A method, cryptographic device, and computer readable memory with instructions, for generating a cryptographic key from at least one prime number, by performing during runtime of the cryptographic device by obtaining from memory a challenge and at least one associated increment number, generating a seed by applying a Physically Unclonable function to said obtained challenge, generating at least one prime number from said generated seed by performing said cryptographic prime numbers generation algorithm and by performing therein as many incrementation steps as said obtained at least one increment number, and generating the cryptographic key from the generated prime number.