2147483647 facts for kids
Quick facts for kids 2147483647 |
|
|---|---|
| Cardinal | two billion one hundred forty-seven million four hundred eighty-three thousand six hundred forty-seven |
| Ordinal | 2147483647th (two billion one hundred forty-seven million four hundred eighty-three thousand six hundred forty-seventh) |
| Greek numeral |  ͵γχμζ´ |
| Binary | 11111111111111111111111111111112 |
| Ternary | 121121222121102021013 |
| Senary | 5530320055316 |
| Octal | 177777777778 |
| Duodecimal | 4BB2308A712 |
| Hexadecimal | 7FFFFFFF16 |
2,147,483,647 is a very special number. It is known as a Mersenne prime, which is a type of prime number with a unique form. This number is also one of only four known double Mersenne primes, making it even more rare and interesting in the world of mathematics.
Contents
What is 2,147,483,647?
This large number, 2,147,483,647, is a whole number that is important in both mathematics and computer science. To understand why it's special, let's first look at what prime numbers are.
Understanding Prime Numbers
A prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself. For example, 2, 3, 5, 7, and 11 are prime numbers. Numbers like 4 (which can be divided by 2) or 6 (which can be divided by 2 and 3) are not prime. Prime numbers are like the building blocks of all other whole numbers.
What Makes a Mersenne Prime?
A Mersenne prime is a special kind of prime number. It must be in the form of 2p - 1, where 'p' itself is also a prime number. For example, if p=3, then 23 - 1 = 8 - 1 = 7, which is a prime number. So, 7 is a Mersenne prime. The number 2,147,483,647 fits this pattern perfectly because it is equal to 231 - 1, and 31 is a prime number.
Double the Fun: Double Mersenne Primes
A double Mersenne prime is even more unique. It's a Mersenne prime where the exponent 'p' (the small number raised to the power of 2) is also a Mersenne prime. In our case, 2,147,483,647 is 231 - 1. Since 31 is a Mersenne prime (because 31 = 25 - 1, and 5 is a prime number), 2,147,483,647 is a double Mersenne prime! These numbers are very rare.
Why is This Number Important?
This number isn't just a math curiosity; it has real-world uses, especially in computers.
Its Role in Computers
The number 2,147,483,647 is the largest positive number that can be stored in a 32-bit signed integer in many computer systems. This means that if a computer program tries to count higher than this number using a 32-bit integer, it can cause an "overflow" error. This error can make programs crash or behave unexpectedly. Many video games, older software, and operating systems use 32-bit integers, so this number often marks a limit in their calculations.
The Search for Big Primes
Mathematicians and computer scientists are always looking for new, larger prime numbers. Finding new Mersenne primes is especially exciting because there's a special test that makes it easier to check if they are prime. The Great Internet Mersenne Prime Search (GIMPS) is a project where many people use their computers to help find these huge prime numbers.
History of Discovery
The number 2,147,483,647 has a long history in mathematics.
Leonhard Euler's Contribution
The famous Swiss mathematician Leonhard Euler proved that 2,147,483,647 is a prime number way back in 1772. This was a huge achievement for his time, as he didn't have computers to help him. It took him a lot of careful calculation to confirm it.
See also
- 2147483647 para niños (In Spanish)
