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Results tagged with prime-numbers
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user 14726
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.
4
votes
1
answer
2k
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form of primes:prime plus a power of 2?
is every prime p equals another prime p' plus or minus a power of 2? p=p'+/-2^n? are there infinitely many primes not of this form?
9
votes
3
answers
2k
views
question in prime numbers
Is it true that in any successive (natural) $2p_n$ numbers there are at least three numbers that are not divisible by any prime less (not equal) than $p_n$? Here, $p_n$ denotes the $n$-th prime numbe …
-4
votes
1
answer
2k
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Is this equivalent to Goldbach's conjecture?
As one can easily prove https://math.stackexchange.com/questions/20564/sums-of-square-free-numbers-is-this-conjecture-equivalent-to-goldbachs-conjec every integer greater than $1$ is a sum of two squa …
4
votes
Constructing prime numbers
maybe you could take the primes on the products in any powers you want , it is a thought that i had before some years and it is also a natural question that one can make reading Euclid's proof since s …
7
votes
2
answers
1k
views
Lower bound of the number of relatively primes(each-other) in an interval
I am trying to find lower and upper bounds for the number of integers that are coprime in pairs in an interval of length n.
What are the best bounds that we have?
Is that true that in any interval o …
11
votes
2
answers
981
views
Is the $n$-th prime $p_n$ expressible as the difference of coprime $A, B$ such that the set ...
We define recursively
$p_1=2,p_2=3$
and
$$p_{n}= \min_{(A,B)\in F_{n-1}}|A-B| $$
Where
$$
\begin{split}
F_n=\{(A,B) |&\gcd (A,B)=1,\quad |A-B| \not =1,
\\\
&\text{both $A$ and $B$ are products of po …
0
votes
Chen's Theorem with congruence conditions.
one should add this :There are infinitely many twin primes if and only if there are infinitely many natural numbers that are not of the form 6nm+/-n +/-m.
Proof:
Every number that is not a multiply of …
2
votes
1
answer
1k
views
Covering Systems of infinite sets of residue classes mod primes
Take an infinite set of distinct primes and a (edit: or 2 , etc.) residue class for every prime. For exammple you can take all the primes bigger than some prime or the primes of a specific form (i.e. …
4
votes
5
answers
2k
views
residue classes of primes, covering intervals and bounds on the different ways
Take the first $n$ primes $p_1,...,p_n$ and the primorial $P_n$ .Denote by $p_i$ every prime bigger than $p_n$ and smaller than $P_n$.
1) Is that true that there always be a number in any interval of …
1
vote
For what subsets S of (Z/nZ)* is there a Euclidean proof that there are infinitely many prim...
This could be helpful: "Certain other cases of Dirichlet's Theorem have been proved by elementary methods; in fact, elementary proofs have been found for general classes…. M. Brauer found a rather sim …