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sauravshakya

  • 2 years ago

t(1)=2 t(2)=3 t(3)=t(1)*t(2)+1 t(4)=t(1)*t(2)*t(3)+1 . . . t(n)=t(1)*t(2)*t(3)*...*t(n-1)+1 PROVE or DISPROVE that t(n) will surely be PRIME

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  1. TuringTest
    • 2 years ago
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    This sounds like a very hard problem.

  2. estudier
    • 2 years ago
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    Maybe not....

  3. sauravshakya
    • 2 years ago
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    I dont know..... But I think it will not be surely prime.

  4. estudier
    • 2 years ago
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    If not, we just need a counterexample.

  5. TuringTest
    • 2 years ago
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    I doubt it is all primes as well.

  6. UnkleRhaukus
    • 2 years ago
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    remainder is gonna be one

  7. klimenkov
    • 2 years ago
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    Looks like an Euclid proof of the infinite number of prime numbers.

  8. estudier
    • 2 years ago
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    Euclid never said there was an infinity of primes (didn't believe in infinity)

  9. swissgirl
    • 2 years ago
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    t(5)=2*3*7*43+1=1807 1807/13=139

  10. estudier
    • 2 years ago
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    Euclid said that you could always construct another one out of a supposedly complete list.

  11. UnkleRhaukus
    • 2 years ago
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    that dosent make sense

  12. klimenkov
    • 2 years ago
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    There are infinitely many primes, as demonstrated by Euclid around 300 BC. http://en.wikipedia.org/wiki/Prime_number

  13. estudier
    • 2 years ago
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    True but he never said anything about infinity (Greeks weren't too keen on that idea)

  14. klimenkov
    • 2 years ago
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    You deepened into the history. But I spoke about the method.

  15. estudier
    • 2 years ago
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    The method, I agree, is very like the question.....

  16. estudier
    • 2 years ago
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    P_n = p1p2p3....+1

  17. UnkleRhaukus
    • 2 years ago
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  18. estudier
    • 2 years ago
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    The "infinitely many" part got added later.....

  19. estudier
    • 2 years ago
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    Personally, I like "you can always get another one" better....

  20. estudier
    • 2 years ago
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    "Construct another one"

  21. UnkleRhaukus
    • 2 years ago
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    do you mean induction

  22. estudier
    • 2 years ago
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    No, it is an explicit construction...

  23. estudier
    • 2 years ago
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    You give me a list of primes and say "That's all there are" And I give you another one not in the list...

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