Math

# There's A Formula That Gives The First 18 Trillion Trillion Digits Of The Constant e

Math can be dry, sure. But it can also blow your mind in unexpected ways. Take this formula for example: (1+9^-4^6x7)^3^2^85, which equals 2.71828... Besides looking like someone accidentally spilled about five extra exponents on it, this formula gives the you the first 18 trillion trillion digits of the mathematical constant e. No typo here—that's 18 trillion trillion. The formula is also pandigital, which is just plain strange.

Related: The Largest Constructive Number: Graham's Number

## Do You Know What Pandigital Means?

This exponents-gone-wild formula is a scarily accurate representation of the mathematical constant e. But, there's another weird-but-cool fact about this incredible formula: it's pandigital. As WolframMathWorld describes it, "A number is said to be pandigital if it contains each of the digits from 0 to 9 (and whose leading digit must be nonzero). However, "zeroless" pandigital quantities contain the digits 1 through 9. Sometimes exclusivity is also required so that each digit is restricted to appear exactly once." Is the fact that this formula pandigital relevant in any way? Not really. But hopefully you at least learned a new vocabulary word.

Related: Belphegor's Prime The Number Of The Beast

## Why Do We Care About e So Much?

The mathematical constant e is one of the most important constants in math. It is sometimes called the Euler constant, after the Swiss mathematician Leonhard Euler, who was the first to use the letter e for the irrational number (the idea that he chose that letter because of his last initial is probably apocryphal).

Related: The Prime Problem With A One Sentence Proof

What's so special about e? Take it from Popular Mechanics: "It's one of the most useful mathematical constants. If you graph the equation y=ex, what you'll find is that the slope of that curve at any given point is also ex, and the area under the curve from negative infinity up to x is also ex. e is the only number in all of mathematics that can be plugged into the equation y=nx for which this pattern is true. In calculus, which is all about finding slopes and areas, you can imagine that e is a pretty important number. It's also an important number in physics, where it shows up in the equations for waves, such as light waves, sound waves, and quantum waves."

## Watch And Learn: Our Favorite Videos About Fascinating Numbers

#### The Incredible Formula

Learn about the formula for e, as well as other pandigital formulas.

##### Incredible Formula - Numberphile
– Numberphile

Remember this classic formula this middle school?

– Brightstorm

#### Graham's Number

It's the largest number our brains can even fathom.

– Numberphile

### Key Facts In This Video

1. If you tried to picture Graham's number, your head would collapse into a black hole because your head cannot store the information required to imagine it. 00:30

2. Three to the power of three to the power of three would be written as 3^(3^3), and the sum exceeds 7 trillion. 01:52

Curiosity Staff  