Bringing Felkel´s table into space
2018, 16 Notations of 59 X 42 cm
Twin touch markers on markers paper

Bringing Felkel ́s table into space is a serie of 16 notations referring to the first list of prime numbers and  factors up to the number 144,000, written by Anton Felkel in 1776. Each of them represents the area of a  15 square meters diagramm that visualizes the decomposition of a number in possible pairs of prime  numbers which, if summed up, come to a same result. This is related to RSA, one of the first Public-Key Cryptographic system  is based on the challenge to decompose a very large number in two prime factors.

In mathematics, a prime number is a natural number greater than 1 that has only two distinct divisors: itself and 1.  On the contrary, composite numbers are natural numbers that have some natural divisor aside from themselves  and 1 and therefore, can be factorized. Factoring a number means simplifying its expression in terms of „fundamental blocks“,  which are called factors. For example, factoring a composite number means writing it as a product of prime numbers.

The history of the construction, organization, correction and publication of factor tables from 1657 to 1817, was a labour  of a considerable magnitude that pushed mathematicians and calculators to organise themselves in networks.  Around 1660, John Pells was the first English mathematician to motivate others to calculate a large factor table,  for which he saw many applications. About a century later (1770), Johan Heinrich Lambert, a Swiss polymath, launched a table project that was to engage many human computers and mathematicians in the (re) production  and extension of Pell‘s table.  Anton Felkel was a Polish-Austrian mathematician, who devoted several years of his  life to write lists of prime numbers and factors.

Felkel‘s table of factors was one ofthe several interesting projects spawned by Lambert’s call for tables.  Calculating the interval from 1 to 144.000 took him two months of work and he hoped to reach 10 millions  several years later.

The construction of factor tables is connected to the development of primality tests and  factoring algorithms. Since the advent of the digital computer and even more since the invention of RSA Public-Key Cryptosystems in 1978, primality tests and factoring algorithms are considered as an important research field for mathematics and its applications. A topic that before 1945 was only  interesting for some mathematicians, it has become interesting worldwide due to its relationship  with digital cryptosystems used for the privacy and security of digital users.