Unit 1

The Primes

Video: View Video Online; Video Transcript
Textbook: Introduction; Math at the Dawn of Time; Number for Number's Sake; Primes; Questions about Primes; Encryption; RSA Encryption
Interactive: Figurate Numbers
Download PDFs: Text Chapter; Facilitator Guide; Participant Guide
Additional Resources: Bibliography

Ishango Bone

The properties and patterns of prime numbers—whole numbers that are divisible only by themselves and one—have been a source of wonder across cultures for thousands of years, and the study of prime numbers is fundamental to mathematics. This unit explores our fascination with primes, culminating in the million-dollar puzzle of the Riemann Hypothesis, a possible description of the pattern behind the primes, and the use of the primes as the foundation of modern cryptography.

Unit Goals

Primes are the fundamental building blocks of arithmetic.
There are infinitely many prime numbers.
The fundamental theorem of arithmetic says that each whole number can be uniquely decomposed into products of primes.
The answer to whether or not there is a pattern behind the primes has eluded mathematicians for millennia.
One can find arbitrarily long "prime deserts" on the number line.
One can find finite arithmetic sequences of primes of any length.
Clock math is a way of generalizing arithmetic.
Primes and clock math can be used together to create strong encryption schemes.

Video Transcript

It is often said that Mathematics is a universal language. No matter one's culture, country, gender, race, or even religion, certain mathematical principles remain true. The fundamental letters of the mathematical alphabet are known as the primes.

Textbook

Long studied for their mysteries, many of which remain unsolved, primes were, until relatively recently, solely the concern of mathematicians. With the explosion of digital communications and our dependence on Internet transactions, however, primes now play a pivotal role in other areas, as well.

Interactive

Some of the first people to study numbers as objects were the Pythagoreans. One of the most important properties to the Pythagoreans was a number's shape. This interactive illustrates how playing with numbers can lead to mathematical discoveries.