Patent Document ID: 9542158
Application ID: 10306072
Patent Flag: 1

Claim One:
1. A computer-implemented method for generating prime numbers for data encryption via a computer system, wherein the computer system comprises one or more processors, a random-access memory, a read-only (non-volatile) memory, and an I/O subsystem, the method comprising: determining at least one element of a T-sequence, the T-sequence being one of a family of related non-montonic sequences and being defined as: T l 0 =2, T l 1 =l and T l n+1 =l·T l n −T l n−1 , wherein the subscript denotes the nth term while the superscript denotes the order l, such that the zeroth term is 2 and the first term is l, and wherein l=3 is the first T-sequence, and each successive term is defined as follows: T 3 0 −2, T 3 1 =3, T 3 2 =7, T 3 3 =18,. .. , T 3 n+1 =3·T 3 n −T 3 n−1 ; using said at least one element to determine primality of at least one arbitrary positive integer by performing a binary decomposition on the at least one arbitrary positive integer in polynomial time; wherein within the random-access memory and the read-only memory a routine is stored for generating T-sequence terms, and wherein the routine is used by one or more other routines, the one or more routines including a primality testing routine, a factoring routine, a prime number generator, and/or a random number generator; and encrypting data using a cryptographic function for data security within a computer system or network utilizing the primality of at least one arbitrary positive integer determined by the binary decomposition.