20060327, 00:29  #34  
Jun 2003
3·5·107 Posts 
Quote:
All numbers that are multiples of 2 can also be excluded. 

20060327, 00:46  #35  
Jun 2003
3·5·107 Posts 
Quote:
ignore this please. 

20060327, 00:50  #36  
Nov 2005
2^{4}·3 Posts 
Quote:


20060327, 00:56  #37 
Jan 2005
Transdniestr
503 Posts 
That's not true, Citrix. Mersenne primes can have zeroes in even bases.
Why use Mathematica anyways? All you need is div and mod to get base values. Last fiddled with by grandpascorpion on 20060327 at 01:00 
20060327, 01:10  #38  
Jun 2003
3×5×107 Posts 
Quote:
Can you give an example? Aside from this, I leave it as a puzzle to find the largest base for all Mp that produces a zero. I have the answer to this one. 

20060327, 01:44  #39 
Jan 2005
Transdniestr
503 Posts 
Not handy. It will be a good exercise for you. Why do you make these silly sweeping statements without a little investigation?
Last fiddled with by grandpascorpion on 20060327 at 01:47 
20060327, 03:30  #40 
Jun 2003
3·5·107 Posts 
Yes you are right
Consider numbers in base 10, which is even. I should think more before posting. Another puzzle (I do not have the answer), which base has the largest number of zero's for M43? 
20060327, 04:03  #41 
Jan 2005
Transdniestr
503 Posts 
Chances are that it's three.
Last fiddled with by grandpascorpion on 20060327 at 04:04 
20060327, 06:08  #42  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
10101010001000_{2} Posts 
Quote:
Assume that all bases will have a roughly even distribution of digits (by this I mean representational characters, e.g. for hexadecimal the 'digits' would be 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F). (Now this won't be true at the higher bases, as many will have a leading 1) Calculate the length (l) of the exponent in base n. Divide l by n (to get an approximation of the number of zeros in the particular base), sum this number for all bases (starting at 3) to M43. The result was: 1,529,591,493 A bit brute force and not exact. Code:
10 Prime = 30402457 : Zeros=0 20 for Base = 3 to Prime 30 L_g = log( Prime ) / log( Base ) 40 N_l = L_g * Prime 50 Digits = ( N_l / Base ) 60 Zeros = Zeros + Digits 70 next Base 80 print Zeros 

20060328, 01:13  #43  
Sep 2002
Database er0rr
2×3^{3}×83 Posts 
Your code is okay, except the loop for "base" should be up to 2^304024571 and not 30402457 . The loop should bail out when digits count became two and instead just add 1 to the count of zeroes  the number 10_{base M43} because it is prime  to save time on the loop
and you could have coded Quote:
A mathematical approach is needed such as given by "patrik" above to get a realististic figure  I haven't checked "patrik"'s claim but at least your brute force method's expected number of zeroes is less than "patrik"'s mathematically computed expected number of them. 

20060328, 01:42  #44  
Sep 2002
Database er0rr
4482_{10} Posts 
And shouldn't
Quote:
Quote:


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