## UnkleRhaukus 2 years ago Which base has the lowest prime number density /

1. sauravshakya

Isnt prime number density is same in all base

2. UnkleRhaukus

why do you say that?

3. sauravshakya

If 7 is prime in base 10 then its value in other base system is also prime right?

4. UnkleRhaukus

yeah, but the density will be different

5. sauravshakya

how?

6. sauravshakya

number of prime numbers will not change

7. UnkleRhaukus

i suppose i mean density of digits

8. sauravshakya

Suppose there are n prime numbers less than x then, Prime number density =n/x IN ANY BASE SYSTEM

9. sauravshakya

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

does the density of a number and it's value have any relation?

11. UnkleRhaukus

any random number has the same density,

12. sasogeek

so prime numbers in base ten have same density as prime numbers in base 5...

13. sasogeek

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

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

\[|\{2,3\}|/|\{0,1,2,3,4\}|=2/5\] \[|\{2,3,5,7\}|/|\{0,1,2,3,4,5,6,7,8,9\}|=4/10=2/5\]

16. UnkleRhaukus

is it alway 2:5?

17. UnkleRhaukus

base three\[|\{2\}|/|\{0,1,2\}=1/3\]

18. sasogeek

interesting :)

19. UnkleRhaukus

in base one and base two the prime density is zero

20. UnkleRhaukus

what base has the highest prime density?

21. sasogeek

infinity

22. UnkleRhaukus

base infinity ? hmm interesting

23. sasogeek

no one ever mentioned it... might as well give it a try xD

24. sasogeek

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

i can't count in base zero

26. sasogeek

so go for one, the next obvious answer lol unless i'm not thinking right :/

27. sasogeek

wait, u cant count in base 1 either... :(

28. sasogeek

next number.... 2? works for me... i can count in base 2... yay!!!

29. UnkleRhaukus

|,||,|||,||||,|||||,||||||,|||||||,||||||||,|||||||||,

30. sasogeek

?

31. UnkleRhaukus

thats base one

32. sasogeek

are you serious!? -_-

33. sasogeek

the only number in base 1, is 0.....

34. sasogeek

35. UnkleRhaukus

oh right, base one 0,00,000,0000,00000,000000,0000000, base two 1,10,11,100,101,110,111,1000

36. sasogeek

no matter the number of 0's, it's still 0.....

37. sasogeek

00000000000=0 00000=0 0=0

38. UnkleRhaukus

id this how to count in base zero ? {}, {{}}, {{{}}}, {{{{}}}}

39. sasogeek

idk either :/ @amistre64 @satellite73 @saifoo.khan ...