac{1}{P} \) has a fundamental period \(5\).

Details and Assumptions:

  • As an explicit example, \(\frac{1}{3}=0.33333\ldots\) has fundamental period \(1\) and \(\frac{1}{101}=0.00990099\ldots\) has a fundamental period \(4\).
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