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UnkleRhaukus

  • 2 years ago

Which base has the lowest prime number density /

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  1. sauravshakya
    • 2 years ago
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    Isnt prime number density is same in all base

  2. UnkleRhaukus
    • 2 years ago
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    why do you say that?

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

  4. UnkleRhaukus
    • 2 years ago
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    yeah, but the density will be different

  5. sauravshakya
    • 2 years ago
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    how?

  6. sauravshakya
    • 2 years ago
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    number of prime numbers will not change

  7. UnkleRhaukus
    • 2 years ago
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    i suppose i mean density of digits

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

  9. sauravshakya
    • 2 years ago
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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

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

  11. UnkleRhaukus
    • 2 years ago
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    any random number has the same density,

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

  13. sasogeek
    • 2 years ago
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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

  14. sasogeek
    • 2 years ago
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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?

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

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

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

  18. sasogeek
    • 2 years ago
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    interesting :)

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

  20. UnkleRhaukus
    • 2 years ago
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    what base has the highest prime density?

  21. sasogeek
    • 2 years ago
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    infinity

  22. UnkleRhaukus
    • 2 years ago
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    base infinity ? hmm interesting

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

  24. sasogeek
    • 2 years ago
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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...

  25. UnkleRhaukus
    • 2 years ago
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    i can't count in base zero

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

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

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

  29. UnkleRhaukus
    • 2 years ago
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    |,||,|||,||||,|||||,||||||,|||||||,||||||||,|||||||||,

  30. sasogeek
    • 2 years ago
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    ?

  31. UnkleRhaukus
    • 2 years ago
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    thats base one

  32. sasogeek
    • 2 years ago
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    are you serious!? -_-

  33. sasogeek
    • 2 years ago
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    the only number in base 1, is 0.....

  34. sasogeek
    • 2 years ago
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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

  35. UnkleRhaukus
    • 2 years ago
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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

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

  37. sasogeek
    • 2 years ago
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    00000000000=0 00000=0 0=0

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

  39. sasogeek
    • 2 years ago
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    idk either :/ @amistre64 @satellite73 @saifoo.khan ...

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