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Results tagged with counterexamples
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user 88804
A counterexample is an example that disproves a mathematical conjecture or a purported theorem. For example, the Peterson graph is a counterexample to many seemingly plausible conjectures in Graph Theory.
1
vote
1
answer
358
views
Primality test for numbers of the form $4k+3$
Can you prove or disprove the following claim:
Let $n$ be a natural number of the form $4k+3$ , and let $c$ be the smallest odd prime such that $\binom{c}{n}=-1$ , where $\binom{}{}$ denotes a Jacobi …
- 2,661
10
votes
0
answers
631
views
Primality testing using Chebyshev polynomials
Can you provide a proof or a counterexample for the claim given below?
Inspired by an alternative definition of the Frobenius primality test which is given in this paper I have formulated the followin …
- 2,661
4
votes
1
answer
182
views
Primality test for specific class of $N=8k \cdot 3^n-1$
This question is related to my previous question.
Can you prove or disprove the following claim:
Let $P_m(x)=2^{-m}\cdot \left(\left(x-\sqrt{x^2-4}\right)^{m}+\left(x+\sqrt{x^2-4}\right)^{m}\right)$
…
- 2,661
2
votes
1
answer
363
views
Primality test for specific class of $N=8kp^n-1$
My following question is related to my question here
Can you provide a proof or a counterexample for the following claim :
Let $P_m(x)=2^{-m}\cdot \left(\left(x-\sqrt{x^2-4}\right)^{m}+\left(x+ …
- 2,661
5
votes
1
answer
332
views
Conjectured primality test for specific class of $N=k \cdot 6^n+1$
I have tested this claim for many random values of $k$ and $n$ and there were no counterexamples .
Test implementation in PARI/GP without directly computing cyclotomic polynomials. …
- 2,661
9
votes
1
answer
416
views
Conjectured primality test for specific class of $N=4kp^n+1$
Can you provide a proof or counterexample for the following claim?
Let $P_m(x)=2^{-m}\cdot((x-\sqrt{x^2-4})^m+(x+\sqrt{x^2-4})^m)$ .
Let $N= 4kp^{n}+1 $ where $k$ is a positive natural number , …
- 2,661
3
votes
0
answers
263
views
Conjectured primality test for numbers of the form $N=4 \cdot 3^n-1$
This is a repost of this question.
Can you provide proof or counterexample for the claim given below?
Inspired by Lucas-Lehmer primality test I have formulated the following claim:
Let $P_m(x)=2^{-m} …
- 2,661
2
votes
1
answer
833
views
Primality test for generalized Fermat numbers
I have tested this claim for many random values of $b$ and $n$ and there were no counterexamples.
A command line program that implements this test can be found here. …
- 2,661
3
votes
1
answer
383
views
Primality test for specific class of $N=k \cdot b^n-1$
This question is successor of Compositeness test for specific class of $N=k \cdot b^n-1$ .
Can you provide a proof or a counterexample to the following claim :
Let $P_m(x)=2^{-m}\cdot \left(\left …
- 2,661
11
votes
2
answers
910
views
Primality test for specific class of Proth numbers
I have tested this claim for many random values of $k$ and $n$ and there were no counterexamples .
Note that for $k=1$ we have Inkeri's primality test for Fermat numbers . …
- 2,661
2
votes
0
answers
305
views
Conjectured initial values of Inkeri's primality test for Fermat numbers
This is a repost of this question .
Can you provide a proof or a counterexample to the claim given below ?
First , we shall give a definition of the Inkeri's primality test for Fermat numbers :
…
- 2,661
66
votes
3
answers
6k
views
Chebyshev polynomials of the first kind and primality testing
I have tested this claim up to $5 \cdot 10^4$ and there were no counterexamples .
EDIT
Algorithm implementation in Sage without directly computing $T_n(x)$ . …
- 2,661
5
votes
0
answers
586
views
Primality test for specific class of generalized Fermat numbers
I have verified this claim for $p \in [7,5000]$ with $n \in [2,10]$ and there were no counterexamples . …
- 2,661