Dublin mathematician gets Fermat's number

Anyone whose interest in numbers reaches beyond the total of fingers and toes only as far as the current Telecom share price …

Anyone whose interest in numbers reaches beyond the total of fingers and toes only as far as the current Telecom share price can probably stop reading now.

The latest Irish breakthrough in theoretical maths is not going to affect their computations.

The news is the discovery of the 10th-largest known prime, that is, a number that can be divided evenly only by one and itself, and a new record for a prime discovered in Ireland.

More importantly, it is a factor of the astronomically large Fermat number F 382247, making the latter the largest known composite (non-prime) Fermat number.

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Before any reader pushes aside the cornflakes to reach for the calculator to try this at home, it is worth noting that the first discovery, the prime, has 115,130 digits.

It would take a day and a quarter to punch it into a calculator at one digit a second, in the unlikely event the calculator was willing to accept it.

Testing its prime status would take some further years of rapid key-punching. The Fermat number is rather larger. Written at four digits per inch it would occupy a board 10-to-the-power-of-57550 light years square.

Dr John Cosgrave made the discovery at St Patrick's College, Drumcondra, Dublin, while running special software on over 40 college computers for two months during the summer break.

The creator of the program, French scientist Yves Gallot, is credited as co-discoverer of the number.

For some 40,000 mathematical researchers around the world, or more particularly for the 800 working seriously on Fermat numbers, the discovery in Dublin on July 24th was significant.

If, as is likely, the Dublin finding is not topped by the factorisation of an even larger Fermat number by the end of the year it is likely to go forward as one of the major discoveries of the last years of the millennium.

The work of Pierre de Fermat, particularly his "Last Theorem" and the series of numbers he formulated in August 1640, have fascinated and puzzled mathematicians ever since.

The series of Fermat numbers 3, 5, 17, 257 . . . rapidly ascends into numbers of dizzying size and the story of finding factors for them over the years has been a yardstick of the progress of computation.