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NY Regents Exam - Global History and Geography: Help and Review30 chapters | 401 lessons | 27 flashcard sets
The Sieve of Eratosthenes: Explanation & Overview
Instructor:
Richard Reid
In this lesson we will learn about the Eratosthenes' Sieve, how it works, and why Eratosthenes was significant to ancient science. Then when you're done, you'll be able to test your newfound knowledge with a quiz!
An Ingenious Technique
What's the best way to find all the prime numbers between one and two hundred? You can always count, double check, multiply, and divide until you get frustrated and look up the answer on the internet. Or you could use an ingenious technique that a Greek mathematician invented over two thousand years ago.
Eratosthenes and His Sieve
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Eratosthenes lived during a time of rich experimentation and intellectual curiosity. This Hellenistic Age (named after the Greek word for Greece, Hellas) saw the expansion of Greek science and philosophy across the western world. Scholars and scientists from all around congregated in new libraries and schools to debate, discuss, and learn from one another. Eratosthenes used many of these ideas (borrowing from the best of Greek, Egyptian, and Mesopotamian thinkers) as the basis for a great number of mathematical discoveries. One of these discoveries (or inventions, depending on your perspective), was the Sieve of Eratosthenes.
The Sieve of Eratosthenes is a mathematical tool that's used to discover all possible prime numbers between any two numbers. Eratosthenes was a brilliant Greek thinker who, among many other important discoveries and inventions, was deeply interested in mathematics. His best known contribution to mathematics is his sieve used to easily find prime numbers. A mathematical sieve is any pattern or algorithm that functions by 'crossing off' any potential numbers that don't fit a certain criteria. In our case, the sieve of Eratosthenes works by crossing off numbers that are multiples of a number that we already know are prime numbers. While this all sounds quite complicated, in practice it's quite simple.
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Refer to the image above to see Eratosthenes' sieve in action.
To start the process, you identify the smallest prime number on your list of integers; in this example, it's 2. Then, you cross off every multiple of two on your list because you know that if a number is divisible by two, it can't be a prime number. Then, you proceed to the next number that is not crossed out to find your next prime number. The reason this works is because if it's not crossed out then it's not divisible by any other smaller number. Now you cross off every number that is a multiple of this new integer; in this example, it's 3. You repeat this process until you've reached the end of your number set and you have a list of all the prime numbers contained within.
This simple algorithm was an important tool that made the process of discovering prime numbers for ancient Greeks without computers (or Google) much, much easier. But here's the ironic twist to that statement: Eratosthenes' sieve has an intimate connection with modern computers! In the 1950s and early 1960s, when computers were first being developed, scientists and engineers looked at sieves like Eratosthenes' as a benchmark for computer performance. Now that computers are ubiquitous, prime numbers and sieves are used in the field of cryptography to encrypt and protect your data online.
However, it's important to note that the sieve had little practical application in the ancient world. While incredibly important to the development of pure mathematics, interest in these types of abstract inquiries seemingly fell out of vogue after the Hellenistic period. This was due in large part to the influence of the Roman empire that ended the Hellenistic Age and encouraged practical, physical sciences like engineering.
Lesson Summary
Eratosthenes made many important contributions to science and mathematics. His prime number sieve provided a simple way for Greek mathematicians (and frustrated modern students!) to find all prime numbers between any two integers. He lived and worked in the Hellenistic Age, a multicultural age where Greek culture spread throughout Eurasia and the exchange of ideas lead to developments like his famous sieve.
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Lesson
31 in chapter 4 of the course:
- The Minoans 9:05
- History of the Alphabet: From Cuneiform to Greek Writing 7:08
- The Iliad: Greek Epic 13:52
- The Odyssey: Greek Epic 18:22
- Bronze Age Greece: Schliemann's Quest for Troy 6:39
- From Mycenae's Collapse to Greek Colonization 9:15
- Greek Myth and Religion 17:21
- Greek City-States and Governments 10:54
- Women of Greece 4:34
- Ancient Greek Art, Pottery and Sculpture 8:07
- Ancient Greek Architecture: Dorian, Ionic & Corinthian 10:03
- The Birth of Philosophy: The Presocratics 17:33
- Phalanx Warfare in Ancient Greece 6:40
- History of Sparta 8:35
- Birth of History: Herodotus' Persian War 9:28
- Slavery in Ancient Greece 6:55
- Greek Temple: Architecture, Construction & Parts
- Achilles, the Ancient Greek Hero: Myth & Achilles Heel
- Aeschylus: Biography, Plays & Poems
- Ajax of Greek Mythology: Story & History
- Archaic Greek Sculpture: Characteristics & Overview 3:21
- Archaic Smile in Ancient Greek Sculpture: Definition & Concept
- Cronos the God? - Mythology, Overview
- King Agamemnon: Mythology & Trojan War 4:23
- Selene, the Greek Moon Goddess: Facts & Overview 4:20
- Spartan Helot: Definition & Revolt
- The Elysian Fields: Definition & Mythology 5:02
- The Hellenistic Period: Definition & History 5:55
- The Oresteia by Aeschylus: Summary & Themes
- The Peloponnesian War: History, Cause & Result 5:57
- The Sieve of Eratosthenes: Explanation & Overview
- Go to NY Regents - History of Ancient Greece: Help and Review
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