A *Mersenne prime* is a prime number of the form 2* ^{n}* − 1, such as 8 (= 2

Pierre de Fermat (1601–1665) spent most of his life as a lawyer in Toulouse, following a legal career. He published little, and communicated with other mathematicians by letter.

He made substantial contributions to the development of analytic geometry, analysing lines, planes and conics algebraically, but is mainly remembered for his contributions to number theory. These include his ‘little theorem’ that *a ^{p}* –

In his copy of Diophantus’s *Arithmetica* Fermat claimed to have ‘an truly marvellous demonstration which this margin is too narrow to contain’ of what became known as *Fermat’s last theorem*: for any integer *n* > 2 there are no non-trivial integer solutions *x*, *y* and *z* of the equation *x ^{n}* +

*[Czech Republic 2000; France 2001; Liechtenstein 2004]*