# On J. T. Condict's Senior Thesis on Odd Perfect Numbers

I am trying to locate a copy of J. T. Condict's senior thesis on odd perfect numbers:

J. Condict, On an odd perfect number's largest prime divisor, Senior Thesis, Middlebury College (1978).

I am sure a soft copy would have been archived somewhere. Would anybody know where (in the Internet) that archive is?

• Why would you expect this to be available online? Your best bet is to use interlibrary loan. Most likely there is only one copy (at Middlebury). – Andy Putman Dec 11 '11 at 5:07
• Depending on the way it is cited you should not assume that everybody citing something always read it or even saw a copy of it. – user9072 Dec 11 '11 at 12:28
• Amie, why are the result you expect to be there that makes you interested by this senior thesis ? – Joël Dec 11 '11 at 21:01
• @Joel, if you will just permit me to ask, may I know the reason why you asked for the "results [that I] expect to be" in J. Condict's senior thesis "that makes me interested" to read/see a copy of it? In particular, may I ask if you have access to the Middlebury College thesis archives? :) – Arnie Bebita-Dris Jun 9 '12 at 22:06
• My advice would be to write to one of the people who has cited Condict's thesis. – Gerry Myerson Jun 13 '12 at 4:09

This is Jim (Condict) Grace, the author. I just saw this post. I'm sorry to hear that Middlebury may have lost their copy. I'm not sure where mine is, but I'll keep an eye out for it. (It may be at a family house 1,000 miles away but I'll look for it at Christmas when I visit.) If I find it, I'll scan and post it somewhere, and I'll comment again here with a link for it. As far as I know there is no existing soft copy. I typed it originally on Middlebury's timesharing academic computer but I long since lost my ability to read the mag tape reel backup -- and subsequently parted with the tape.

When I finished the thesis I sent another hard copy as a courtesy to Peter Hagis Jr. at Temple U., since he and McDaniel had done the research on which I based my work. Hagis subsequently cited my work in a published paper, and it may be that others have just copied this citation without seeing the original.

The main innovation in my thesis over previous work is that I wrote a FORTRAN program to automate some of the algebraic manipulations that had previously been done by hand, making it practical to extend the previous result upwards. It still took several months on Middlebury's academic 16-bit PDP11-45 computer to finish all the computations. I managed to install the program to start as a low-priority background job whenever the computer restarted, and I programmed it to pick up from where it had left off.

If you have any other questions about the thesis, let me know and I might be able to answer them. :) Cheers, Jim

My answer to Arnie Dris's question below is too long to be entered as a comment, so I'm putting it here:

I'm happy to help as I am able, although I've spent the 35 years since my BA thesis as a software developer and my number theory is a bit rusty! Also I don't have access to my thesis, or immediate access to the prior work it was based on. But I may still be able to answer your questions. The number theory part of my work was as explained by Peter Hagis Jr. and Wayne L. McDaniel in "On the largest prime divisor of an odd perfect number." II, Math. Comp. 29 (1975), 922–924. I did not attempt to add or subtract from the number theory analysis they had done. My only innovation was to automate by computer some of the algebra they had done by hand, which made it more practical to get a higher result.

My memory of this is a bit fuzzy, but I seem to recall that there were two rather tedious steps in the proof. The first involved some algebraic manipulations which Hagis and McDaniel did by hand and I did by computer. The second involved some more straightforward computations which they did by computer and so did I. If you have access to their paper, I expect that you will see what I mean as you read it. If this doesn't make sense on reading their paper, please let me know. I do live near a college that I expect would have the Mathematics of Computation, so I could go and reread their article. It might help to improve my memory! ;) Cheers, Jim

• Wow! This could make a wonderful story for Best of MathOverflow! – François G. Dorais Aug 23 '13 at 22:39
• Hi again @jim-condict-grace. Let $N = {q^k}{n^2}$ be an odd perfect number given in the so-called Eulerian form (i.e., $q$ is prime with $q \equiv k \equiv 1 \pmod 4$ and $\gcd(q, n) = 1$). In your senior thesis at Middlebury, did you consider the possibility of the Euler prime $q$ being the same as the largest prime factor of $N$? Yes or no, can you comment slightly on what bearing the data you have obtained from running your program before on the PDP11-45 had on this particular question? Thanks! -- Arnie Dris – Arnie Bebita-Dris Sep 9 '13 at 14:57
• Arnie, these look like good questions. Please see my answer above. – Jim Condict Grace Oct 10 '13 at 13:21
• Here is the link to the paper alluded to by Jim - ams.org/journals/mcom/1975-29-131/S0025-5718-1975-0371804-2 – Arnie Bebita-Dris Oct 10 '13 at 14:27
• Thanks Arnie, I hadn't realized the text would be free online. The details are in their earlier work: ams.org/journals/mcom/1973-27-124/S0025-5718-1973-0325508-0. Looks like it was Phase I that they did by hand and I automated. I hope the thesis isn't lost -- a first search by a family member turned up empty. :( I'll check myself at Christmas. Cheers. – Jim Condict Grace Oct 10 '13 at 15:00