# Ishango bone

What is the oldest table of primes? Some (e.g., [BS96], [Shurkin84 p21]) suggest perhaps the Ishango bone. This bone, now at the Musee d'Histoire Naturelle in Brussels has been dated about 6500 BC (some date it to 9000 BC [BNW87]). It has three rows of notches, and one of the columns has 11, 13, 17, and 19 notches (thought this last group could be two 5+14).

Are the four groups of notches on the Ishango bone an intentional list of primes? Probably not. Suppose we pick four positive integers less than 30 at random. There are ten primes in this range, so the probability of all four being primes is 1/81. We would not have to look at many calendar sticks, especially those with multiple rows of notches, before we found a row of primes (and there are many thousands of such artifacts). There is no reason to conclude the person cutting the notches knew they were prime.

"If a man who cannot count finds a four-leaf clover, is he entitled to happiness?" (Stanislaw Lec Unkempt Thoughts)

This Ishango bone is old, but the oldest "mathematical artifact" currently known is much older. The oldest is a piece of baboon fibula with 29 notches, dated 35,000 BC. This older bone was discovered in the mountains between South Africa and Swaziland. There is also a Czechoslovakian wolf's bone with 57 notches that dates from 30,000 BC. Bushmen clans in Nambia use similar bones for calendar sticks today.

Related pages (outside of this work)

References:

BNW87
J. Bogoshi, K. Naidoo and J. Webb, "The oldest mathematical artefact," Math. Gazette, 71:458 (1987) 294.  MR 89a:01003
BS96
E. Bach and J. Shallit, Algorithmic number theory, Foundations of Computing Vol, I: Efficient Algorithms, The MIT Press, Cambridge, MA, 1996.  pp. xvi+512, MR 97e:11157 (Annotation available)
Heinzelin62
J. de Heinzelin, "Ishango," Scientific American, 206:6 (June 1962) 105--116.
Joseph91
G. Joseph, The crest of the peacock, Penguin Books, 1991.  MR 92g:01004
Marshack72
A. Marshack, The roots of civilization, McGraw-Hill, 1972.
Shurkin84
J. Shurkin, Engines of the mind: a history of the computer, W. W. Norton \& Co., 1984.