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 Mp=2p-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
edit- 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
edit- ^ a b Caldwell, Chris. The largest known prime by year.
External links
edit
- O'Connor, John J.; Robertson, Edmund F., "Pietro Cataldi", MacTutor History of Mathematics Archive, University of St Andrews
- Galileo Project
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