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Must Mersenne numbers be divisible by arbitrary large primes with exponent one?
Let $M_n$ denote the Mersenne numbers $M_n=2^n-1$.
As $n$ varies, must $M_n$ be divisible by arbitrary large prime $p$
with exponent one, i.e. $p \mid M_n, p^2 \nmid M_n$?
In other words, must the ...
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7
votes
1
answer
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$\log \log p / \log \log n$, where $p|n$, gets equidistributed in [0,1] (for almost all $n$)
According to Hardy-Ramanujan/Erdős-Kac we know that usually there are $\sim\log\log n$ prime numbers in a factorization. But if you pick up a natural number at random, and you factor it, what is the ...
- 1,384
2
votes
1
answer
450
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Is there a "small $\omega$" number theorem?
In my studies of how primes jump (search this forum for a link), a question has been raised which may have been studied. Can anyone jump-start my literature search with references regarding the ...
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