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Math Help - prime numbers

  1. #1
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    prime numbers

    Following Euclid's proof that there are infinitely many primes, and starting the list with 5 and 7, you form the number 5*7+1=36, and you get the new prime numbers 2 and 3 because 36=2*2*3*3. Which new prime numbers would you get if your starting list were the following?

    a. 2,3,5

    b. 2,3,5,7

    c. 3,5
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by ihavvaquestion View Post
    Following Euclid's proof that there are infinitely many primes, and starting the list with 5 and 7, you form the number 5*7+1=36, and you get the new prime numbers 2 and 3 because 36=2*2*3*3. Which new prime numbers would you get if your starting list were the following?

    a. 2,3,5

    b. 2,3,5,7

    c. 3,5
    c. 3*5+1=16. Now what are the prime factors of 16?
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  3. #3
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    3*5+1+16=2*2*2*2=16, so 2 is the only new prime number?

    a. 2*3*5+1=31, so is 31 the only new prime number?

    b. 2*3*5*7+1=211, so is 211 the only new prime number?
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  4. #4
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by ihavvaquestion View Post
    3*5+1+16=2*2*2*2=16, so 2 is the only new prime number?

    a. 2*3*5+1=31, so is 31 the only new prime number?

    b. 2*3*5*7+1=211, so is 211 the only new prime number?
    Correct!
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