Abstract This article presents properties of primitive Pythagorean triples (PPTs) that have potential applications to cryptography. It shows that the six classes of primitive Pythagorean triples can be put into two groups, and autocorrelation and cross-correlation functions of the six classes derived from the gaps between each class type have been computed. It is shown that Classes A and D (in which the largest term is divisible by 5) are different from the other four classes in their randomness properties if they are ordered by the largest term. In the other two orderings, each of the six random sequences has excellent randomness properties.