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Here we define those primes $p$ for which $\operatorname{ord}_p(2)=s$, where $s$ is the minimum of the set $S$ of all divisors $d\mid p-1$ such that $2^d-1\geq p$.

For example: for $p=7$, $s=3$, $7\mid 2^3-1$ thus $\operatorname{ord}_p(2)=s=3$ ($7$ is such a prime).

Questions: how many such primes are there? Are such primes interesting?

Thanks.

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    JFYI: I've [opened a bug report](http://meta.stackexchange.com/questions/87685/migrating-from-meta-to-main-site-loses-user-information) about tomerg losing ownership to this question after the migration. This is somewhat unexpected.2011-04-17

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