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Results tagged with prime-numbers
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user 74668
Questions where prime numbers play a key-role, such as: questions on the distribution of prime numbers (twin primes, gaps between primes, Hardy–Littlewood conjectures, etc); questions on prime numbers with special properties (Wieferich prime, Wolstenholme prime, etc.). This tag is often used as a specialized tag in combination with the top-level tag nt.number-theory and (if applicable) analytic-number-theory.
2
votes
1
answer
740
views
Have there been any new developments in the Firoozbakht conjecture? [duplicate]
Let $(p_{n})_{n∈ℕ}$ be the sequence of consecutive primes. In P. Ribenboim, The New Book of Prime Number Records, Springer-Verlag, 1995, page 185, the author says:
A new conjecture by F. Firoozbak …
- 1,197
2
votes
1
answer
132
views
Results relating prime numbers with extremely abundant numbers
A positive integer $n$ is extremely abundant if either $n=10080$, or $n>10080$ and
$$σ(n)/(n×log(log (n)))>σ(m)/(m×log(log (m)))$$
for all $10080≤m<n$. Here $σ(n)$ is the sum-of-divisors function a …
- 1,197
5
votes
2
answers
794
views
Is the result of Schmidt conditional to RH
From this page:
https://en.wikipedia.org/wiki/Chebyshev_function#Asymptotics_and_bounds
A theorem due to Erhard Schmidt states that, for some explicit positive constant $K$, there are infinitely ma …
- 1,197
4
votes
1
answer
506
views
A weaker version of the Brocard's Conjecture
Brocard's conjecture states that: If $p_{k}$ and $p_{k+1}$ are consecutive prime numbers greater than $2$, then between $p_{k}²$ and $p_{k+1}²$ there are at least four prime numbers.
I know that is st …
- 1,197