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Math Help - n^2 + n + 41 and primes

  1. #1
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    Exclamation n^2 + n + 41 and primes

    consider the relation n^2 + n + 41
    one person claim that this relation does not apply for primes:
    for n=1 it gives 43 : its prime
    for n=2 it gives 47:its prime
    for n=3 it gives 53 : its prime;etc...
    Does this man have a reason for his claim?
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  2. #2
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    old favorite

    This problem is often used to help students see the importance of mathematical proof. If you try many values of n, the expression yields a prime. Can we therefore assume that it will ALWAYS yield a prime?

    What happens if n=41?
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  3. #3
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    if n=41
    then 41^2 + 41 + 41=1763
    it still prime!!!!
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  4. #4
    MHF Contributor Bruno J.'s Avatar
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    No, it is obviously divisible by 41.

    It's an easy exercise to show that no polynomial with integer coefficients yields only primes.
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  5. #5
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    Quote Originally Posted by lebanon View Post
    if n=41
    then 41^2 + 41 + 41=1763=43*41
    it still prime!!!!
    It must surely be the only composite prime number, then. ; )
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  6. #6
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    There aren't very many of them, I've heard!
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