00165 THE ISHANGO BONE: The World's First Known Mathematical Sieve and Table of the Small Prime Numbers

Reference Article

Kamalu, C. (2021, February 28). THE ISHANGO BONE: The World's First Known Mathematical Sieve and Table of the Small Prime Numbers. https://doi.org/10.31730/osf.io/6z2yr

Abstract

This paper aims to show that the Ishango bone, one of two bones discovered in the 1950s buried in ash on the banks of Lake Edward in Democratic Republic of Congo (formerly Zaire), after a nearby volcanic eruption, is the world's first known mathematical sieve and table of the small prime numbers. The bone is dated approximately 20,000 BC. Key to the demonstration of the sieve is the contention that the ancient Stone Age mathematicians of Ishango in Central Africa conceived of doubling or multiplication by 2 in a more primitive mode than modern Computer Age humans, as the process of "copying" of a singular record (that is, a mark created by a stone tool as encountered in Stone Age people's daily experience). Similarly, the doubling of any number was, by logical extension, a process of copying of any number of records (marks) denoting an integer, thereby doubling the exhibited number (marks). Some evidence for this process of "copying" and thus representing numbers as consisting of "copies" of other numbers, is displayed on the bone and can still be found to exist in the number systems of modern Africans in the region. Unlike previous speculations on the use of the bone tool by other studies, the ancient method of sieving of the small primes suggested here is notable for unifying (making use and explanation of) all columns of the Ishango bone; whilst all numbers exhibited form an essential part of the primitive mathematical sieve described. Furthermore, it is stated that the middle column (M) of the bone inscriptions houses the calculations of the Ishango Sieve. All numbers deduced in the middle calculation column relate to a process of elimination of the non-prime numbers from the sequence of numbers 1,2,3,4,5,6,7,8,9,10 (although numbers 1 and 2 are omitted). The act of elimination is proven by the display of the numbers deduced in the middle column; namely: 4, 6, 8, 9, and 10 and the subsequent omission of these same numbers from the following list leaving only: 5, 7 at the bottom of column M. This elimination process described above is repeated to obtain the primes 11,13,17,19 when eliminating non-primes from the sequence 11,12,13,14,15,16,17,18,19,20. However, only calculations for the sequence 1 to 10 (for numbers above 2) are displayed in column M; as if to exemplify the Ishango Sieve method for the benefit of posterity.