**Did Africans discover prime numbers 20 000 years before the Greeks?**

Researchers found a bone, called the Ishango bone, in the Democratic Republic of Congo in the 1950s. The bone dates back to approximately 20 000 B.C., and has notches carved into it, which some believe represent a special group of numbers called prime numbers. Prime numbers are whole numbers greater than 1 that cannot be produced by multiplying two smaller whole numbers. For instance, 2, 3, 5, 7, 11, 13, 17, and 19, are the first 8 prime numbers.

Some scholars believe the people living in this time and place may have devised a way of finding prime numbers.

This would be a fantastic discovery because our current knowledge indicates that primes were first conceived almost 20 000 years later by a Greek scholar in Egypt. Researchers believe that groups of notches on the Ishango bone represent numbers. For instance, 2 notches next to each other may represent the number 2 and 5 notches next to each other may represent the number 5.

In this study, researchers argue that the Ishango bone demonstrates the first known method of finding primes. This would mean African people, not the Greeks, first conceived of prime numbers.

The author looked for mathematical patterns in the bone’s carvings. They looked for instructions to sort primes from other numbers. They used modern methods to explain the process that may be depicted on the bone.

The author found carvings on the bone that may represent a number next to a number that is double the first. For example, there may be a 4 next to an 8. They believe the people of the time doubled numbers to eliminate them as possible primes.

The author says that previous studies chose only the carvings that supported their explanations, while this author claims to use all the carvings to support their theory.

Many scholars assume that African peoples living 22 000 years ago were too backwards to have understood mathematics in this way. Such assumptions may have prevented scholars from investigating the opposite hypothesis, that indeed these people may have been so mathematically inclined that they could have been the first to discover prime numbers.

It is important to note that the author is presenting a potential hypothesis in this study. There is still some debate on how the notches should be grouped, so it is also possible that the numbers represented on the bone may not indicate a calculation of prime numbers. If this is the case, their theory would be invalid.

The author sought to credit the African people who made the carvings, as they may have discovered prime numbers long before the world widely believed they were.

## 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.

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