How to solve prime factorization! Introducing an innovative solution

Hello. This is Tenmei Watanabe from Seito Medical School. This time we will talk about the method of prime factorization.

I would like to factorize 2521×2411=6078131 into prime factors. First of all, since prime number x prime number, prime numbers are always odd, except for 2, which is an even prime number. In other words, prime number x prime number is odd number x odd number.

Now, suppose we represent one prime number as 2a+1 and another prime number as 2b+1. In other words, one method of prime factorization is to solve for a and b of (2a+1)x(2b+1)=6078131. Expanding this formula, 4ab+2a+2b+1=6078131 and 2ab+a+b=3039065.

Now, I would like to use a remainder operation called mod. How to use 1mod2 means that when you divide a number by 2, the remainder is 1. For example, 3=1mod2, 7=1mod2, -1=1mod2.

In 2ab+a+b=3039065, 2ab on the left side is an even number, so the remainder when divided by 2 is 0mod2. The problem is a+b, and if a is odd and b is odd, then 1+1=0mod2, and if a is even and b is even, then 0+0=0mod2. On the other hand, if a is an even number (odd number) and b is an odd number (even number), then a+b=1+0=0+1=1mod2.

In other words, if a and b are each divided by 2, if the remainders are the same, they will add up to an even number, that is, 0mod2, and if a and b have different remainders, then they will add up to an odd number, i.e. It means that it becomes 1mod2.

Since 3039065=1mod2 on the right side, we can see that a+b=1mod2. In other words, if a is an odd number, then b is an even number.

Here, we want a+b=0mod2, so let's subtract 1 from a in the previous equation. In other words, a-1=c, and substitute a=c+1. (2(c+1)+1)x(2b+1)=(2c+3)x(2b+1)=6078131.2cb+b+3c=3039064.

Here, b+3c are even numbers or odd numbers, so 3039064=0mod2 on the right side. Now, let's add the coefficients of cb, b, and c. 2+1+3=6.

If you do 3039064mod6, you get 4mod6, and subtracting this 4 from 3039064 again and doing mod(6×2) is 0mod12, so you can see that a and b are both even numbers.

Because c=b=0, 2cb+c+b=2x0x0+0+0=0mod12=0mod24. Because c=b=1, 2x1x1+1+1=6mod12=6mod24. Furthermore, c=b=2, 2x2x2+2+2=12mod24, c=b=3, 2x3x3+3+3=0mod24.

In fact, 2c+3=2411,c=1204=0mod2. On the other hand, 2b+1=2521, b=1260. In other words, c=2d=0mod2, b=2e=0mod2.

Shall we do this two more times?

Substituting 2d and 2e for c and b, respectively, gives (4d+3)x(4e+1)=6078131. When expanded, it becomes 4de+d+3e=1519532. 1519532=0mod2, so d and e become d=e=0mod2 or d=e=1mod2.

The coefficients of de, d, and e are 4+1+3=8, so 1519532=4mod8=12mod16. (12-4) Since mod16=8mod16, we know that d=e=1mod2. d=e=1mod2 is incorrect because 4d+3=2411, d=602=2f=0mod2 and 4e+1=2521, e=630=2g=0mod2.

The next round is (8f+3)x(8g+1)=6078131. When expanded, 8fg+f+3g=759766=0mod2. Since f=g=0mod2 or f=g=1mod2, the coefficient is 8+1+3=12. Since 759766=10mod12=22mod24, (22-10)mod24=12mod24, and f=g=1mod2.

In fact, f=301=2h+1=1mod2, g=315=2i+1=1mod2, which is correct. I'd like to try it one more time quickly.

(16h+11)x(16i+9)=6078131。16fg+9f+11g=379877=1mod2。j=i-1。i=j+1。(16h+11)x(16j+25)=6078131。16hj+25h+11j=379866。

h+j=0mod2.16+25+11=52.379866=6mod52=58mod104. (58-6)=52mod104. h+j=1mod2. h=150=0mod2 ,j=156=0mod2 is incorrect.

Here, (16h+11)x(16i+9)=6078131 which was incorrect earlier, k=h-1, h=k+1. (16k+27)x(16i+9)=6078131.16ik+27i+9k=379868=0mod2.

i+k=0mod2.16+27+9=52.8mod52=60mod104. (60-8)=52mod104. i=k=1mod2.16k+27=2411, k=149=1mod2.16i+9=2521,i=157=1mod2. Therefore, it is correct.

(4d+3)x(4e+1)=6078131。d=s+2,e=t+2。(4s+11)x(4t+9)=6078131。4st+9s+11t=1519508。4+9+11=24。1519508=20mod24=20mod48。(20-20)mod48=0mod48。s=t=0mod2。s=600=0mod2。t=628=0mod2。

It seems important to do the math.

Try reading a book or working on your computer while sitting cross-legged on your feet Full concentration! ! by Nada 20231007

Lately, I've been studying and working while sitting cross-legged, without using a chair. The other day I talked about how important posture is for studying, and at the end I wrote that it's good to have a slightly hunched back. Even when sitting cross-legged, I can now work for longer periods of time by placing my laptop on my feet and leaning forward slightly to maintain balance. Even when it comes to my hobby of research, I forget to eat and drink and immerse myself in it for 12 hours straight, but even then I don't lean back in my chair. My room only has a kotatsu desk, so furniture like a chair naturally goes well with it, but my favorite thing to do is to sit cross-legged on my bed without leaning on anything. It has become.

Of course, I'm a man and have been doing weight training, so I might be muscular. I doubt that a woman with no muscles could do the same work in the same position as me. However, even though I can devote myself to research for 12 hours, I could only stay focused for 2 or 3 hours when reading a book for study. However, when I adopted this method of sitting cross-legged, I found that my work became more comfortable and enjoyable, and I was able to concentrate tremendously. I don't know if this method is because I have a backbone or if anyone can do it the same way. However, if you have strong muscles, you will be able to maintain a sitting position for a long time, so I would also recommend light weight training.

There are many famous sayings in the world. ``A healthy mind resides in a healthy body.'' For me, this is often a misconception, but when I say it, I tend to spend a lot of time and purposefully thinking about it. Many people tend to think that famous quotes by great people were improvised, but they may have intended to say them that way from the beginning. In particular, the speech should not be ad-libbed, but should have materials that were thought out by the secretary from the beginning. That being said, once you gain muscle, it is difficult to lose it. In today's world, it's not that difficult to train like an athlete. Build muscle and lose fat. Your life should move in a better direction. See you soon.

What remains after posting content on SNS? Operate a personal website and use that website as the main link with SNS by Nada 20231006

Hello. This is Nada. Perhaps SNS has matured recently, and the number of users does not seem to increase much in the future. Of course, if you consider the potential users who are starting to use computers and smartphones in parts of Asia and Africa, there may be a reasonable growth rate.

For example, I think that in the past, social networking sites (SNS), such as short message posting sites and video posting sites, were controlled by the companies that managed the platforms. However, it is not necessary to completely cut off from such SNS platforms, but by having a personal site, there is a possibility that posting activities that do not have a high profit rate on SNS may bring more profit. I would like to suggest that.

Even when posting a short article, some people may feel that they can expect more value from posting it as an article on their own blog. Even if you post content one after another on a posting site forever, most of your posts will never be seen. Rather, if you add even one line of content to your personal site, it becomes your asset.

I want to say Why do you use SNS? If you want to become famous on SNS, there is no problem with posting short texts and videos as content. However, if your goal is to earn money from such content, I think it would definitely be better to focus on your personal site. Naturally, SNS is an important tool in terms of attracting customers. You can use it as much as you want, but if your goal is to make money, I think it's much smarter to create your own site and prioritize that.

If you think blogging on a personal site is old-fashioned, you can upload the video to a video posting site, paste the video into your own article on WordPress, and write an explanation, and the video and text become one. You can create your own original site. If you focus on your personal site activities rather than the number of video views, you will have more freedom in your activities. I think there is a chance of winning there.

See you soon.

To turn an enemy into an ally, try talking to him while holding a gift for him It’s not like I’ve given up on being a beautiful person by Nada 20231006

Hello. This is Nada. Today I would like to observe a creature called Happo Bijin.

Turning enemies into allies may seem difficult at first glance. It can be inferred that even though they are not enemies, but rivals, they are not allies in the sense of being opponents. I sometimes see the opinion that Happo Bijin is not a very good style. I've read a book about Adler's psychology of the courage to be hated, but I don't remember much of it. On top of that, the attitude of not caring about being disliked can be said to be compromising yourself.

If you really want to change yourself proactively, you should try to find ways to be liked even more by the people you currently like, and to build good relationships with people you don't currently get along with, even if it takes time. The attitude that it's okay for that person to hate you ends up setting a high bar for being liked by a lot of people, and your relationships become based on being hated. Even if it is a bit more taxing, if you have a policy of being liked by as many people as possible, you will have a desire to improve and you will be able to ride a virtuous cycle of growth. I'm by no means suggesting to other people that they should try to be beautiful in every way and perfect it. There are probably ways to be liked by people even if you're not a beautiful person, and the negative image of beautiful people, which is broad and shallow, is not necessarily a good thing.

However, if you look at social media these days, it can be said that the wide-ranging and shallow relationships of the beautiful people in all directions give you a chance to approach more people, and in the end, you can have more fun than a closed group of friends. If you settle into a group of only a few friends, even the smallest thing will be treated as a serious problem within the group, and you may even be kicked out of the group.

Returning to the theme of this article, the best way to turn an enemy into an ally is to give them an advantage. When you go on a trip, you might buy pudding or deer souvenirs, but try handing them out to people you're against. If one of them approaches the other, the wind will naturally pass through them. Alternatively, when your rival is inevitably attacked and you are losing, sending salt to your enemy is of course a risky move, but it can also be said to have many benefits. Above all, you don't see your enemy as an enemy; once you recognize him as an enemy, you can't get him out of your head, and your hostility increases. Even if it's just a can of coffee, give someone you think you don't like as a gift. Then, if you talk to him, you might realize that he wasn't really that bad. The worst part is that there is no communication at all. Maybe it would be a good idea to try and make some excuse to talk to her, like you would with that girl you like. If that doesn't cure your dislike, I think it's enough to just communicate by greeting each other.

What impression did you get? See you soon.

introducing the approximation formula for prime numbers, next time I would like to introduce the approximation formula for twin prime numbers by Nada 20231005

Prime number expressions 60c=a+(a+2), 60c=a+(a+14), 60c=a+(a+22), 60c=a+(a+26)

The first formula 60c=a+(a+2) → 60×1=(29)+(29+2)= 29 + 31 , 60×2=(59)+(59+2)= 59 + 61 , 60× 3=(89)+(89+2)= 89 + 91 , ….

The second formula 60c=a+(a+14)→ 60×1=23+(23+14)= 23 + 37 , 60×2=(53)+(53+14)= 53 + 67 , 60×3= (83)+(83+14)= 83 + 97 , ….　

The third formula 60c=a+(a+22)→ 60×1=19+(19+22)=19+41, 60×2=(49)+(49+22)=49+71, 60×3= (79)+(79+22)=79+101, ….　

The fourth formula 60c=a+(a+26)→ 60×1=17+(17+26)=17+43, 60×2=(47)+(47+26)=47+73, 60×3= (77)+(77+26)=77+103, ….　

Is the 80:20 rule true? If the skills of the top 20% of employees were given to the remaining 60%, sales would more than triple by Nada 20231004

Hello. This is Nada. Do you know about the 80:20 rule? It is said that the top 20% of customers contribute to 80% of sales. For businessmen, the top 20% of employees generate 80% of sales. I would like to ask a question here. Is it really true that only the top 20% of employees can increase sales by 80%? Therefore, by teaching the skills of the top 20% of employees and educating the remaining 60%, it is possible to calculate that the sales of the top 80% of employees will be 80x4 = 320% or more of the original sales. . (However, the sales of the bottom 20% of employees will remain constant.)

Depending on what you do, you can see that sales can easily triple or more. So, how can we spread the skills of the top 20% of employees to the top 80% of employees? I thought that if I could teach the remaining 80% of employees the useful work tips that the top 20% of employees knew, things would go well.

Therefore, what we should do is to add ``teaching'' to personnel evaluations, that is, evaluations of work. You cannot teach unless you know more about the subject than the other person. In other words, they already have a high level of ability, and the skills that can be taught are added to that. However, it is normal for the top 20% of employees to worry if their advantageous position is threatened. If the person you taught becomes at the same level as you, your advantage over the person you taught will be shaken.

Regarding this issue, I think that talented employees should become more proactive in teaching, and see this as an opportunity to become better at this act of teaching, which is also necessary for management. .

If you learn more than you teach, your skills will improve dramatically, and you can feel the tension of knowing that your colleagues and subordinates are closing in on you. A particularly important point is that the act of teaching helps improve communication. You will be able to communicate well, build good relationships with your co-workers, and be grateful to others. I can see that you have good eyes. Furthermore, if you become a manager, you will have the opportunity to teach your skills, which is a path you should take if you want to get promoted anyway.

Instead of thinking that teaching is a bad thing that creates rivalries and worsens one's advantageous situation, we now believe that teaching is important for the organization and that we can improve our own skills and communication skills. I think it's a good idea to think that it will be useful for you. The skill of teaching is to systematically organize one's own knowledge, so teaching others often leads to learning for oneself as well. If someone is having trouble and you feel you are the right person to help, why not give them some advice? Depending on your advice, the other person's opinion may change. See you soon.

Read materials to give form to ideas rather than study for the sake of studying by Nada 20231002

Hello. This is Nada. Rather than studying for the sake of studying, you read as a resource for researching something or coming up with ideas. In this way, people can focus on what they are working on, so they can proactively gain knowledge from books rather than just vaguely reading them. If you are passive about anything, you will lose the battle. How unreliable it is to let yourself be attacked even when your opponent is attacking instead of defending you. I don't want to criticize the passive attitude. This is because there are times when it is a rule to take on challenges with that attitude. However, if you just listen to what your professor says at university and copy it down in your notebook, you won't get much out of it or remember anything.

The best thing to do is to create your own assignments. On a slightly more advanced level, I'll give you the insurance that I've never done it before, but I'll try to create a problem, even if it's just a business idea. I think it would be interesting to actually research books and internet materials and interview people in the industry to see if the task is achievable. It is difficult to bring even a single business into shape, and many things must be simulated, from costs to customer base. If you are able to launch your business but it does not sell, you will end up in the red. Even if your business goes well and you are building your first company, you will need to research various things, from laws to taxation. It might be easier if you have a mentor to teach you, but if you try to do it on your own, you'll have to study a lot just to get a part-time job.

So far, it seems possible to have a virtual experience just by imagining it, without actually starting a business. How do you deal with the challenges that come your way? You may end up hearing a silent voice telling you that your company is on fire. Not a company! If I could tell him that I was on fire for my own passion, a kind gentleman would walk away. This time, it ended in a way that I didn't understand. You might have better luck if you try creating an assignment for now. There will probably be a lot of people working tomorrow, but do your best! ! See you soon.