Square root word problem

rcwitt · 2011-01-13 14:00:10

I was given the following problem to work out:

"Find two prime numbers that, if multiplied, would generate a 400-digit number."

I have no idea where to begin looking for how to figure this.

I DO NOT WANT THE ANSWER ! I just want to know how to find the answer.

Thanks,
Charlie

rcwitt · 2011-01-13 15:03:22

First off, I need to apologize for the missleading subject line. The problem has nothing to do with square roots.

Second, I think I may have had a brainstorm (or maybe a light shower, anyway).

Any number that is a multiple of 100 is a prime number if you add the number 1 to it, right? like, 101, 201, 100000001, 2000000001, 1000000000001, 2000000000001, etc....

Therefore, I think I can sufficiently solve the problem as follows:

Does this make any sense? Or am I just confusing myself? After re-reading the question, I discovered that the 400 digit number does not have to be a prime.

Thanks,
Charlie

rcwitt · 2011-01-13 15:18:47

Just realized I had it wrong. The solution should read as:

The answer isn't important, provided it has 400 digits

Thanks,
Charlie

Last edited by rcwitt (2011-01-13 15:29:20)

gAr · 2011-01-13 16:10:55

Hi Charlie,

Any number that is a multiple of 100 is a prime number if you add the number 1 to it, right? like, 101, 201, 100000001, 2000000001, 1000000000001, 2000000000001, etc....

Not true, only 101 is prime.
There is no easy pattern or equation to find prime numbers, though there is a prime number theorem: http://en.wikipedia.org/wiki/Prime_number_theorem

Anyway, what's the correct question?
If I assume the question to be : "Find two numbers that, if multiplied, would generate a 400-digit number.", then one possible answer would be

Last edited by gAr (2011-01-13 16:15:22)

bobbym · 2011-01-13 16:37:00

Hi

Find two prime numbers that, if multiplied, would generate a 400-digit number.

That is a very difficult problem. Proving the primality of two 200 digit numbers is not easy without a computer. 100^200 +1 is not prime.

But if you need an answer...

So you could square that to produce a 400 digit number. Or if you needed two different 200 digit numbers that were prime you could use.

They are both prime and when multiplied together will give a 400 digit number.

Bob · 2011-01-13 22:20:17

hi Charlie,

"Find two prime numbers that, if multiplied, would generate a 400-digit number."

So what are you allowed to 'know'?

eg. If you can find two 200-digit primes those would probably meet the criteria, so are you allowed to look at a list of big primes, or use one from a known subset of the primes?

And are you hoping to do the multiplication?, because that will need mathematical software.

Or, is this a question requiring an analytical, number theory, type answer?

Bob

Last edited by Bob (2011-01-13 22:36:34)

rcwitt · 2011-01-14 21:38:40

To be honest, I have no idea what the purpose of this problem is. I am supposed to list the two numbers and "explain your strategy". That's it. I think I will just put the answer I found here and explain my strategy as "researched the problem on the internet". It is for a Problem Solving class that I am taking. Since there really isn't a simple way to solve the problem (my TI calc won't do it), I don't see how anyone can figure it out without looking online at lists of Mersenne primes.

Charlie

rcwitt · 2011-01-14 21:40:36

Incidentally, this is the same instructor who, when asked for a more detailed explanation of a different problem, told the student to "Google it". That's why I come here. You folks are much better instructors.

Charlie

bobbym · 2011-01-14 21:48:45

Hi;

You can tell him that you did your research at the MathsIsFun forum.

Bob · 2011-01-14 23:19:35

And if you Google 'list prime numbers' you will find there are sites that do exactly that although I didn't find 200 digits that easy, because there seem to be sites that give the first n primes and sites that give very large primes (over 10000 digits, say) and not much in between. You may need to tweak your search and that's a problem solving skill ... hence the nature of the task.

Best of luck,

Bob

Bob · 2011-01-15 02:09:44

Got some.

Just added "200 digits" ( in quotes ) to my search.

Site at bottom of post so you can find it yourself if you want.

But you'll also have to prove the product has 400 digits, not 399 or 401.

(note. 100 x 100 is 5 digits, but 900 x 900 is 6 digits, so you cannot just assume it's ok to add the digits 200 + 200 = 400 )

Bob

.......................spoiler below ...........................

http://primes.utm.edu/lists/small/small2.html

ps. These are considered 'small' !!!

Last edited by Bob (2011-01-15 02:12:01)

bobbym · 2011-01-15 03:13:58

Hi Charlie;

Bob has raised good points:

You can use my two numbers and here is the proof that they are in the required range.

First some prerequisites:

10^399 is the smallest 400 digit number. 10^400 is the smallest 401 digit number.

Start with the inequality.

Expand

Divide through by 10^399.

The inequality holds so it is a 400 digit number. You can give your teacher the numbers I gave you in post #5 and you are safe.

rcwitt · 2011-01-15 07:22:51

******************EDITTED AGAIN IN FOLLOW UP POST BELOW*******************

Just a couple of points I'd like to clarify. I am sure your answer is correct, but I'd like to understand the process. Please reference my questions below as indicated by the asteriks:

bobbym wrote:

Hi Charlie;
Bob has raised good points:
You can use my two numbers and here is the proof that they are in the required range.
First some prerequisites:
10^399 is the smallest 400 digit number. 10^400 is the smallest 401 digit number.
Start with the inequality.
Expand
****** How did you get the exponent of 400 in the center number above? ******
Divide through by 10^399.
****** Here, I see what happened on the left side of the equation, but what happened to the exponent on the right side (the 400)?******
The inequality holds so it is a 400 digit number. You can give your teacher the numbers I gave you in post #5 and you are safe.

Last edited by rcwitt (2011-01-15 07:35:22)

rcwitt · 2011-01-15 07:28:59

rcwitt wrote:

Just a couple of points I'd like to clarify. I am sure your answer is correct, but I'd like to understand the process. Please reference my questions below as indicated by the asteriks:

bobbym wrote:
Hi Charlie;
Bob has raised good points:
You can use my two numbers and here is the proof that they are in the required range.
First some prerequisites:
10^399 is the smallest 400 digit number. 10^400 is the smallest 401 digit number.
Start with the inequality.
Expand
****** How did you get the exponent of 400 in the center number above? ******
Divide through by 10^399.
****** Here, I see what happened on the left side of the equation, but what happened to the exponent on the right side (the 400)?******
The inequality holds so it is a 400 digit number. You can give your teacher the numbers I gave you in post #5 and you are safe.

******Also,where did you manage to find the two prime number you started with?

and
******

Last edited by rcwitt (2011-01-15 07:32:34)

bobbym · 2011-01-15 09:53:56

Hi Charlie;

Also,where did you manage to find the two prime number you started with?

This is the easiest question of your bunch. Those two numbers came from a computer. They are after all 200 digit numbers!

exponent on the right side (the 400)

I divided both sides by !0^399. When you divide 10^400 by 10 ^ 399 you minus the exponents. 400 - 300 = 1. 10^1 = 10.

The center one comes from doing the multiplication. This might be a little ahead of you right now. I do not want you jumping ahead of what you are being taught. Might be confusing. But if you really want to learn it...

rcwitt · 2011-01-15 10:06:23

Bobby,
That is part of what makes this class rather difficult. For a "final project" we are supposed to solve several problems that are found in chapters of our text that we will not cover in class. I basically have to learn how to solve them on my own. The instructor is pretty much useless. She refuses to help you understand the underlying principles.
I keep thinking that, since this is a college class, it may be assumed that I know how to solve them based on knowledge obtained during high school. But, I dropped out of high school in the 10th grade back in 1984, So, not only did I not learn the material (if it was even taught back then), it has been over two decades since I cracked a math book. I have a pretty good grasp of how things work, but I never learned it in the past. Now, I am somewhat behind the curve on understanding it.
I would love to understand the underlying principles and formulas involved. If for no other reason than to prove to the instructor that I can learn the material outside of class.
As a side not, I have spoken with both the department head and the dean of the school regarding this instructor. They agree that she should be doing a better job as an instructor, but I haven't seen any significant changes in her instructional manner.

Charlie

bobbym · 2011-01-15 10:13:40

Hi;

The instructor is pretty much useless. She refuses to help you understand the underlying principles.

A couple of questions. What is the name of your textbook? Can you post the problems you will be getting?

I would love to understand the underlying principles and formulas involved. If for no other reason than to prove to the instructor that I can learn the material outside of class.

Okay, first look here:

http://www.mathsisfun.com/exponent.html

http://www.mathsisfun.com/algebra/exponent-laws.html

http://www.mathsisfun.com/algebra/varia … tiply.html

See if you can cover them by yourself. If not just ask.

rcwitt · 2011-01-15 13:17:57

Bobby,
The questions are all different topics. Some cover prime numbers, others velocity, others density, etc. I can get them all posted if you'd like, but I can probably figure out most of them. The book is called "Strageties for Problem Solving". It is the text for one of my classes at ITT Tech.
And thanks for the website links, I will study them and get back with you if I have any problems.
Incidentally, the last post I made (about the unsolvable equations) helped me get a full grasp on the concept. I have taught it to my wife and had two other students come to the house so I could help them out. I have been giving you guys all the credit, though. I really appreciate all of your help.

Charlie

Last edited by rcwitt (2011-01-15 13:19:34)

bobbym · 2011-01-15 14:10:17

Hi Charlie;

Okay, post if you have problems. Good luck!

rcwitt · 2011-01-19 17:05:08

Ironically, enough, I spoke with the instructor today regarding this problem and I asked how we are expected to calculate the two prime numbers. I told her that I had researched it online and that I have the answer, but I couldn't figure out how to get the answer without accepting that the numbers I found online were accurate. She said "That's the answer". Apparently, we are supposed to simply look it up online and give the results of our research with a citation. Hell, I've been killing myself trying to figure out how to calculate it.

Charlie

bobbym · 2011-01-19 17:07:31

Hi Charlie;

Research is part of solving the problem. Just tell her I demand you get full credit or else.

Math Is Fun Forum

#1 2011-01-13 14:00:10

Square root word problem

#2 2011-01-13 15:03:22

Re: Square root word problem

#3 2011-01-13 15:18:47

Re: Square root word problem

#4 2011-01-13 16:10:55

Re: Square root word problem

#5 2011-01-13 16:37:00

Re: Square root word problem

#6 2011-01-13 22:20:17

Re: Square root word problem

#7 2011-01-14 21:38:40

Re: Square root word problem

#8 2011-01-14 21:40:36

Re: Square root word problem

#9 2011-01-14 21:48:45

Re: Square root word problem

#10 2011-01-14 23:19:35

Re: Square root word problem

#11 2011-01-15 02:09:44

Re: Square root word problem

#12 2011-01-15 03:13:58

Re: Square root word problem

#13 2011-01-15 07:22:51

Re: Square root word problem

#14 2011-01-15 07:28:59

Re: Square root word problem

#15 2011-01-15 09:53:56

Re: Square root word problem

#16 2011-01-15 10:06:23

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#17 2011-01-15 10:13:40

Re: Square root word problem

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Re: Square root word problem

#19 2011-01-15 14:10:17

Re: Square root word problem

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