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UnkleRhaukus

Which base has the lowest prime number density /

  • one year ago
  • one year ago

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  1. sauravshakya
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    Isnt prime number density is same in all base

    • one year ago
  2. UnkleRhaukus
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    why do you say that?

    • one year ago
  3. sauravshakya
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    If 7 is prime in base 10 then its value in other base system is also prime right?

    • one year ago
  4. UnkleRhaukus
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    yeah, but the density will be different

    • one year ago
  5. sauravshakya
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    how?

    • one year ago
  6. sauravshakya
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    number of prime numbers will not change

    • one year ago
  7. UnkleRhaukus
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    i suppose i mean density of digits

    • one year ago
  8. sauravshakya
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    Suppose there are n prime numbers less than x then, Prime number density =n/x IN ANY BASE SYSTEM

    • one year ago
  9. sauravshakya
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    though different number may come in different base system If we convert them all in same base number then their value will be same

    • one year ago
  10. sasogeek
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    does the density of a number and it's value have any relation?

    • one year ago
  11. UnkleRhaukus
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    any random number has the same density,

    • one year ago
  12. sasogeek
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    so prime numbers in base ten have same density as prime numbers in base 5...

    • one year ago
  13. sasogeek
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    this is my first time reading about number density so i'm only making statements out of deduced logic :/ i hope i'm not going astray lol

    • one year ago
  14. sasogeek
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    and if density remains the same no matter the base, doesn't it mean that there couldn't possibly be any base with "lowest prime number density" since it's the same everywhere?

    • one year ago
  15. UnkleRhaukus
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    \[|\{2,3\}|/|\{0,1,2,3,4\}|=2/5\] \[|\{2,3,5,7\}|/|\{0,1,2,3,4,5,6,7,8,9\}|=4/10=2/5\]

    • one year ago
  16. UnkleRhaukus
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    is it alway 2:5?

    • one year ago
  17. UnkleRhaukus
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    base three\[|\{2\}|/|\{0,1,2\}=1/3\]

    • one year ago
  18. sasogeek
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    interesting :)

    • one year ago
  19. UnkleRhaukus
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    in base one and base two the prime density is zero

    • one year ago
  20. UnkleRhaukus
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    what base has the highest prime density?

    • one year ago
  21. sasogeek
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    infinity

    • one year ago
  22. UnkleRhaukus
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    base infinity ? hmm interesting

    • one year ago
  23. sasogeek
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    no one ever mentioned it... might as well give it a try xD

    • one year ago
  24. sasogeek
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    but ur question... maybe u should choose 0.... cos base zero has prime number density of 0 and zero is less than 1...

    • one year ago
  25. UnkleRhaukus
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    i can't count in base zero

    • one year ago
  26. sasogeek
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    so go for one, the next obvious answer lol unless i'm not thinking right :/

    • one year ago
  27. sasogeek
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    wait, u cant count in base 1 either... :(

    • one year ago
  28. sasogeek
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    next number.... 2? works for me... i can count in base 2... yay!!!

    • one year ago
  29. UnkleRhaukus
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    |,||,|||,||||,|||||,||||||,|||||||,||||||||,|||||||||,

    • one year ago
  30. sasogeek
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    ?

    • one year ago
  31. UnkleRhaukus
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    thats base one

    • one year ago
  32. sasogeek
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    are you serious!? -_-

    • one year ago
  33. sasogeek
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    the only number in base 1, is 0.....

    • one year ago
  34. sasogeek
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    please ask the question in a new thread and add "Cont'd" and put the link here, this one is becoming too long

    • one year ago
  35. UnkleRhaukus
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    oh right, base one 0,00,000,0000,00000,000000,0000000, base two 1,10,11,100,101,110,111,1000

    • one year ago
  36. sasogeek
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    no matter the number of 0's, it's still 0.....

    • one year ago
  37. sasogeek
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    00000000000=0 00000=0 0=0

    • one year ago
  38. UnkleRhaukus
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    id this how to count in base zero ? {}, {{}}, {{{}}}, {{{{}}}}

    • one year ago
  39. sasogeek
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    idk either :/ @amistre64 @satellite73 @saifoo.khan ...

    • one year ago
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