Pietro Antonio Cataldi (15 April 1548,

Bologna Bologna ( , , ; ; ) is the capital and largest city of the Emilia-Romagna region in northern Italy. It is the List of cities in Italy, seventh most populous city in Italy, with about 400,000 inhabitants and 150 different nationalities. Its M ...

– 11 February 1626, Bologna) was an Italian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. A citizen of Bologna, he taught mathematics and

astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

and also worked on military problems. His work included the development of

simple continued fraction A simple or regular continued fraction is a continued fraction with numerators all equal one, and denominators built from a sequence \ of integer numbers. The sequence can be finite or infinite, resulting in a finite (or terminated) continued fr ...

s and a method for their representation. He was one of many mathematicians who attempted to prove

Euclid Euclid (; ; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of geometry that largely domina ...

's fifth postulate. Cataldi discovered the sixth and seventh

perfect number In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfec ...

s by 1588.Caldwell, Chris
''The largest known prime by year''
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 Myth is a genre of folklore consisting primarily of narratives that play a fundamental role in a society. For scholars, this is very different from the vernacular usage of the term "myth" that refers to a belief that is not true. Instead, the ...

that the

s had

units digit A numerical digit (often shortened to just digit) or numeral is a single symbol used alone (such as "1"), or in combinations (such as "15"), to represent numbers in positional notation, such as the common base 10. The name "digit" originate ...

s 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 Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...

discovered that 2³¹ - 1 was the eighth Mersenne prime. 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.

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External links

*
Galileo Project
1548 births 1626 deaths 16th-century Italian mathematicians 17th-century Italian mathematicians People from the Papal States {{Italy-mathematician-stub

See also

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External links