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Occasional Random thoughts from us.
Narcissistic Numbers: Numbers That Contain Their Own Secret
153 = 1³ + 5³ + 3³. There are exactly 88 numbers like this in base 10, the largest with 39 digits, and a simple argument proves the list must end. Here is how.
Happy Numbers: Can a Number Make You Happy?
Square the digits, add them, repeat. Some numbers reach 1 and are "happy." Every other number falls into the same eight-number loop. Here is why, and why every starting point must end in one or the other.
What Is a Palindromic Number?
A palindromic number reads the same forward and backward. Every even-length palindrome is divisible by 11, and nobody knows whether 196 ever becomes one. Here is the math of numbers that mirror themselves.
Winning with Numbers: How Math Powers Success in Sports
Sports and mathematics might seem like two separate worlds, but beneath the surface of every game, match, and race lies a foundation of mathematical…
Perfect Numbers: Numbers That Equal the Sum of Their Parts
6 = 1 + 2 + 3. 28 = 1 + 2 + 4 + 7 + 14. Only 52 perfect numbers are known, all even, and nobody knows if an odd one exists. Here is the 2,300-year story.
Mersenne Primes and the Search for Huge Numbers
The largest known prime has over 41 million digits, and nearly every record prime for decades has had the form 2^p − 1. Here is why, and how a simple test makes the hunt possible.
Twin Primes: The Mystery of Primes That Travel in Pairs
Are there infinitely many prime pairs like 11 and 13? Nobody knows. But in 2013 an almost unknown mathematician proved something close, and a hunt for their sum exposed a bug in Intel's Pentium chip.
Real life uses of LCM and GCF
In math, the GCF is better known as the Greater Common Factor. The greatest common factor is commonly used to simplify a fraction by dividing both the…
The Sieve of Eratosthenes: One of the Oldest Algorithms Still in Use
A method devised over 2,000 years ago still finds primes faster than testing numbers one at a time. Here is how the sieve works, why it starts at p², and how modern versions scale it up.
Significant Numbers and Their Meanings
Math is particularly special because of the array of significant numbers. There are certain numbers and formulas that has likely stuck with you since high…
Why There Are Infinitely Many Primes
Euclid proved it around 300 BC in a few lines, and the proof still works perfectly. Here is the argument, a common misunderstanding of it, and what we know about how primes thin out.
What Makes a Number Prime?
A prime has exactly two divisors: 1 and itself. Here is why 1 isn't prime, why you only need to check up to the square root, and how computers test numbers with hundreds of digits.