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Some digging reveals that a common method for generating OTPs is through repeated hash function applications. A good hash function should produce uniformly distributed outputs.

There are 78,498 primes less than 10^6 (so, primes less than 6 digits), meaning that there is about a 7.9% chance of independently seeing a prime OTP if the OTPs are uniformly distributed. That seems pretty high. The expected value for seeing a prime OTP after multiple trials is just 15.

So I wonder if your friend is just unlucky or if his OTP provider is using another method for OTP generation.



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