Is (1237)^2 prime? 42 chairs put in rect.; find all prime p

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twisted_logic89

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any help/explanation of these is greatly appreciated!

1. Are the following numbers prime? why or why not?
a) (1237)^2
b) 1311279
c) 99999097

2. How many ways can you arrange 42 chairs in a rectangle if you must use all chairs?

3. Are there any pairs of prime numbers (p, p+2)? If so find at least 2 such pairs

4. If 12345 = P1 + P2 (where P1, P2 are prime), what are P1 and P2?

5. Find 3 positive integers so that the sum of any 2 is a prime number. Now find all sets of 3 positive integers such that the sum of any 2 is a prime number.

6. How many 3-digit numbers that can be made using the digits 1, 3, and 5 are prime? repeats allowed

7. Find all prime numbers (p) such that 2p + 1 = n^2

8. Show that a triangle with integer sides cannot have an area that is prime.
 
Re: contemporary math problems

twisted_logic89 said:
any help/explanation of these is greatly appreciated! ... < laundry list of 10 exercises snipped >
Click to expand...

Hello Twisted:

Any help/explanation of why you're stuck on these is greatly appreciated!

I realize that it's missing from the Arithmetic Board's index, but at the top of the Advanced Math Board's index (the board where you posted the same list of problems two minutes earlier), there is a post titled, "READ BEFORE POSTING".

This same post (which is missing from the Arithmetic Board) also appears on several of the other boards, in addition to the Advanced Math Board.

Please, read it.

It outlines your responsibilities for seeking help at this web site. Its main points are that (1) we don't complete exercises for posters (in general), and (2) people make it difficult for us to help when they keep everything other than the exercise itself secret.

Please read these guidelines, and then come back to your post and show whatever work you've been able to do on each of these 10 exercises. We also appreciate some clues as to why you're stuck.

Cheers,

~ Mark :)

PS: If you double-posted this request for help because you decided, after posting on the Advanced Math Board, that this board is more appropriate, then you had at that time (and, perhaps, still do) an opportunity to delete your original post.

As long as nobody has replied to a post, the owner of that post will see a button with an [X] in the upper-right corner of the text area near the
button. A poster can use this to delete their post. Once somebody responds to a post, this button disappears from it.
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These exercises range from the trival (elementary-school level) to somewhat more involved topics. Since you are at a level of study such that you are expected to be able to answer the last few exercises, then you must be able at least to show some progress on the grammar-school exercises. For instance, surely you know whether or not a square is prime...? :shock:

Please reply with a clear listing of your work and reasoning so far. Thank you! :D

Eliz.
 
Re: contemporary math problems

twisted_logic89 said:
any help/explanation of these is greatly appreciated!

1. Are the following numbers prime? why or why not?
a) (1237)^2
b) 1311279
c) 99999097

2. How many ways can you arrange 42 chairs in a rectangle if you must use all chairs?

3. Are there any pairs of prime numbers (p, p+2)? If so find at least 2 such pairs

4. If 12345 = P1 + P2 (where P1, P2 are prime), what are P1 and P2?

5. Find 3 positive integers so that the sum of any 2 is a prime number. Now find all sets of 3 positive integers such that the sum of any 2 is a prime number.

6. How many 3-digit numbers that can be made using the digits 1, 3, and 5 are prime? repeats allowed

7. Find all prime numbers (p) such that 2p + 1 = n^2

8. Show that a triangle with integer sides cannot have an area that is prime.
Click to expand...

What have you been taught about divisibility of a number by 2,3,5,7,11,.... etc?

Please show us your work, indicating exactly where you are stuck, so that we know where to begin to help you.

For example, you cannot possibly be stuck at problem #1(a). Any fourth grader who knows the definition prime number and square number - would be able to answer this question.
 
ok, I put my reasoning in bold.... please help.... :?

1. Are the following numbers prime? why or why not?
a) (1237)^2 (ok, for this one I used like an x^2 = x times x to put it in different terms. By this reasoning, it can be divided by 1, x, and x^2 therefore making it not prime.)
b) 1311279 (divisible by itself, one, and three, so not prime)
c) 99999097 (all the digits add up to 61, which I believe is prime... so I would say this number IS prime...?)

2. How many ways can you arrange 42 chairs in a rectangle if you must use all chairs? (if one were to keep rotating every chair to say, for example, the right, wouldnt there be an infinite amount of ways to arrange them?)

3. Are there any pairs of prime numbers (p, p+2)? If so find at least 2 such pairs. (1, 3 and 3, 5) Im not sure if this is right or not

4. If 12345 = P1 + P2 (where P1, P2 are prime), what are P1 and P2? (2 + 12343 is what I came up with. Although Im not completely sure if 12343 is prime... do you just add up the digits and if their sum is prime, the number itself is prime too?)

5. Find 3 positive integers so that the sum of any 2 is a prime number. Now find all sets of 3 positive integers such that the sum of any 2 is a prime number. (I came up with 0,1,2 and 0,2,11 but I have no idea how to find ALL the sets)

6. How many 3-digit numbers that can be made using the digits 1, 3, and 5 are prime? repeats allowed (135, 153, 315, 351, 513, 531) the digits always add up to nine, which is divisible by 3, so none of them are prime right?)

7. Find all prime numbers (p) such that 2p + 1 = n^2 (dont even know where to begin on this one! please help!)

8. Show that a triangle with integer sides cannot have an area that is prime. (same as above!)
 
twisted_logic89 said:
ok, I put my reasoning in bold.... please help.... :?

c) 99999097 (all the digits add up to 61, which I believe is prime... so I would say this number IS prime...?)

Where, when, how did you learn that Law?

Do you know the rule of divisibility by 11?

3. Are there any pairs of prime numbers (p, p+2)? If so find at least 2 such pairs. (1, 3 and 3, 5) Im not sure if this is right or not - 1 is not considered a prime

4. If 12345 = P1 + P2 (where P1, P2 are prime), what are P1 and P2? (2 + 12343 is what I came up with. Although Im not completely sure if 12343 is prime... do you just add up the digits and if their sum is prime, the number itself is prime too...? No

6. How many 3-digit numbers that can be made using the digits 1, 3, and 5 are prime? repeats allowed (135, 153, 315, 351, 513, 531) the digits always add up to nine, which is divisible by 3, so none of them are prime right - ?) No - what about 553
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What level of mathematics are you doing? - if have no idea how to start a problem - how come you have been assigned these problems?

Does not look like you have studied properties of prime numbers - carefully.

All primes - except 2 - are odd numbers. Thus when you add two prime numbers (excluding 2) - the result is an even number - which is not a prime.
 
Subhotosh Khan said:
What level of mathematics are you doing? - if have no idea how to start a problem - how come you have been assigned these problems?

Does not look like you have studied properties of prime numbers - carefully.

All primes - except 2 - are odd numbers. Thus when you add two prime numbers (excluding 2) - the result is an even number - which is not a prime.
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ok... I dont know, IM SORRY, I am VERY bad at math. I did not come here for disparaging comments, I came here for help. I am in a math class called "contemporary math". I dont know what level it would be considered.

1. I dont know the divisibility rule by 11
2. What will be the dimensions? Is this something I should already know or are you asking me? 4 sides to a triangle, length * width for the area....... sorry i dont really know what you are asking
3. Ok, 1 is not considered prime so...... 3, 5 and 2, 11
4. so when you say "no", you are telling me 12343 is not prime? How do I know if it is? When those digits are added up, it comes out as 13, which is not divisible by 3. I have to disagree and say that 12343 is prime... please prove me wrong if I am.
5. 0,2,11 will still work but 0,1,2 wont since 1 isnt prime. 0,2,3 works right? is there a rule for this that I am overlooking that will show me all the sets?
6. oops....... my bad, I messed that one up really bad. So in addition to the numbers I mentioned there would also be 555, 553, 551, 535, 515, 333, 335, 353, 331, 313, 111, 115, 151, 113, 131 correct? 553, 551, 535, 515, 335, 353, 331, 313, 115, 151, 113, and 131 are all prime if i am not mistaken...
 
twisted_logic89 said:
6. oops....... my bad, I messed that one up really bad. So in addition to the numbers I mentioned there would also be 555, 553, 551, 535, 515, 333, 335, 353, 331, 313, 111, 115, 151, 113, 131 correct? 553 (divisible by 7), 551(divisible by 19), 535, 515 , 335 (divisible by 5), 353, 331, 313, 115, 151, 113, and 131 -are all prime if i am not mistaken... I did not check others
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Well, to be honest with you, if you think that a number that ends with a 5 (like 515) is prime,
when you can easily see that it is divisible by 5, then you're sure not ready for all those exercises
you were given.
 
twisted_logic89 said:
can someone PLEASE tell me how to check if a larger number is prime? please?
Click to expand...

What does your text book /class notes say?

Have you heard of Eratosthenes's sieve?

If not - do a google search - then tell us what did you find from google/text-book/class-notes.
 
here's a result that might help (at least a little): :wink:

Let n be a positive integer. If p is a positive integer s.t. p >= sqrt(n) and p|n, then there is a positive integer k, s.t. 1 < k <= sqrt(n) and pk = n.
 
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