Book 24. The sense of unity I felt with prime numbers at that time. We are living in a great era where the reality of prime numbers exists.

 Hello. I'm Ten Watanabe. Nice to meet you.

Prime numbers. I know a lot about prime numbers, but I'd like to talk about the possibilities of prime numbers. The bravest prime number among prime numbers is probably 2. It is the only even number and the only number 2.

When I think of prime numbers, I think of something. It could be a story about my distant ancestors or a recent hot topic. Among prime numbers, there is a genre of prime numbers called Mersenne primes. They are prime number search devices that are used when investigating the largest prime numbers.

The largest prime number in Mersenne primes produces prime numbers with an astronomical number of digits. There is a joke that anyone can become famous for 15 minutes by using Mersenne primes, which can find the largest prime number, just like Cinderella for 15 minutes.

Of particular note regarding prime numbers is that axa + bxb = 1 mod 4 prime. Mod refers to a prime number that leaves a remainder of 1 when divided by 4, just like 1 mod 4 leaves a remainder of 1 when divided by 4. What's particularly noteworthy is that the only prime numbers that exist are 3 mod 4 and 1 mod 4, with the brave prime number 2 being a special exception.

For me, the hottest topic regarding prime numbers right now is prime formulas, and there are many different formulas for deriving prime numbers. There's something called Euler's prime formula, and nxn+n+41 can calculate dozens of consecutive prime numbers. If you try substituting values ​​for n=0 in order, starting with 1, 2, 3, and so on, you'll see that prime numbers are mass-produced. It's a miracle.

However, I managed to come up with an even more amazing formula for prime numbers. It is 2xpxp+p-2, and by substituting a prime number for p, one after another, it calculates prime numbers and squares of prime numbers. If you try substituting some numbers, you get p=3, 2x3x3+3-2=19, p=5, 2x5x5+5-2=53, and p=7, 2x7x7+7-2=103.

If you're interested, while you're learning what Mersenne primes are, try substituting as many prime numbers as you can into this prime formula. I'm sure you'll get some interesting results. As you can see, there are many different prime formulas, and they can give you a nostalgic feeling, like the grandfather you met just the other day. They'll remind you of grand theories and nostalgia, like the secret hideouts we explored as children.

We may say, "Those were wonderful times. Those places, those people, at those times. A vast space of dreams was created because of all that." We too can reminisce about a variety of things, from prime formulas that symbolize the good old days, such as Euler's prime formula, to the largest Mersenne prime number that exists today, and even the most cutting-edge prime formula that I have devised.

The sense of unity with prime numbers that I felt then. If I could go back to that time, I'm sure I would go and search for that fantasy world. We live in a great age where prime numbers are a reality. Just as this article is a rewrite of an article I wrote a year and a half ago, when I was still a novice blogger, the world is moving forward with dynamism.

I've grown a lot in the past year and a half, and I'm sure you've grown a lot in that time as well. With the blessings of the past year and a half, I believe that you and I will have grown a lot in another year and a half. With that, I'll close this article, but if you have any questions or comments, please feel free to leave your opinions and thoughts in the comments section.

That's all. Thank you very much. This is Watanabe Ten.