The Ishango bone is an animal bone that was discovered by Jean de Heinzelin in the 1950s in what is today Zaire. The bone has been dated to somewhere between 9,000 and 6,500 B.C. What is particularly of interest about this bone is the notches on it, carved by a human hand, may in fact be the earliest known record of a catalog of prime numbers.

The bone has notches in several columns. One of the columns lists the numbers 11, 13, 17, and 19, through groupings of notches (meaning that there is a group of 11, followed by a group of 13, followed by a group of 17, and ending with a group of 19). The other columns exhibit other mathematical patterns as well that are easily decipherable. This bone is the oldest record we have of a noteworthy series of consecutive prime numbers.

Bone notches at this time in human history were often used for basic counting as well as for calendar purposes, as people kept track of the number of days. This was far before the use of papyrus or other writing methods, so bone was one of the few methods for storing information over a sizeable period of time.

So, the big question is whether or not the Ishango bone is actually a record of primes. The debate over this has gone on for decades without a clear conclusion. What follows are both sides of the argument, followed by my own conclusion.

The Ishango bone is not a record of prime numbers. Mathematically, it's easy to argue against it. Suppose we pick four positive integers less than 30 at random. There are ten primes in this range (meaning the probability of any one random number being prime is 1/3), so the probability of all four being primes is 1/81 (or 1/(3^4)). Thus, we would not have to look at many marked bones, especially those with multiple rows of notches, before we found a row of primes. There is no reason to conclude the person cutting the notches knew they were prime.

Another approach to debunking the idea that it is a prime number record is philosophical. Why should an adult Mesolithic man or woman, before the advent of agriculture, be spending his or her time playing arithmetic games? There is no evidence of anything in that timeframe indicating anything other than notches being used for bookkeeping, and given a life of hardship and seeking of food and shelter as a hunter/gatherer, there is no good reason for a Mesolithic man or woman to spend their time contemplating numbers and making notches relating them on a piece of bone.

As a result, the best conclusion one can take from this bone is that it is an interesting pattern, but it is merely the result of ancient bookkeeping that resulted in an interesting sequence of numbers.

The Ishango bone is a record of prime numbers. The key thing to remember is that it is a list of consecutive primes in the correct order. Given random selection from the positive integers less than thirty gives 1/30^4 random orders, and only seven possible orderings in that set. This means that roughly 1 in every 86500 random selections of four numbers will result in a series of four consecutive primes between 1 and 30. That's a significant number, and indicates the unusual nature of this event.

Philosophically, it is easy to conceive of a curious young man or woman discovering the idea of counting and being curious about it. After considering it for a while, the child might have noticed some patterns, and much like a diary, sought to record them on the only available resource, bone. Or perhaps an elder of a tribe doing the same thing. Mesolithic man was still a thinking and reasoning man; just because they were not modern man doesn't mean that they did not think.

As a result, it makes a great deal of sense to believe that this bone in fact does present the first record of prime numbers that we have yet discovered.

The middle ground. This is where I sit on the subject and what is generally being adopted as a moderate stance on the issue. I don't think that the numbers on the bone represent the discovery of primes, but I do think that it was recorded for a particular use. These are numbers that cannot be divided evenly. Through trial and error, the Mesolithic peoples likely discovered that certain numbers of items couldn't be divided up fairly, so to save themselves arguments, they remembered not to acquire certain numbers of items. That's what the numbers on the bone meant, to me: do not get an amount equal to these numbers. This would be useful for a young child sent into the woods to locate fruits, or perhaps an early artisan making crude weapons. In essence, they are primes, but they were recorded for use in bookkeeping.

The Ishango bone is an interesting artifact of early humanity that is quite thought provoking. It now resides in the Musee d'Histoire Naturelle in Brussels, Belgium.

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