The so-called prime number is a number that cannot be divisible by other positive integers except 1 and itself, such as 2, 3, 5, 7, 1 1 ... The most important point in algebra is that any integer greater than 1 can be uniquely expressed as the product of some prime numbers. The position of prime numbers in integers feels like color to primary colors.
If you say the word "red" to 50 people, you can imagine that there will be 50 kinds of reds in their minds, and almost no one is the same. About "the beauty of mathematics", I think it's almost the same. My favorite mathematician, Paul Edith, said:
"It's like asking Beethoven's ninth symphony what's the beauty. If you can't hear why it is beautiful, then no one can tell you. I know the numbers are beautiful. If they are not beautiful, nothing can be called beauty. 」
A long time ago, there was a kind of numbers that were considered beautiful by ancient Greek mathematicians. They can write the sum of all their positive factors (except themselves). Such numbers are called "perfect numbers". For example, the positive factor of 6 is 1, 2, 3, 6, which is exactly1+2+3 = 6; The positive factor of 28 is 1, 2,4,7, 14,28, which is exactly 1+2+4+7+ 14=28, so 6 and 28 are perfect numbers, and June 28th every year is also called "perfect number".
▲ Intuition uses pictures to express the perfect number (from Wikipedia). The smallest perfect number is 6, which is my favorite jersey number since I started college basketball. I hope to have a perfect performance in every competition. However, you know, I often make mistakes, sometimes I can't even make free throws. More practice is still more useful than superstition.
This year's 65438+10.3, the largest perfect number in history was discovered. However, my computer screen space is too small to write down (I bet that even after Fermat's 300 years, someone will still use XD). However, when I said that the space was too small to write down, I meant it. Wait a minute, you will know how big it is to write down the values of each position one by one, and it will be very troublesome to read them with your mouth. If you don't mind my being lazy, you can write in this form.
2772329 16(2772329 17- 1)
It looks a little ugly on the outside, but it's perfect on the inside. Really, I promise. You may still not believe it.
However, you can't believe that mathematicians are always like this. A long time ago, Euclid, the sage of mathematics, had a clear concept of perfect number in his heart.
As long as 2n- 1 is a prime number, 2n- 1 (2n- 1) is a perfect number.
From the point of view of modern mathematics, we only need a little factor multiple and geometric progression's mathematical concept.
Photo credit: Admirably, the author provided that Euclid knew about this kind of thing about 2300 years ago! More than one thousand years later, another superman mathematician Euler put forward a further conclusion:
All even numbers must be of the form 2n- 1 (2n- 1).
Up to now, no one in this world knows whether there are infinite perfect numbers (I hope there are infinite perfect numbers based on the idea of making this world more perfect); At the same time, no one has seen an odd perfect number. If you meet it, please take me to that place.
A few days before the task of super prime number, the organization Great Intermersene Prime Search (GIMPS) published the largest prime number at present, 2772329 17- 1, reaching 23,249,425 digits. How big is this super number? For example, suppose there is the fastest speaker in the world who can read 10 numbers per second, so even if he doesn't eat, drink, laugh or walk, it will take him nearly a month to finish reading this number from beginning to end.
This super prime number was discovered by Pace, a FedEx employee in Tennessee, USA. As for how to find such a big prime number, of course, computers are indispensable. It is said that the cpu of his computer is Intel quad-core i5-6600, which is similar to our general home computer, but it will take several days to test this super prime number with this level of computer.
On the other hand, this form of prime 2n- 1 has a special name called mersenne prime. As the name implies, this is to commemorate marin mersenne, a French monk who studied this number in the17th century. In fact, this kind of prime number is not common. So far, only 50 prime numbers have been found, of which 17 was found by GIMPS or the program provided by GIMPS. GIMPS also made a bold statement, offering a reward as high as 1 50,000 US dollars (about NT$ 4 million) to see who can find the super prime number with more than1100 million digits first.
I don't know which is the better return on investment, digging bitcoin or finding 100 million super prime numbers? Are you ready?
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