BigInteger Multitasking Agrawal, Kayal, and Saxena (AKS) Primality Test (c) June 19, 2016, by James Pate Williams, Jr. Microsoft TechNet Project Description

This application implements the algorithm described in the paper at the URL http://www.cse.iitk.ac.in/users/manindra/algebra/primality_v6.pdf. I replaced Step 1 of the algorithm with the Miller-Rabin probabilistic primality test. If that test shows that the number is composite, I return the value COMPOSITE. This algorithm is much easier to implement and understand that Wieb Bosmer’s Primality Proving with Cyclotomy also known as the Jacobi sums primality test. As a test we determine that the following Mersenne numbers are prime: M_1279, M_2203, M_2281, M_3217, and M_4253 where M_n = 2 ^ n – 1, and the primes have 386, 664, 687, 969, and 1281 decimal digits, respectively. M_1279 was first proven prime by Raphael M. Robinson on June 25, 1952, using the Lucas-Lehmer test on a SWAC computer. The same author found that M_2203 was prime on October 7, 1952, and M_2281 was prime on October 9, 1952, using the same method and computer. Hans Riesel determined that M_3217 was prime on September 8, 1957, using the Lucas-Lehmer test on a BESK computer. M_4253 was proven prime on November 3, 1961 by Alexander Hurwitz using the Lucas-Lehmer test on an IBM 7090 mainframe computer. See http://www.mersenne.org/primes/ for many more Mersenne primes. All of the computations illustrated below were performed on a late November 2015 Dell XPS 8900 computer with 16 GB RAM Intel(R) Core(TM) i7-6700K CPU @ 4.00 GHz running Windows 10 Pro. The .Net framework is .Net 4.5.2. This is a multitasking version of the original BigInteger variant of the application. Someone with a quad core CPU with 8 virtual processors can try NumberTasks = 8 to see if that speeds up this application more or less. I usually try to limit the number of tasks to actual number of cores.

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Author: jamespatewilliamsjr

My whole legal name is James Pate Williams, Jr. I was born in LaGrange, Georgia approximately 70 years ago. I barely graduated from LaGrange High School with low marks in June 1971. Later in June 1979, I graduated from LaGrange College with a Bachelor of Arts in Chemistry with a little over a 3 out 4 Grade Point Average (GPA). In the Spring Quarter of 1978, I taught myself how to program a Texas Instruments desktop programmable calculator and in the Summer Quarter of 1978 I taught myself Dayton BASIC (Beginner's All-purpose Symbolic Instruction Code) on LaGrange College's Data General Eclipse minicomputer. I took courses in BASIC in the Fall Quarter of 1978 and FORTRAN IV (Formula Translator IV) in the Winter Quarter of 1979. Professor Kenneth Cooper, a genius poly-scientist taught me a course in the Intel 8085 microprocessor architecture and assembly and machine language. We would hand assemble our programs and insert the resulting machine code into our crude wooden box computer which was designed and built by Professor Cooper. From 1990 to 1994 I earned a Bachelor of Science in Computer Science from LaGrange College. I had a 4 out of 4 GPA in the period 1990 to 1994. I took courses in C, COBOL, and Pascal during my BS work. After graduating from LaGrange College a second time in May 1994, I taught myself C++. In December 1995, I started using the Internet and taught myself client-server programming. I created a website in 1997 which had C and C# implementations of algorithms from the "Handbook of Applied Cryptography" by Alfred J. Menezes, et. al., and some other cryptography and number theory textbooks and treatises.

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