Luigi Poletti (mathematician)

Luigi Poletti (1864 – 1967) was an Italian mathematician and poet. He was born in Pontremoli, where he also died, aged 103 ( 103 is a prime number !, his main field of research were prime numbers ). His mathematical studies have been related to the expansion of the table of prime numbers, using an algorithm that he called Neocribrum.Named after Poletti are the so-called Poletti-periods, which are the product of the first prime numbers until a limit. For example, Poletti-period ( also called " prime number period" ) PP4 is the product of the first four prime numbers: 2 times 3 times 5 times 7, thus PP4 is 210.PP1=2, PP2 = 2 times 3=6, PP3 = 2 times 3 times 5 = 30, PP5 = 2310 and so on ( PP7= 510 510 ).The Poletti periods are used to find potential candidates for prime numbers: PPx plus 1 and PPx minus 1 are promising candidates for prime numbers. If they are not prime, one can easily find vast areas on the number ray which are free of prime numbers: PP36, a number with 60 digits, has a neighbour, PP36 minus 1 which is not prime, and all the following 166 smaller numbers ( at least) are not prime. Of course there are larger areas that are prime number free elsewhere, but the ones found by using Poletti-periods are easily predictable. see also :

* Mersenne-numbers,
* repunit-numbers

and number theory

cite web|title = Luigi Poletti|work = La guida di Pontremoli|publisher = Lunigiana.net|date = 1998|url = http://www.lunigiana.net/pontremoli/personaggi/personaggi08.htm|accessdate = 2007-12-13 it icon]

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