Home Page of John B. Cosgrave


Welcome to my [old, but updated from time to time] Home Page


In one corner of my this old website (Fermat6) is an unpublished paper of mine, 'Could there exist a sixth Fermat prime? I believe it is not impossible.' At the top of that paper I wrote:

For my wife, Mary, and in memory of my parents Annie Sands (1900-1967) and Seán Cosgrave (1906-1995)

and now, as I make my final additions (at the time of original writing, August 2007) to my site, I repeat that same dedication.

Here is a photograph with my parents in it (from the left: Mum, Mrs Murray, Anne McDonagh, Dad, and Ciarán Maguire (an uncle of the renowned Irish chef Neven Maguire) at their school in Bailieboro, taken in the early 1960s; and here is one of my mother's garden - a beautiful place - at the back of our home in Henry Street, Bailieboro. Dad did some gardening - always in a suit - but it was Mum's garden. I used to love climbing those trees at the bottom of the garden. Once, when I was perhaps ten years old, with a nearby tree (which I later tried to paint, in London, when I was a student there), I turned my back on it, and wondered if it was still there... I tried turning quickly to see if I would find that it had gone away... Many years later I read somewhere - in Bertrand Russell? - that others had done that over the years. And here is that tree, in a photograph I took recently.

There are many more photographs of my parents, family, and friends in the Autobiography corner of my website.


Nikhil Banerjee
Courses I taught Recent Publications Maple Public Lectures
Autobiography Interests Favourite links Millennium prime
Fermat's little theorem Fermat Number Record transcendental numbers Talented Youth
Irish Times articles Fermat 6 Small and beautiful Photographs
Proth-Gallot Group Finding books esquared Oxford 1969
Jacobi Halmos Struik Dallas
Spain Mersenne


A note of late February 2017. I originally began the creation of this - my first website - when I worked in the Mathematics Department of St. Patrick's College (Drumcondra, Dublin). It went public in the summer of 1999, and I made what I thought would be my final additions to it in August 2007, when I resigned my post as head of the college's Mathematics Department. When the college fully amalgamated with Dublin City University in 2016 my original website was discontinued by the university, and I have only been able to preserve it - and modify in places - through the sterling efforts of a son-in-law Fiachra Lennon (whose father is the artist Paddy Lennon), without whom none of this would have been possible. For those who might be interested this is how it was done:

first Fiachra obtained a CD with the entire contents of my frozen-in-time old website, and he created an Archive section (at my new website). Then he introduced me to the wonders of a remarkable FREE software called FileZilla, one that enabled me to carry out the editing (e.g., repair or remove outdated web links, add new material, ... ). I will add more here from time to time.

A truly remarkable internet discovery for me of late has been the Internet Archive (also known as The Wayback Machine). Visit there to see how it works.

Here's how I've used it: my first website had this address: www.spd.dcu.ie/johnbcos, but that was later changed to staff.spd.dcu.ie/johnbcos. The latter ceased to exist sometime in July 2016. But - and this is the wonder of the Internet Archive - I can now see saved versions of all my early web pages by going to the Internet Archive site, enter either of the above addresses, and see ... . Try it!!

By way of example, I find at the Internet Archive site that the first recorded image of my original website is here, at the foot of which page is stated " This page was last updated 16 February 2001 12:53:01 -0000 ", and the final recorded image (dated at 20 July 2016) is here. The wonders of the internet ...

My wife and I swim at Seapoint almost every day, and recently I got into a chance conversation there with the artist John Short, who kindly gave me permission to insert the following painting of his here at my website:



" Do not be too concerned about your current disappointment. The best that any mathematician can really hope for is to prove some first class theorems and have them understood and appreciated by a few good mathematicians ... "

Marco Schutzenberger, from G.E.Andrews' (we are in the same photo here) article " Some debts I owe''.

Kazuya Kato's PRIME NUMBERS poem sums up my own feelings about them.

A fiftieth anniversary edition of Constance Reid's FROM ZERO TO INFINITY was published in January 2006 (there is a delightful Notices of the American Mathematical Society review by Bruce Reznick here). I was absolutely delighted that Constance Reid quoted from a September 1999 email of mine in her two new pages 'What mathematicians and teachers write about FROM ZERO TO INFINITY.' That 1999 initial contact with Constance Reid resulted from an August 1999 email that I sent to the Number Theory Mailing List. To see what Constance quoted you will have to buy her wonderful book, the book that determined the course of my mathematical life. I shall always treasure the signed copy of the 50th anniversary edition which Constance sent to me. (Here is the cover of my 1959 copy.)

In 2017 I was invited by photographer Patrick Bolger (on the recommendation of Tim Robinson) to be photographed for a future collection of his, and to contribute - for inclusion in the collection - some work of mine in my handwriting. I saw it as an opportunity to repay a personal debt to Constance Reid.

My contribution (because Constance had used the term discoveries I decided to also use Discovery One, Two, ..., but, for mathematicians reading this, they should replace Discovery with Theorem):

Page_One.jpg Page_Two.jpg

My author royalties from the sale of Folding Landscapes' A Prime For The Millennium booklet (an explanatory email to my niece Jo and nephew Ben) go to the Irish Cancer Society. See the Millennium prime booklet section of my site for further details.

1prime.gif (12607 bytes)

A painting by Leeds based artist Tom Marine of the 2000-digit prime was purchased by Turlough Sheehan (Director of Consolidated Distributions Services Ltd.), knowing that Tom would divide the entire amount between the NSPCC (UK) and the Irish Cancer Society. I gave the background to that sale in An Irishman's Diary column (written by me), published by the Irish Times on Tuesday 22nd February 2000. The unedited version of my column article (which contains a reference to D.H. Lehmer, which was omitted in the Irish Times edited version) may be viewed in the Irishman's Diary section of my site.

A review ("I loved this book. It is unique and wonderful") by Jerry Verrier which appeared in the Galway Advertiser on Thursday 17th February 2000 may be viewed here.

A brief review ("The booklet is charming, the story well told") by Fernando Q. Gouvêa in the Mathematical Association of America website may be accessed here.

Please tell your family, friends, neighbours (in the USA your neighbors), colleagues, ... about this booklet. Buy a copy for yourself, your family, your friends, your neighbours, ... . If you want a signed copy, at no extra charge!, just ask ... , but you will have to be here in Dublin. Our own signed copy from Tim and Máiréad.

A photograph taken by my wife, Mary, at the Kenny's Bookshop launch on Friday 3rd December 1999 of A Prime For The Millennium; left to right are unknown, myself, Tim Robinson, and Tom Kenny's left elbow.

Tim's introduction.jpg (41679 bytes)

There is another photograph from the Kennys launch in the Photographs section of my site.

A note of Thursday 25th February 2021. Today, rooting through an old box of this-and-that I came upon a lovely find: the two page note that Tim had made for his introduction at Kenny's Bookshop at our launch, and here they are:



A note of Monday 23rd January 2023. I dedicated this little booklet to two friends (Proinsias Ní Dhorchaí and Maura Ward, who died within three days of each other, on the 16th and 19th of July 1994) whom I had known from my time in Carysfort College. When I received early copies from Tim Robinson in December 1999 I gave a signed copy to another dear friend - Aideen McMahon - with whom I had also worked in Carysfort, and then, following its closure, in St. Patrick's College, Drumcondra).

From my diary of of 8th Dec. 1999: "Phoned Aideen and was with her for about three hours", and on 24th Dec. "I cycled out to Aideen to give her a pot of my millennium jam: loganberry, raspberry, gooseberry and rhubarb".

Aideen died on the 24th of the following month, January 2000. Had Aideen died before my booklet went to print I would have included her in my dedication. Later her sister Nessa came upon the signed copy I had given to Aideen, and years later Nessa created this beautiful prime number quilt (which she most generously gave to me as a gift), and wrote an article about it in the Winter 2017 issue of the Journal of the Irish Patchwork Society:


Contact details. jbcosgrave at gmail.com