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Results tagged with prime-numbers
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user 18494
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.
3
votes
Infinitely many primes of the form $2^n+c$ as $n$ varies?
Hi there, I hope I'm not duplicating anything with what I will write. Here goes: If one considers the Bateman-Horn conjecture, it predicts that
$$
\sum_{n \leq x}\Lambda(f(n)) \sim \prod_p\left(\frac{ …
- 1,075
3
votes
Accepted
Can the relative count of the primefactors in $\small \lim_{w\to\infty}\prod_{k=1}^w (p_k-1)...
Mr Helms,
This is the $n=1$ case. Your formula gives $e_{1,q}=q$.
Say we want to study how often prime $q=q_k$ divides $\prod_{p \leq x}(p-1)$. Maybe write this product as
$$
\left(\prod_{i=1}^m\prod …
- 1,075
2
votes
Generalizing Euclid's proof of the infinity of primes
Not claiming to be a real number theorist or anything of that sort...Just wondering, is one possible approach to Mark Sapir's strong conjecture (assuming an answer isn't already known) to calculate
$$ …
- 1,075
2
votes
Accepted
Primes in generalized fibonacci sequences
These are Lucas Sequences (http://en.wikipedia.org/wiki/Lucas_sequence), of which the Fibonacci Sequence is a specific case, and they share with the usual Fibonacci Sequence the following characterist …
- 1,075
0
votes
Proof of infinitude of primes whose reversal in base 10 is also prime
Hello all,
I must be overlooking something, but I wonder if the systems $\Psi:\mathbb{Z}^d\rightarrow \mathbb{Z}^t$ in the Green-Tao paper "Linear Equations in Primes" could apply to this question.
- 1,075
1
vote
Proof of infinitude of primes whose reversal in base 10 is also prime
Now, thinking about this a bit, let's say $f$ is the function that reverses the digits, so that $f(n)$ is the number that has the digits of $n$ in base 10 reversed. I think that when estimating $$|\{n …
- 1,075
8
votes
0
answers
785
views
Two different ways to count Mersenne Primes
Hi there, the motivation for this question is to better understand the heuristics of Mersenne primes, and I was motivated by the recent questions (Mersenne quasi-primes) and (Primes in generalized Fib …
5
votes
2
answers
652
views
How are these number-theoretical constants actually distributed?
I'm very curious about this and would be really grateful for any help or comments in this direction. If we consider any of the following number-theoretical constants:
1)The various singular series a …
- 1,075
4
votes
Mertens-like sum in arithmetic progressions
This paper I believe might give such estimates:
Languasco, A.; Zaccagnini, A. A note on Mertens' formula for arithmetic progressions. J. Number Theory 127 (2007), no. 1, 37–46
Theorem 2 there works …
- 1,075
3
votes
Primes and Ackermann's function
Hartley (http://primes.utm.edu/curios/page.php/71.html) gives that 13 and 71 divide $A(m,n)$ for sufficiently large $m$.
Since $\{A(m+1,n): n \geq N\} \subset \{A(m,n): n\geq A(m+1,N-1)\}$, we need o …
- 1,075
4
votes
1
answer
920
views
Primes and Ackermann's function
If $A(m,n)$ is Ackermann's function, and $c$ is a fixed integer, are there any heuristics/conjectures/obvious things that can be said about primes of the form $A(m,n)+c$, $m \geq 4$,at all?
EDIT:
I …
- 1,075