The Concept of Prime Numbers and Zero
MTH/110
March 14, 2011

The Concept of Prime Numbers and Zero Have you ever wondered about the origins of prime numbers or the numeral zero? The ancient philosophers and mathematicians from such early civilizations in Egypt, Greece, Babylon, and India did. Their efforts have provided the basic fundamentals for mathematics that are used today.
Prime Numbers A prime number is “any integer other than a 0 or + 1 that is not divisible without a remainder by any other integers except + 1 and + the integer itself (Merriam-Webster, 1996). These numbers were first studied in-depth by ancient Greek mathematicians who looked to numbers for their mystical and numerological properties, seeking perfect and amicable numbers. (O’Connor & Robertson, 2009) In 300 BC, Greek mathematician, Euclid of Alexandria proved and documented in his Book IX of the Elements that prime numbers were infinite. He started with what he believed to be a comprehensive list of prime numbers, created a new number, N, by multiplying all of the prime numbers together and adding 1. This resulted in a number not on his list and not divisible by any of his prime numbers. N therefore had to be either prime itself or be a composite number that was a product of at least two other prime numbers not on his list. In 1747, a mathematician named of Euler demonstrated that all even numbers were perfect numbers. However, one hundred years later in 200 BC, Eratosthenes of Cyrene, a famous Greek mathematician known for his studies regarding prime numbers as well as for measuring the diameter of the earth, devised a procedure or algorithm for calculating prime numbers called the Sieve of Eratosthenes (O’Connor & Robertson, 2009). The study of prime numbers seemingly ceased to exist during the period of time known as the Dark Ages. Studies on the subject were not noted again until the early 17th century when another prominent mathematician named Fermat, who reportedly was inspired by Euler’s work with the factoring of prime numbers, began his studies.
The Zero The word Zero, according to the Merriam-Webster Collegiate Thesaurus (1988), has several associated synonyms for it such as cipher, goose egg, naught, nothing, and zilch as well as the numerical symbol for the digit 0, and as a circle or an ellipse in written form. Furthermore, the Arabic term for zero (sefr) was originally a Hindi word meaning empty or hallow. During the 2nd millennium, the ancient Babylonians used a sexagesimal positional system that showed the lack of positional value between numbers with a space, and later with two slanted wedges (Kaplan, 2000). In today’s modern times, India is believed to have devised the concept of using a zero, not only as a place holder, but also as a number. The 0 is the integer that precedes the number 1. It was identified as such in most cultures before the concept of negative numbers was accepted by scholars. The zero is divisible by 2, thus considered an even number, and some believe it to be a natural number because it is neither positive nor negative. Furthermore, Penner (1999) stated, “The number zero is not the same as the digit zero that is used in numerical systems as a positional notation” (p. 34). The rules for the use of the zero were initially noted in a book from 628 AD titled Brahmasputhta Siddhanta (The Opening of the Universe). Brahmasputhta’s thoughts differed from those of modern mathematicians in regards to his rule “Zero divided by zero is zero,” because modern scholars do not assign a value to the zero (O’Conner & Robertson, 2000). Other cultures civilizations have a history regarding the use of the zero. The zero, in the form of a hieroglyph or glyph, was an integral component to the Mayan numeral system, most notably seen in their calendars. In 130 AD, Ptolemy was noted using a small circle with a long overbar to note a zero within a sexagesimal numeral system, and because it was not used alone, this use of a zero, referred to as the Hellenistic zero, was probably the first recorded usage of it as a numeral in the Old World (O’Conner & Robertson, 2000). In conclusion, the early scholars broke the ground for future generations. The results of their efforts are seen in almost everything we use and appreciate today, from art and music, to science and technology. Modern society would not be what it is today without the ancient scholars and their quest and love of knowledge.

References
Kaplan, Robert (2000). The Nothing That Is: A Natural History of Zero. Oxford: Oxford University Press. Retrieved from Wikipedia website: http://en.wikipedia.org/w/index.php?title=0
Merriam-Webster (1996). Merriam-Webster’s Collegiate Dictionary (10th ed.). Springfield, MA.
Merriam-Webster (1988). Merriam-Webster’s Collegiate Thesaurus. Springfield, MA.
O’Connor, J. J., & Robertson, E. F. (2009). History Topic: Prime Numbers. Retrieved from University of Phoenix website: http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Prime_Numbers.html
O’Connor, J. J., & Robertson, E. F. (2009). History Topic: A history of Zero. Retrieved from University of Phoenix website: http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Prime_Numbers.html
Penner, Robert C. (1999). Discrete Mathematics: Proof Techniques and Mathematical Structures. World Scientific. Retrieved from Wikipedia website: http://en.wikipedia.org/w/index.php?title=0