Pietro Cataldi

Due lettioni, 1613

Pietro Antonio Cataldi (15 April 1548, Bologna – 11 February 1626, Bologna) was an Italian mathematician. A citizen of Bologna, he taught mathematics and astronomy and also worked on military problems. His work included the development of simple continued fractions and a method for their representation. He was one of many mathematicians who attempted to prove Euclid's fifth postulate.

Cataldi discovered the sixth and seventh perfect numbers by 1588.^[1] His discovery of the 6th, that corresponding to p=17 in the formula M_p=2^p-1, exploded a many-times repeated number-theoretical myth that the perfect numbers had units digits that invariably alternated between 6 and 8. (Until Cataldi, 19 authors going back to Nicomachus are reported to have made the claim, with a few more repeating this afterward, according to L.E.Dickson's History of the Theory of Numbers). Cataldi's discovery of the 7th (for p=19) held the record for the largest known prime for almost two centuries, until Leonhard Euler discovered that 2³¹ - 1 was the eighth Mersenne prime.^[1] Although Cataldi incorrectly claimed that p=23, 29, 31 and 37 all also generate Mersenne primes (and perfect numbers), his text's clear demonstration shows that he had genuinely established primality through p=19.

See also

• Ibn Fallus, who discovered the sixth and seventh perfect numbers more than 300 years earlier, but also included non-perfect numbers in his list

References

1. Caldwell, Chris. The largest known prime by year.

External links

• O'Connor, John J.; Robertson, Edmund F., "Pietro Cataldi", MacTutor History of Mathematics Archive, University of St Andrews
• Galileo Project