All Questions
Tagged with experimental-mathematics prime-numbers
9 questions
9
votes
3
answers
2k
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May $p^3$ divide $(a+b)^p-a^p-b^p$?
Do there exist positive integers $a,b$ and a prime $p>\max(a,b)$ such that $p^3$ divides $(a+b)^p-a^p-b^p$?
The reader of Kvant magazine A. T. Kurgansky asked to prove that such $a,b,p$ do not ...
- 109k
6
votes
0
answers
479
views
Existence of an explosive prime
The motivation to introduce explosive prime is Carmichael's totient conjecture (see why below).
Let $\mathbb{N}_{SF}$ be the set of positive square-free integers. Consider the map $f:\mathbb{N}_{SF} \...
5
votes
1
answer
1k
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Lines in image; are they significant to prime numbers if so how?
Amateur math question. I was playing around generating some 2D images, and wondered what it would look like if placed $P_{i}$ dots on a circle with diameter of $i$ for increasing values of $i$, where $...
- 151
5
votes
1
answer
354
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Gadgets as primality tests
From the literature, showed below, I know two gadgets that provide a way to know if a positive integer (a positive quantity of units) is composite or a prime number. I would like to know if in the ...
3
votes
1
answer
163
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Increasing sequences and Wieferich primes
We are trying to show that primes of the form $a(n)$ can't be
Wieferich primes.
For natural $n$ define $J(n)=(2^{n-1}-1) \bmod n^2$
and if $n$ is power of two define $J(2^n)=1$ (this is artificial, ...
- 25.4k
2
votes
0
answers
93
views
Primes of the form $a+b^k$ for $k=(a \bmod 2),\ldots,n$?
Procrastinal problem: Given $n$, one can ask for integers $a,b>1$ of different parities
such that $a+b^k$ is prime for $k=(a\bmod 2),\ldots,n$.
A few examples are:
$2+4995825^k$ is prime for $k=0,\...
- 17.9k
2
votes
0
answers
237
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On the cardinality of the set of right-truncatable primes
We say that the (base ten) prime number $p=a_{n}a_{n-1}a_{n-2}\cdots a_{1}a_{0}$ is right-truncatable if all of the following numbers are prime:
\begin{eqnarray*}a_{n},\\a_{n}a_{n-1},\\ a_{n}a_{n-1}...
- 8,842
1
vote
0
answers
376
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Astonishing affinity of Wolfram's rule 110 to the numbers 2 and 7
I investigated the evolution of a single black cell on 1-dimensional grids with periodic boundary conditions of variable sizes $N$ under Wolfram's rule 110 which is the only one for which Turing ...
- 9,720
0
votes
1
answer
492
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New experiments involving Ramanujan primes: Benford's law
I know that in the literature there are interesting articles involving the sequence of Ramanujan primes, I refer the Ramanujan Prime from the online encyclopedia Wolfram MathWorld. This week I ...