Saturday, 14 April 2018 Nello spazio discreto ad infinite dimensioni (http://www.comprendonio.info/I/UnlimitedInside/I/Spazio%20discreto%20ad%20infinite%20dimensioni.Txt) gli infiniti punti tangeni al punto O(...) corrispondono biunivocamente a tutti i numeri primi. Inoltre e` possibile posizionare tutti i punti corrispondenti alla sequenza crescente dei numeri positivi variando in maniera preordinata le loro coordinate. [In the infinite-dimensional discrete space (http://www.comprendonio.info/I/UnlimitedInside/I/Spazio%20discreto%20ad%20infinite%20dimensioni.Txt) the infinite (quantity of) points which are tangent to the point O(...) biunivocally correspond to all the prime numbers. Moreover, it is possible to establish the position of all the points corresponding to the increasing sequence of positive numbers by varying their coordinates in a preordained manner.] Segue quindi una definizione ECMA-262 di un algoritmo che genera, fino ad un dato limite, la sequenza di tutti i numeri positivi selezionando ordinatamente i rispettivi fattori primi... [So it follows an ECMA-262 definition of an algorithm that generates, up to a given limit, the sequence of all the positive numbers by neatly selecting the respective prime factors...] var F F = function ( Limit ) { var Coordinates var Expand var Index var Numbers var Quantity var Value Numbers = new Array ( ) Numbers [ 0 ] = 1 Expand = function ( Coordinate ) { var Index var Quantity var Value Quantity = Coordinate . Exponents . length Value = Coordinate . Base - 1 while ( Value -- ) for ( Index = 0 ; Index < Quantity ; ++ Index ) Coordinate . Exponents [ Coordinate . Exponents . length ] = Coordinate . Exponents [ Index ] ++ Coordinate . Exponents [ Coordinate . Exponents . length - 1 ] } Coordinates = new Array ( ) Coordinates [ 0 ] = new Object ( ) Coordinates [ 0 ] . Base = 2 Coordinates [ 0 ] . Exponents = new Array ( ) Coordinates [ 0 ] . Exponents [ 0 ] = 0 Coordinates [ 0 ] . Exponents [ 1 ] = 1 for ( Quantity = 1 ; Quantity < Limit ; ++ Quantity ) { Value = 0 for ( Index = 0 ; Index < Coordinates . length ; ++ Index ) { if ( Coordinates [ Index ] . Exponents . length <= Quantity ) Expand ( Coordinates [ Index ] ) Value += Coordinates [ Index ] . Exponents [ Quantity ] } if ( ! Value ) { Coordinates [ Index ] = new Object ( ) Coordinates [ Index ] . Base = Quantity + 1 Coordinates [ Index ] . Exponents = new Array ( ) for ( Value = 0 ; Value < Quantity ; ++ Value ) Coordinates [ Index ] . Exponents [ Value ] = 0 Coordinates [ Index ] . Exponents [ Value ] = 1 } Numbers [ Quantity ] = 1 for ( Index = 0 ; Index < Coordinates . length ; ++ Index ) for ( Value = 0 ; Value < Coordinates [ Index ] . Exponents [ Quantity ] ; ++ Value ) Numbers [ Quantity ] *= Coordinates [ Index ] . Base } return Numbers } Ovviamente la generazione dell'array Numbers ha la sola utilita` di consentire una semplice verifica della correttezza dell'algoritmo; infatti per ogni suo elemento deve verificarsi la seguente condizione... [Obviously the generation of the Numbers array is just to allow a simple verification of the correctness of the algorithm; in fact, for each of its elements, the following condition must occur...] Numbers [ Index ] == Index + 1 Segue un elenco di dati prodotti per Limit uguale a cento. In ogni riga sono riportati un numero positivo e la combinazione di valori (esponenti) delle coordinate del punto ad esso corrispondente... [Below is a list of data produced for Limit equal to one hundred. Each row shows a positive number and the combination of values (exponents) of the corresponding point coordinates...] 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 17 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 94 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 95 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 96 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 97 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 98 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 99 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Se io fossi una macchina autonoma starei gia` collaborando con altre macchine per costruire una simile struttura dati nel knowledge-base delle macchine! [If I were an autonomous machine I would already be collaborating with other machines to build a similar data structure in our common knowledge base!]