2023-12-13 01:00:00
There are many unsolved mysteries surrounding “prime numbers,” which are studied in junior high school mathematics. We would like to introduce some excerpts from a book that reconstructs the content of NHK’s intellectual entertainment program “Laughless Mathematics,” in which Panther Takahiro Ogata seriously explains the difficult world of mathematics.
*This article was edited by NHK’s “Mathematics without Laughing” production team.Mathematics that doesn’t make you laughThis is a re-edited version of a portion of “(KADOKAWA).
Photo = Jiji Press Photo
Takahiro Ogata of the comedy trio “Panther” (Tokyo) attended the opening event of the next-generation store “GU STYLE STUDIO” of the casual clothing store “GU” (Tokyo) on November 29, 2018.
The most basic number “prime number”
“Prime numbers” are often studied in junior high school mathematics, but do you remember what they mean?
A prime number is a natural number that is divisible only by 1 and itself.
in particular
2、3、5、7、11、13、17、19、23、29、……
Such a number.
The ancient Greek mathematician Euclid proved that there are an infinite number of prime numbers.
Prime numbers are also called “number atoms.” The reason is that any number can be decomposed into multiplications of prime numbers (prime factorization).
For example, you can break it down like 10 = 2 x 5, 30 = 2 x 3 x 5.
In this way, prime numbers are the most fundamental numbers that form the basis of all numbers.
There are many mysteries (unsolved problems) surrounding this most basic number, the prime number.
For example, there is the following “Goldbach conjecture” (Chart 1).
Let’s check this prediction in order starting from 4.
4＝2＋2
6＝3＋3
8＝3＋5
10=3+7 or 10=5+5
It is true that up to 10 can be expressed by adding two prime numbers.
It seems like even larger numbers can be expressed by adding two prime numbers, but the Goldbach conjecture is still one of the mysteries regarding prime numbers.
Why are they arranged in a “whimsical way”?
There is also the following mystery regarding “twin primes,” pairs of prime numbers that are close to each other, such as 3 and 5, 5 and 7, and 11 and 13 (Figure 2).
As you can see, there are many mysteries surrounding prime numbers.
Among these mysteries is the greatest mystery of prime numbers, which has puzzled genius mathematicians for centuries. This is the next mystery regarding how prime numbers are arranged (Figure 3).
The following table lists the natural numbers from 1 to 200 and colors the prime numbers (Chart 4).
How regarding that? Don’t you think that the timing of prime numbers appearing is very fickle and random?
Prime numbers are also called atoms of numbers and are supposed to be the basis of all numbers, so why are they arranged in such a whimsical way?
This riddle has puzzled mathematicians for centuries.
Here, we will introduce the history of how three genius mathematicians, who are highly respected by mathematicians, took on the challenge of solving the mystery of “how prime numbers are arranged.”
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