Math Happenings
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,
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,
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