1. An apparatus that generates a physical random number sequence, comprising: a physical random number generator configured to generate physical random numbers; a test circuit configured to perform a test process to check randomness of the physical random numbers, the test process including counting a number of subsequent bits having the same value as a first bit in a predetermined number of bits of the physical random numbers, to output the counted number of subsequent bits as statistical information; a minimum entropy estimating circuit configured to estimate a minimum entropy based on the statistical information generated as a byproduct of the test process; an entropy compressing circuit configured to perform an entropy compression process using the physical random numbers as an input to produce the physical random number sequence; and an entropy control circuit configured to control based on the minimum entropy a number of bits of the physical random numbers input into the entropy compression process performed by the entropy compressing circuit, wherein a result of the test process indicating satisfactory randomness causes the physical random numbers generated by the physical random number generator to be retained and used in the entropy compression process, and a result of the test process failing to indicate satisfactory randomness causes the physical random numbers generated by the physical random number generator to be discarded and unused in the entropy compression process.