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 2006-03-23, 23:44 #12 paulunderwood     Sep 2002 Database er0rr 118F16 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.
2006-03-23, 23:49   #13
Citrix

Jun 2003

3×5×107 Posts

Quote:
 Originally Posted by Uncwilly Incorrect. Once you get past the base that is the number itself, you will run out of 0's. Right, Bob?
Wrong answer, you never run out of bases.

2006-03-24, 00:25   #14
Uncwilly
6809 > 6502

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Aug 2003
101×103 Posts

22×7×389 Posts

Quote:
 Originally Posted by Citrix Wrong answer, you never run out of bases.
I understood it Paul's way. No decimals, no negatives. My answer is correct in that manner.

 2006-03-24, 00:33 #15 Citrix     Jun 2003 3×5×107 Posts Still incorrect. Learn to count.
 2006-03-24, 00:50 #16 paulunderwood     Sep 2002 Database er0rr 106178 Posts The maximum base is base M43 which is one digit. No zeroes there. The first digit is non-zero 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...
 2006-03-24, 01:10 #17 grandpascorpion     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.
 2006-03-24, 02:26 #18 Citrix     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
2006-03-24, 02:27   #19
Citrix

Jun 2003

3·5·107 Posts

Quote:
 Originally Posted by paulunderwood The last digit in any base is not zero because it is prime.

Can you prove this?

2006-03-24, 02:41   #20
grandpascorpion

Jan 2005
Transdniestr

50310 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:
 No after M43 it will be the same decimal represntation as M43 not one digit.
Think carefully about that statement. Decimal representation is only pertinent to base 10. There's a unique zero for each base. Think of hexidecimal notation. Does anyone write 10 in a digit's place for a hex number. No, they write A. You need a unique "character" for each possible digit in a base.

Last fiddled with by grandpascorpion on 2006-03-24 at 02:48

 2006-03-24, 03:21 #21 paulunderwood     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...
2006-03-24, 04:50   #22
Uncwilly
6809 > 6502

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Aug 2003
101×103 Posts

101010100011002 Posts

Quote:
 Originally Posted by Uncwilly Once you get past the base that is the number itself, you will run out of 0's.
I stand by this for all natural bases. (note the added emphasis in the quote) Leading zeros are not counted (it is chasing your tail). Those to the right of the units column don't count either, because we are dealing with a whole number. The number is finite, but if it is calculatable is beyond me. I would have to use tools and brute force it.

Last fiddled with by Uncwilly on 2006-03-24 at 04:52

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