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I was looking for the minimum size of a base35 secret_key to be able to generate at least 1,000,000 secret key.

The result is 35*35*35*35 = 1500625

How do you call this operation of counting the number of euclidian division until the denominator is lower than the remainder ?

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I think where you wrote "remainder" you mean "quotient" and where you write "quotient" you mean divisor. This is essentially an integer logarithm. – Thomas Andrews Feb 7 '13 at 15:20
up vote 1 down vote accepted

I don't think there is a special name, but in a formula this boils down to $$\left\lceil\frac{\ln 1000000}{\ln 35}\right\rceil=4.$$

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I love it thanks. – Natim Feb 7 '13 at 15:23
35^x > 1000000 | log_b(35^x) > log_b(1000000) | x . log_b(35) > log_b(1000000) | x > log_b(1000000) / log_b(35) | x > 3.88... – Natim Feb 7 '13 at 18:12
So if we are 7 billions on the planet. If everybody knows 100 persons you can reach anybody in 5 hop. Great. Thank you for this demonstration. – Natim Feb 7 '13 at 18:17

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