20060323, 23:44  #12 
Sep 2002
Database er0rr
118F_{16} Posts 
I was asking about positive integer bases: How many zeroes in total in all bases of the largest known Mersenne prime? If you can't answer exactly then please give an educated guess.

20060323, 23:49  #13  
Jun 2003
3×5×107 Posts 
Quote:


20060324, 00:25  #14  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2^{2}×7×389 Posts 
Quote:


20060324, 00:33  #15 
Jun 2003
3×5×107 Posts 
Still incorrect. Learn to count.

20060324, 00:50  #16 
Sep 2002
Database er0rr
10617_{8} Posts 
The maximum base is base M43 which is one digit. No zeroes there.
The first digit is nonzero by definition. The last digit in any base is not zero because it is prime. Therefore all two digit representations cannot have any zeroes. That cuts it down a bit... 
20060324, 01:10  #17 
Jan 2005
Transdniestr
503 Posts 
Uncwilly's right.
Except for n=0, if you are talking about positive integers represented in positive bases, there will necessarily be no more zeroes for a number n above after base n so the total number of zeroes must be finite. After base n, the digit itself is n OBVIOUSLY. 
20060324, 02:26  #18 
Jun 2003
3·5·107 Posts 
No after M43 it will be the same decimal represntation as M43 not one digit. Think about it.
So since there are infinite bases, there are infinite #'s produding OO 0's. Citrix 
20060324, 02:27  #19  
Jun 2003
3·5·107 Posts 
Quote:
Can you prove this? 

20060324, 02:41  #20  
Jan 2005
Transdniestr
503_{10} Posts 
That's not correct Paul There's an exception. Prime p only has a zero in the first digit if you are writing the number in base p. It would be 10.
If the last digit is zero in base b, it must be a mulitple of b. That's obvious. 10 in base 10 is a multiple of 10. Right? 10 in base 2 is a multiple of 2. Right? Since a prime p's only factor above 1 is p. It can only have a 0 in the unit's digit in it's own base. Quote:
Last fiddled with by grandpascorpion on 20060324 at 02:48 

20060324, 03:21  #21 
Sep 2002
Database er0rr
5·29·31 Posts 
You're right on both accounts: M43 is not the maximum base and 10 in base M43 is M43...

20060324, 04:50  #22  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
10101010001100_{2} Posts 
Quote:
Last fiddled with by Uncwilly on 20060324 at 04:52 

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