large numbers as counterexamples [duplicate]
This question already has an answer here:
Conjectures that have been disproved with extremely large counterexamples?
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Some mathematical patterns stay true for a set of integers $1..n$ only to break at $n+1$.
What are some nontrivial examples where $n$ is ``large''?
As an example $x^2+x+41$ is prime for $x=1..40$, but not at $41$.
I am particularly looking for examples other than prime producing polynomials. Especially examples suitable for an introductory class.
geometry number-theory discrete-mathematics
asked Nov 26 at 14:16
Maesumi
2,6881523
marked as duplicate by Travis, Matthew Towers, Robert Israel number-theory
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Nov 26 at 14:26
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
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This question already has an answer here:
Conjectures that have been disproved with extremely large counterexamples?
15 answers
Some mathematical patterns stay true for a set of integers $1..n$ only to break at $n+1$.
What are some nontrivial examples where $n$ is ``large''?
As an example $x^2+x+41$ is prime for $x=1..40$, but not at $41$.
I am particularly looking for examples other than prime producing polynomials. Especially examples suitable for an introductory class.
geometry number-theory discrete-mathematics
asked Nov 26 at 14:16
Maesumi
2,6881523
marked as duplicate by Travis, Matthew Towers, Robert Israel number-theory
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Nov 26 at 14:26
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$$binom nr>0$$ for $0le rle n$
– lab bhattacharjee
Nov 26 at 14:20
math.stackexchange.com/a/111461/76284
– user76284
Nov 26 at 14:20
In any case, a standard example is Skewes' Number: mathworld.wolfram.com/SkewesNumber.html
– Travis
Nov 26 at 14:22
add a comment |
This question already has an answer here:
Conjectures that have been disproved with extremely large counterexamples?
15 answers
Some mathematical patterns stay true for a set of integers $1..n$ only to break at $n+1$.
What are some nontrivial examples where $n$ is ``large''?
As an example $x^2+x+41$ is prime for $x=1..40$, but not at $41$.
I am particularly looking for examples other than prime producing polynomials. Especially examples suitable for an introductory class.
geometry number-theory discrete-mathematics
asked Nov 26 at 14:16
Maesumi
2,6881523
This question already has an answer here:
Conjectures that have been disproved with extremely large counterexamples?
15 answers
Some mathematical patterns stay true for a set of integers $1..n$ only to break at $n+1$.
What are some nontrivial examples where $n$ is ``large''?
As an example $x^2+x+41$ is prime for $x=1..40$, but not at $41$.
I am particularly looking for examples other than prime producing polynomials. Especially examples suitable for an introductory class.
This question already has an answer here:
Conjectures that have been disproved with extremely large counterexamples?
15 answers
geometry number-theory discrete-mathematics
geometry number-theory discrete-mathematics
asked Nov 26 at 14:16
Maesumi
2,6881523
asked Nov 26 at 14:16
Maesumi
2,6881523
asked Nov 26 at 14:16
Maesumi
2,6881523
asked Nov 26 at 14:16
Maesumi
2,6881523
asked Nov 26 at 14:16
Maesumi
2,6881523
2,6881523
marked as duplicate by Travis, Matthew Towers, Robert Israel number-theory
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Nov 26 at 14:26
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Nov 26 at 14:26
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$$binom nr>0$$ for $0le rle n$
– lab bhattacharjee
Nov 26 at 14:20
math.stackexchange.com/a/111461/76284
– user76284
Nov 26 at 14:20
In any case, a standard example is Skewes' Number: mathworld.wolfram.com/SkewesNumber.html
– Travis
Nov 26 at 14:22
add a comment |
$$binom nr>0$$ for $0le rle n$
– lab bhattacharjee
Nov 26 at 14:20
math.stackexchange.com/a/111461/76284
– user76284
Nov 26 at 14:20
In any case, a standard example is Skewes' Number: mathworld.wolfram.com/SkewesNumber.html
– Travis
Nov 26 at 14:22
$$binom nr>0$$ for $0le rle n$
– lab bhattacharjee
Nov 26 at 14:20
$$binom nr>0$$ for $0le rle n$
– lab bhattacharjee
Nov 26 at 14:20
math.stackexchange.com/a/111461/76284
– user76284
Nov 26 at 14:20
math.stackexchange.com/a/111461/76284
– user76284
Nov 26 at 14:20
In any case, a standard example is Skewes' Number: mathworld.wolfram.com/SkewesNumber.html
– Travis
Nov 26 at 14:22
In any case, a standard example is Skewes' Number: mathworld.wolfram.com/SkewesNumber.html
– Travis
Nov 26 at 14:22
add a comment |
1 Answer
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It's not number theory, but I've always found the Borwein integrals to be fascinating.
https://en.wikipedia.org/wiki/Borwein_integral
answered Nov 26 at 14:20
Olivier Moschetta
2,7761411
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
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active
oldest
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active
oldest
votes
It's not number theory, but I've always found the Borwein integrals to be fascinating.
https://en.wikipedia.org/wiki/Borwein_integral
answered Nov 26 at 14:20
Olivier Moschetta
2,7761411
add a comment |
It's not number theory, but I've always found the Borwein integrals to be fascinating.
https://en.wikipedia.org/wiki/Borwein_integral
answered Nov 26 at 14:20
Olivier Moschetta
2,7761411
add a comment |
It's not number theory, but I've always found the Borwein integrals to be fascinating.
https://en.wikipedia.org/wiki/Borwein_integral
answered Nov 26 at 14:20
Olivier Moschetta
2,7761411
It's not number theory, but I've always found the Borwein integrals to be fascinating.
https://en.wikipedia.org/wiki/Borwein_integral
answered Nov 26 at 14:20
Olivier Moschetta
2,7761411
answered Nov 26 at 14:20
Olivier Moschetta
2,7761411
answered Nov 26 at 14:20
Olivier Moschetta
2,7761411
answered Nov 26 at 14:20
Olivier Moschetta
2,7761411
2,7761411
add a comment |
add a comment |
$$binom nr>0$$ for $0le rle n$
– lab bhattacharjee
Nov 26 at 14:20
math.stackexchange.com/a/111461/76284
– user76284
Nov 26 at 14:20
In any case, a standard example is Skewes' Number: mathworld.wolfram.com/SkewesNumber.html
– Travis
Nov 26 at 14:22