Results 1 to 3 of 3

Math Help - Primes in an Infinite Sequence

  1. #1
    Member
    Joined
    Sep 2006
    Posts
    221

    Primes in an Infinite Sequence

    1.) Given the following infinite sequence:

    9, 98, 987, 9876, ..., 987654321, 9876543219, 98765432198, ...

    What are all the primes?

    2.) David has this unique social security number. The 9 digits in the social security number have the digits from 1 all the way through 9. The number also has the following properties: when you read it from left to right, the first two digits will form a number that is divisible by 2, the first 3 digits will form a number that's divisible by 3, the first 4 digits... and so forth until the whole number is divisible by 9. What is David's social security number?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,707
    Thanks
    626
    Hello, Ideasman!

    Given the following infinite sequence:
    . . 9, 98, 987, 9876, ..., 987654321, 9876543219, 98765432198, ...

    What are all the primes?
    All the even numbers can be eliminated.


    We have the sequence ending with odd digits:

    . . . . . . . 9, 987, 98765, 9876543, 987654321, ...
    . . - - . . . . . . - . . . . . . . . - - . .
    Divisors: .9 - 3 . . . 5 . - - . .3 . . . . . . 9


    So far, the first five odd numbers are composite.
    Let's consider the next five in the sequence.


    If we append 9, we have: .9876543219, which is still divisible by 9.

    If we append 987, we have: .987654321987, which is still divisible by 3.

    If we append 98765, we have: .98765432198765, which is divisible by 5.

    If we append 9876543, we have: .9876543219876543, which is divislble by 3.

    If we append 987654321, we have: .987654321987654321, which is divisible by 9.


    It seems that there are no primes in the sequence.

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2006
    Posts
    221
    Quote Originally Posted by Ideasman View Post
    1.) Given the following infinite sequence:

    9, 98, 987, 9876, ..., 987654321, 9876543219, 98765432198, ...

    What are all the primes?

    2.) David has this unique social security number. The 9 digits in the social security number have the digits from 1 all the way through 9. The number also has the following properties: when you read it from left to right, the first two digits will form a number that is divisible by 2, the first 3 digits will form a number that's divisible by 3, the first 4 digits... and so forth until the whole number is divisible by 9. What is David's social security number?
    Thanks Soroban. My prof. is tricky. I was trying to find prime numbers for #1. No wonder I couldn't find any. Yes, this is correct.

    For the 2nd one, does it relate to #1 at all? They are in the same "section".
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Infinite Primes Proof is complete ?
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: November 2nd 2009, 04:49 AM
  2. infinite primes
    Posted in the Number Theory Forum
    Replies: 8
    Last Post: January 30th 2009, 09:42 AM
  3. infinite primes?
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: October 13th 2007, 04:42 PM
  4. my last question-infinite number of primes
    Posted in the Number Theory Forum
    Replies: 15
    Last Post: December 28th 2006, 10:12 AM
  5. Infinite Primes Proof
    Posted in the Number Theory Forum
    Replies: 7
    Last Post: April 11th 2005, 08:40 AM

Search Tags


/mathhelpforum @mathhelpforum