||mmk150 'at' rutgers.edu
||Distribution of Witnesses
My project concerns the distribution of witnesses used in the Rabin-Miller Test for primality.
- Week 1:
- More details of the project were discussed. A literature search has revealed some promising articles related to the topic, the first couple of which I am beginning to read through in the hopes that more information can be gleaned from observations made in them. I have coded some programs in Matlab and Java to assist in gathering some data, and am aiming to make them efficient enough to handle some truly large inputs.
- Week 2:
- I am investigating and going through the information in the paper by Rabin. After retooling and optimizing some of my code in C, I think I am just about ready to start the data collection process. After that, the real fun can begin!
- Week 3:
- The data collection is just about finished. Alas, there may be some space constraints on the amount of data I can collect, since storing all this has used up about 210 GB of space on my hard drive, something I'm not quite sure how to improve without sacrificing functionality or convenience. I have developed a more thorough understanding of the papers. Looking through what data there is so far, I can see a couple plausible conjectures pertaining to the witness distribution.
- Week 4:
- Some new numerics were discussed, and I think that a particular theorem involving exponential sums can be used to prove or disprove some facts regarding the distribution of witnesses, without knowing too much about the actual set. I will have to prove some constraints about the set or its complement, though.