Re: IMPORTANT Re: Zero digits in powers




On 22/06/2005 19:45, vkarlamov@xxxxxxxxx wrote:

> Jean-Claude Arbaut wrote:
>> On 21/06/2005 22:22, vkarlamov@xxxxxxxxx wrote:
>>
>>> Jean-Claude Arbaut wrote:
>>>> On 21/06/2005 21:05, vkarlamov@xxxxxxxxx wrote:
>>>>
>>>>
>>>>> I don't understand what you have written. Could you please:
>>>>>
>>>>> 1. State exactly and succinctly your hypothesis
>>>>
>>>> * (one I read) if n>86, decimal representation of 2^n contains at least one
>>>> "0" digit. It holds for n<10^9 (I am almost certain other people tried much
>>>> greater values)
>>>>
>>>
>>> Excuse me if I am not a great expert on computers, but how can a
>>> computer generate and analyze a decimal repesentation of 2^(10^9)? How
>>> many digits are there?
>>>
>>
>> You just need to compute the last few digits (say 100 or 200) to find a "0".
>> And these only require few additions. That's why it is very fast to reach
>> 10^9.
>>
>
> Tell me exactly: does it indeed take no more than, say, 200 digits to
> find a zero for each n < 10^9 or arethere a few examples that take more
> digits?

I am (almost) certain it was < 300, not sure if it was 200 or 250.

> Also, what is exactly the algorithm that you were using to find zeros?
> How does it do the flexible job of generating only enough digits to see
> the first zero?

You need to carry N digits for all computations, otherwise you loose
information. To find a zero, it suffice to look at the array (computation
are done in base 10, and digits are stored in an array T (n x 1).

.

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