Skewes's number facts for kids
Skewes' number is a super-duper big number in mathematics. It's so huge that it's hard to even imagine! This number is important in a part of math called Number theory, which studies numbers and their properties.
Mathematicians once thought that Skewes' number marked a special point. They believed that after this number, prime numbers would start to appear differently than expected. Prime numbers are numbers like 2, 3, 5, 7, and 11, which can only be divided evenly by 1 and themselves.
Recent studies have shown that this special point might actually be a much smaller number. But Skewes' number is still famous for being one of the biggest numbers ever used in a serious math problem!
Contents
What Is Skewes' Number?
Skewes' number is written as 10101034. To understand how big this is, let's break it down:
- 1034 means 1 followed by 34 zeros. That's already a huge number!
- Now, imagine 10 raised to the power of that huge number (1034).
- Then, imagine 10 raised to the power of *that* even bigger number.
It's a number so large that if you tried to write it out, it would take up more space than all the atoms in the known universe!
Who Discovered Skewes' Number?
This amazing number was first found by a mathematician named Stanley Skewes. He was a South African mathematician who lived from 1886 to 1977. He discovered this number in 1933 while working on a famous problem about prime numbers.
Why Is This Number Important?
Skewes' number is connected to how prime numbers are spread out. Mathematicians have a special function called the "prime-counting function" (written as π(x)). This function tells you how many prime numbers there are up to a certain number 'x'.
There's also another function called the "logarithmic integral function" (written as Li(x)). This function gives a very good estimate of how many prime numbers there should be up to 'x'. For a long time, mathematicians thought that Li(x) was always bigger than π(x).
Skewes' number was the first number ever found where it was proven that π(x) actually becomes larger than Li(x)! This was a huge surprise and showed that the way prime numbers are distributed is even more complex than thought.
The Prime Number Theorem
The idea that Li(x) is a good estimate for π(x) comes from something called the Prime number theorem. This theorem is a very important rule in number theory. It helps us understand the general pattern of how prime numbers appear as numbers get larger.
How Has Skewes' Number Changed?
When Stanley Skewes first found his number, it was incredibly large. Later, mathematicians found a slightly smaller version of it. And as math tools and computers got better, they found that the actual point where π(x) overtakes Li(x) is much, much lower than Skewes' original number.
Even though the exact value has changed, Skewes' number remains a famous example of how complex and surprising mathematics can be. It shows that even in areas like prime numbers, which seem simple, there are deep and unexpected patterns to discover!
See also
In Spanish: Número de Skewes para niños
