Pietro Antonio Cataldi (15 April 1548,

Bologna Bologna (, , ; egl, label= Emilian, Bulåggna ; lat, Bononia) is the capital and largest city of the Emilia-Romagna region in Northern Italy. It is the seventh most populous city in Italy with about 400,000 inhabitants and 150 different nat ...

– 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, structure, space, models, and change. History On ...

. A citizen of Bologna, he taught mathematics and

astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...

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

continued fraction In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer ...

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

Euclid Euclid (; grc-gre, Wikt:Εὐκλείδης, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Euclid's Elements, Elements'' trea ...

'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 divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number. T ...

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 folklore genre consisting of Narrative, narratives that play a fundamental role in a society, such as foundational tales or Origin myth, origin myths. Since "myth" is widely used to imply that a story is not Objectivity (philosophy), ...

that the

s had

units digit A numerical digit (often shortened to just digit) is a single symbol used alone (such as "2") or in combinations (such as "25"), to represent numbers in a positional numeral system. The name "digit" comes from the fact that the ten digits (Latin ...

s that invariably alternated between 6 and 8. (Until Cataldi, 19 authors going back to

Nicomachus Nicomachus of Gerasa ( grc-gre, Νικόμαχος; c. 60 – c. 120 AD) was an important ancient mathematician and music theorist, best known for his works ''Introduction to Arithmetic'' and ''Manual of Harmonics'' in Greek. He was born in ...

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 ''History of the Theory of Numbers'' is a three-volume work by L. E. Dickson summarizing work in number theory up to about 1920. The style is unusual in that Dickson mostly just lists results by various authors, with little further discussion. T ...

''). Cataldi's discovery of the 7th (for p=19) held the record for the

largest known prime The largest known prime number () is , a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018. A prime number is a posi ...

for almost two centuries, until

Leonhard Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...

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.

References

External links

*
Galileo Project
1548 births 1626 deaths 16th-century Italian mathematicians 17th-century Italian mathematicians {{Italy-mathematician-stub