Summary: Based on the properties of prime numbers, two categories of image scrambling algorithms, double-secret-key and single-secret-key algorithms are presented. The disorder degrees are computed and are compared with the well-known Arnold method. Our new methods can disorder the image quickly, it extends the dimension of the secret key space and satisfies the Kerckhoffs hypothesis in cryptology. Experiments show that our methods have high security and can obtain the expected disorder degree quickly.