Irishman's Diary
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The unedited version of my Irish Times'
'An Irishman's Diary' column of 22nd Feb. 2000

An e-mail of 8th January 1999 to a young niece and nephew - explaining in simple terms my serendipitous discovery of a beautifully constructed 2000-digit prime number - has just resulted in a painting of that prime number being bought by Turlough Sheehan of Consolidated Distribution Services to the benefit of the Irish Cancer Society (ICS) and the NSPCC (UK). This is the story of that year long link.

     About 2300 years ago, Euclid, the renowned Greek mathematician, contemplated this question: how many prime numbers are there altogether? Prime numbers - a fundamental goldmine for profound mathematical questions and real world applications (being a cornerstone of modern public-key cryptography) - are those whole numbers which are evenly divisible only by 1 and themselves. The first several, and some later ones are: 2, 3, 5, 7, 11, 13, 17, ... , 127, ... , 1009, ... , 8191, ... , 65537, ... .

     Part of Euclid’s fame rests on his giving a definite proof that there are infinitely many prime numbers, but a fundamental difficulty with his existence proof is that although it provides a guarantee that there are infinitely many primes, it does not provide an easy means of finding a particular prime; a completely unresolved question is: given a definite prime number, what is the one immediately following? The next prime after 8191 happens to be 8209, whereas the one following 65537 is 65539; gaps of 18 and 2 respectively. Again, what is the billionth (say) prime number? That number actually exists, but it is by no means easy to produce it. In short, there is no ready means for producing a particular prime, or an especially large one.

     In January last year, wishing to illustrate for my students a beautiful idea of the English mathematician Henry Cabourn Pocklington (1870-1952), I discovered a prime number with exactly 2000 digits. Pocklington wasn’t a professional mathematician; he was a physicist, who enjoyed the distinction of being a Fellow of the Royal Society, but he produced one short (only two pages!), magnificent mathematical paper during the First World War which has guaranteed his place in history. Pocklington’s seminal paper was rescued from oblivion in 1927 by the renowned US mathematician Derrick Henry Lehmer (1905-1991). I dubbed my lucky discovery a millennium prime, and informed professional colleagues world-wide. Within a few days it featured in Ivars Petersen’s wonderful MathTrek column in the US weekly Science News, and at the same time I wrote a lengthy e-mail to niece Jo and nephew Ben, explaining in simple terms my discovery of the 2000-digit prime, and that at the time was that. Then in late July I was the fortunate joint discoverer with Yves Gallot (Toulouse) of the (then, and still) largest known composite Fermat number, a number so large that it could not be written out in the entire universe, even if the universe was filled with paper of atomic levels of thinness, and the digits written as micro-dots. (The html text of a public lecture I gave last October about the history of Fermat numbers may be viewed here). That discovery - which resulted in many sleepless nights! - attracted a lot of interest and much friendly correspondence, amongst which was a delightful one from author/cartographer Tim Robinson.

     Tim - who studied mathematics in Cambridge - sent me a copy of an article he had written about prime numbers for inclusion in Marie Heaney’s Sources, and I reciprocated with my January millennium prime e-mail. Within a few days I heard from Tim and his wife Máireád, seeking my consent to publish the text of my explanatory e-mail under the imprint of their Folding Landscapes, and I immediately agreed. The resulting booklet - A Prime For The Millennium - designed by Simon Cutts and Tim Robinson, was recently published, and the ICS agreed to accept my author royalties.

     The Guardian of November 22nd contained a lengthy article by David Ward about the booklet, together with a visually stunning display of all 2000 digits of the millennium prime. There followed several interesting responses: besides hearing from two composers (one of whom wanted to use all 2000 digits as the basis of a composition; the other seeking a 216-digit prime for his purposes) I also heard from a Leeds-based painter, Tom Marine.

     In recent months the British NSPCC launched its Full Stop campaign ("Put a full stop to child abuse"), and Tom Marine contemplated a work with sale price donated to them. On reading the Guardian article, Tom Marine conceived the idea of a 40 by 50 inch canvass, with the entire 2000 digits entered into the unit squares, each digit represented by a different shade of red, with one exception: a single green (representing the Full Stop of the NSPCC campaign) in a square of my choice. I opted for the 27th square in the 49th row.

     I got the idea of finding a carrier who would bring Tom Marine’s work to Ireland to find a buyer here, with the sale price to be divided equally between the NSPCC and the ICS. Coming to hear of this, Turlough Sheehan immediately offered to be the carrier and purchaser. I contacted Tom Marine and he accepted Turlough Sheehan’s generous offer. Bravo to Tim, Máireád, Tom and Turlough.

John Cosgrave