Mathematician:Pietro Antonio Cataldi

Italian mathematician who taught mathematics and astronomy.
 * Worked on the development of continued fractions.
 * Attempted in vain (as so many before and since) to prove Euclid's fifth postulate.
 * Supposed to have discovered the 6th and 7th Mersenne primes $$M_{17}$$ and $$M_{19}$$ in 1588.

Nationality
Italian

History

 * Born: April 15, 1548
 * Died: February 11, 1626

On Mersenne Primes
Cataldi is supposed to have discovered the 6th and 7th Mersenne primes $$M_{17}$$ and $$M_{19}$$ in 1588. Recent researches, however, suggest that these may have already been discovered by 1460. But as no evidence has been found from that date that they had been proven to be prime, it is possible that these were just lucky guesses.

Cataldi also claimed the primality of the Mersenne numbers $$M_{23}, M_{29}, M_{31}$$ and $$M_{37}$$. Fermat proved him wrong about $$M_{23}$$, which has $$47$$ as a divisor, and $$M_{37}$$ which has $$223$$ as a factor. Euler showed in 1738 that $$M_{29}$$ has the factor $$233$$. However, by 1772 Euler had shown that $$M_{31}$$ is indeed prime.

As Cataldi had not actually demonstrated the primality of $$M_{31}$$ (and because of his mistakes regarding $$M_{23}, M_{29}$$ and $$M_{37}$$), he is not credited with its discovery - that one goes fair and square to Euler.

Books and Papers

 * "Trattato de nvmeri perfetti di Pietro Antonio Cataldo" (1603).