Universal Mathematical Principles (02:10)
Prime numbers comprise the math "alphabet" and are divisible only by themselves and 1. SETI has suggested mathematics and primes might be used for interstellar communication. In 1974, Frank Drake sent a pictogram with 1,679 binary digits into space—a semi prime number.
Ishango Bone (01:20)
A carved artifact originated in Africa 20,000 years ago and shows early humans had a mathematical understanding beyond counting, including prime numbers.
Intrinsic Value (02:45)
Greek philosophers developed an abstract interest in numbers. Whole numbers and multiplication were visually represented by pebbles arranged into squares and rectangles; primes did not fit.
Infinitude of Primes (02:47)
In the fundamental theorem of arithmetic, Euclid identified prime numbers as basic building blocks of any positive integer. View examples of prime factors and hear how he proved there are an infinite number of primes.
Sieve of Eratosthenes (01:49)
Euclid's proof does not provide a systematic way to find all prime numbers. Eratosthenes designed an algorithm sifting out composite numbers from prime numbers; learn how it works. Mathematicians try to find more efficient formulas.
Mersenne Primes (02:08)
In 1644, French monk Marin Mersenne identified the formula 2 to the Nth Power minus 1 would often yield a prime number. The GIMPS computer network tries to find larger Mersenne primes; the 44th discovered is a number larger than atoms in the universe.
Carl Friedrich Gauss (02:32)
Mathematics offers explorers freedom bound only by the laws of logic. Euclid's infinite twin prime conjecture remains unproved. An 18th century mathematician calculated primes into the millions and identified a structure to their occurrence.
Riemann Hypothesis (03:01)
Mathematician Terry Tao explains that looking at prime number statistics reveals a curved logarithm on a graph. Bernard Riemann compared small errors to sound waves.
Prime Progression Patterns (02:17)
Tao identifies prime sequences with equal spacing. He compares working on mathematics problems to climbing a cliff.
Data Encryption (02:52)
The study of primes has resulted in internet safety measures. Ray Perlner works in the NIST cryptography lab and explains the concept of public key cryptography, an algorithm using prime numbers.
Public Key Cryptography Safety (02:28)
Perlner explains that the likelihood of cracking a data encryption code is very slim. His work involves solving prime number problems. Prime numbers are the building blocks of mathematics, our universal language.
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