Number of zero's in largest prime...

[paulunderwood]

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.

[Citrix]

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.

[Uncwilly]

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.

[Citrix]

Still incorrect. Learn to count.

[paulunderwood]

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...

[grandpascorpion]

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.

[Citrix]

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

[Citrix]

Originally Posted by paulunderwood

The last digit in any base is not zero because it is prime.

Can you prove this?

[grandpascorpion]

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.

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.

[paulunderwood]

You're right on both accounts: M43 is not the maximum base and 10 in base M43 is M43...

[Uncwilly]

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.