A polynomial whose range gaps are the primes [closed]Elements of cyclotomic fields whose powers are rationalSplitting of primes in the splitting field of a polynomialElements whose conjugates are of the same absolute value in cyclotomic fieldsQuestions on some maps involving rings of finite adeles and their unit groups.Are there Groups of Strictly PrimesIs there an elementary proof that there are infinitely many primes p satisfying the following:What are the missing gaps to prove Goldbach Conjecture?Quartic polynomial whose coefficients are product of symmetrical quantitiesWhich primes are ramified?Chebotarev Density Theorem answers to factorization of polynomials
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A polynomial whose range gaps are the primes [closed]
Elements of cyclotomic fields whose powers are rationalSplitting of primes in the splitting field of a polynomialElements whose conjugates are of the same absolute value in cyclotomic fieldsQuestions on some maps involving rings of finite adeles and their unit groups.Are there Groups of Strictly PrimesIs there an elementary proof that there are infinitely many primes p satisfying the following:What are the missing gaps to prove Goldbach Conjecture?Quartic polynomial whose coefficients are product of symmetrical quantitiesWhich primes are ramified?Chebotarev Density Theorem answers to factorization of polynomials
$begingroup$
Not sure what to add here. I responded to hardmath in TN e Peter. If you feel it doesn't generate discussion I will rethink the question and read the purpose of your platform and try to reform the question.
Given that there is interest in a prime producing polynomial, is a sequential non-prime producing polynomial whose gaps in the range are all the primes just as important?
Thank you
algebraic-number-theory
asked Mar 12 at 20:30
InkInk
142
New contributor
Ink is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
closed as off-topic by Eevee Trainer, Vinyl_cape_jawa, Lee David Chung Lin, Leucippus, hardmath Mar 13 at 2:27
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, Vinyl_cape_jawa, Lee David Chung Lin, Leucippus, hardmath
add a comment |
$begingroup$
Not sure what to add here. I responded to hardmath in TN e Peter. If you feel it doesn't generate discussion I will rethink the question and read the purpose of your platform and try to reform the question.
Given that there is interest in a prime producing polynomial, is a sequential non-prime producing polynomial whose gaps in the range are all the primes just as important?
Thank you
algebraic-number-theory
asked Mar 12 at 20:30
InkInk
142
New contributor
Ink is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
closed as off-topic by Eevee Trainer, Vinyl_cape_jawa, Lee David Chung Lin, Leucippus, hardmath Mar 13 at 2:27
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, Vinyl_cape_jawa, Lee David Chung Lin, Leucippus, hardmath
2
$begingroup$
Can you elaborate more and give an example?
$endgroup$
– user
Mar 12 at 20:49
$begingroup$
Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For equations, please use MathJax.
$endgroup$
– dantopa
Mar 13 at 1:41
$begingroup$
It is unclear what "gaps in the range" means for a general polynomial. Discussion of "a prime producing polynomial" often involves multiple variables, so Readers may be unclear whether that is the notion of polynomial you intend to explore.
$endgroup$
– hardmath
Mar 13 at 2:26
$begingroup$
It is more than a one variable polynomial. The range is produced such that only prime elements are missing in the the natural number set. The image of A to B leaves the primes as the outputs differ in that the unproduced values by the polynomial from an original function that creates all odd natural numbers are the primes
$endgroup$
– Ink
Mar 13 at 5:51
add a comment |
$begingroup$
Not sure what to add here. I responded to hardmath in TN e Peter. If you feel it doesn't generate discussion I will rethink the question and read the purpose of your platform and try to reform the question.
Given that there is interest in a prime producing polynomial, is a sequential non-prime producing polynomial whose gaps in the range are all the primes just as important?
Thank you
algebraic-number-theory
asked Mar 12 at 20:30
InkInk
142
New contributor
Ink is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Not sure what to add here. I responded to hardmath in TN e Peter. If you feel it doesn't generate discussion I will rethink the question and read the purpose of your platform and try to reform the question.
Given that there is interest in a prime producing polynomial, is a sequential non-prime producing polynomial whose gaps in the range are all the primes just as important?
Thank you
algebraic-number-theory
algebraic-number-theory
asked Mar 12 at 20:30
InkInk
142
New contributor
Ink is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 12 at 20:30
InkInk
142
New contributor
Ink is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Mar 13 at 7:11
Ink
asked Mar 12 at 20:30
InkInk
142
New contributor
Ink is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 12 at 20:30
InkInk
142
asked Mar 12 at 20:30
InkInk
142
142
New contributor
Ink is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Ink is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Ink is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
closed as off-topic by Eevee Trainer, Vinyl_cape_jawa, Lee David Chung Lin, Leucippus, hardmath Mar 13 at 2:27
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, Vinyl_cape_jawa, Lee David Chung Lin, Leucippus, hardmath
closed as off-topic by Eevee Trainer, Vinyl_cape_jawa, Lee David Chung Lin, Leucippus, hardmath Mar 13 at 2:27
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, Vinyl_cape_jawa, Lee David Chung Lin, Leucippus, hardmath
2
$begingroup$
Can you elaborate more and give an example?
$endgroup$
– user
Mar 12 at 20:49
$begingroup$
Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For equations, please use MathJax.
$endgroup$
– dantopa
Mar 13 at 1:41
$begingroup$
It is unclear what "gaps in the range" means for a general polynomial. Discussion of "a prime producing polynomial" often involves multiple variables, so Readers may be unclear whether that is the notion of polynomial you intend to explore.
$endgroup$
– hardmath
Mar 13 at 2:26
$begingroup$
It is more than a one variable polynomial. The range is produced such that only prime elements are missing in the the natural number set. The image of A to B leaves the primes as the outputs differ in that the unproduced values by the polynomial from an original function that creates all odd natural numbers are the primes
$endgroup$
– Ink
Mar 13 at 5:51
add a comment |
2
$begingroup$
Can you elaborate more and give an example?
$endgroup$
– user
Mar 12 at 20:49
$begingroup$
Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For equations, please use MathJax.
$endgroup$
– dantopa
Mar 13 at 1:41
$begingroup$
It is unclear what "gaps in the range" means for a general polynomial. Discussion of "a prime producing polynomial" often involves multiple variables, so Readers may be unclear whether that is the notion of polynomial you intend to explore.
$endgroup$
– hardmath
Mar 13 at 2:26
$begingroup$
It is more than a one variable polynomial. The range is produced such that only prime elements are missing in the the natural number set. The image of A to B leaves the primes as the outputs differ in that the unproduced values by the polynomial from an original function that creates all odd natural numbers are the primes
$endgroup$
– Ink
Mar 13 at 5:51
2
2
$begingroup$
Can you elaborate more and give an example?
$endgroup$
– user
Mar 12 at 20:49
$begingroup$
Can you elaborate more and give an example?
$endgroup$
– user
Mar 12 at 20:49
$begingroup$
Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For equations, please use MathJax.
$endgroup$
– dantopa
Mar 13 at 1:41
$begingroup$
Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For equations, please use MathJax.
$endgroup$
– dantopa
Mar 13 at 1:41
$begingroup$
It is unclear what "gaps in the range" means for a general polynomial. Discussion of "a prime producing polynomial" often involves multiple variables, so Readers may be unclear whether that is the notion of polynomial you intend to explore.
$endgroup$
– hardmath
Mar 13 at 2:26
$begingroup$
It is unclear what "gaps in the range" means for a general polynomial. Discussion of "a prime producing polynomial" often involves multiple variables, so Readers may be unclear whether that is the notion of polynomial you intend to explore.
$endgroup$
– hardmath
Mar 13 at 2:26
$begingroup$
It is more than a one variable polynomial. The range is produced such that only prime elements are missing in the the natural number set. The image of A to B leaves the primes as the outputs differ in that the unproduced values by the polynomial from an original function that creates all odd natural numbers are the primes
$endgroup$
– Ink
Mar 13 at 5:51
$begingroup$
It is more than a one variable polynomial. The range is produced such that only prime elements are missing in the the natural number set. The image of A to B leaves the primes as the outputs differ in that the unproduced values by the polynomial from an original function that creates all odd natural numbers are the primes
$endgroup$
– Ink
Mar 13 at 5:51
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Such a polynomial would not have the same importance. Suppose, we have a polynomial only generating primes (an example is known for which every positive value is a prime). Then, if we find a value (in the case of the known polynomial a positive value), then we know that this value must be a prime number. In principle very useful !
Now, suppose, we have a polynomial only generating composite values. Now to show that a number is prime with this polynomial, we would have to show that the polynomial cannot have this value, which will not be possible in general.
answered Mar 12 at 21:48
PeterPeter
48.8k1139136
$endgroup$
$begingroup$
Thank you for the response. To show no primes are produced you just need to prove the definition of a prime, N, factors only 1 and itself, is not met in the possible output range.
$endgroup$
– Ink
Mar 13 at 7:00
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Such a polynomial would not have the same importance. Suppose, we have a polynomial only generating primes (an example is known for which every positive value is a prime). Then, if we find a value (in the case of the known polynomial a positive value), then we know that this value must be a prime number. In principle very useful !
Now, suppose, we have a polynomial only generating composite values. Now to show that a number is prime with this polynomial, we would have to show that the polynomial cannot have this value, which will not be possible in general.
answered Mar 12 at 21:48
PeterPeter
48.8k1139136
$endgroup$
$begingroup$
Thank you for the response. To show no primes are produced you just need to prove the definition of a prime, N, factors only 1 and itself, is not met in the possible output range.
$endgroup$
– Ink
Mar 13 at 7:00
add a comment |
$begingroup$
Such a polynomial would not have the same importance. Suppose, we have a polynomial only generating primes (an example is known for which every positive value is a prime). Then, if we find a value (in the case of the known polynomial a positive value), then we know that this value must be a prime number. In principle very useful !
Now, suppose, we have a polynomial only generating composite values. Now to show that a number is prime with this polynomial, we would have to show that the polynomial cannot have this value, which will not be possible in general.
answered Mar 12 at 21:48
PeterPeter
48.8k1139136
$endgroup$
$begingroup$
Thank you for the response. To show no primes are produced you just need to prove the definition of a prime, N, factors only 1 and itself, is not met in the possible output range.
$endgroup$
– Ink
Mar 13 at 7:00
add a comment |
$begingroup$
Such a polynomial would not have the same importance. Suppose, we have a polynomial only generating primes (an example is known for which every positive value is a prime). Then, if we find a value (in the case of the known polynomial a positive value), then we know that this value must be a prime number. In principle very useful !
Now, suppose, we have a polynomial only generating composite values. Now to show that a number is prime with this polynomial, we would have to show that the polynomial cannot have this value, which will not be possible in general.
answered Mar 12 at 21:48
PeterPeter
48.8k1139136
$endgroup$
Such a polynomial would not have the same importance. Suppose, we have a polynomial only generating primes (an example is known for which every positive value is a prime). Then, if we find a value (in the case of the known polynomial a positive value), then we know that this value must be a prime number. In principle very useful !
Now, suppose, we have a polynomial only generating composite values. Now to show that a number is prime with this polynomial, we would have to show that the polynomial cannot have this value, which will not be possible in general.
answered Mar 12 at 21:48
PeterPeter
48.8k1139136
answered Mar 12 at 21:48
PeterPeter
48.8k1139136
answered Mar 12 at 21:48
PeterPeter
48.8k1139136
answered Mar 12 at 21:48
PeterPeter
48.8k1139136
48.8k1139136
$begingroup$
Thank you for the response. To show no primes are produced you just need to prove the definition of a prime, N, factors only 1 and itself, is not met in the possible output range.
$endgroup$
– Ink
Mar 13 at 7:00
add a comment |
$begingroup$
Thank you for the response. To show no primes are produced you just need to prove the definition of a prime, N, factors only 1 and itself, is not met in the possible output range.
$endgroup$
– Ink
Mar 13 at 7:00
$begingroup$
Thank you for the response. To show no primes are produced you just need to prove the definition of a prime, N, factors only 1 and itself, is not met in the possible output range.
$endgroup$
– Ink
Mar 13 at 7:00
$begingroup$
Thank you for the response. To show no primes are produced you just need to prove the definition of a prime, N, factors only 1 and itself, is not met in the possible output range.
$endgroup$
– Ink
Mar 13 at 7:00
add a comment |
2
$begingroup$
Can you elaborate more and give an example?
$endgroup$
– user
Mar 12 at 20:49
$begingroup$
Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For equations, please use MathJax.
$endgroup$
– dantopa
Mar 13 at 1:41
$begingroup$
It is unclear what "gaps in the range" means for a general polynomial. Discussion of "a prime producing polynomial" often involves multiple variables, so Readers may be unclear whether that is the notion of polynomial you intend to explore.
$endgroup$
– hardmath
Mar 13 at 2:26
$begingroup$
It is more than a one variable polynomial. The range is produced such that only prime elements are missing in the the natural number set. The image of A to B leaves the primes as the outputs differ in that the unproduced values by the polynomial from an original function that creates all odd natural numbers are the primes
$endgroup$
– Ink
Mar 13 at 5:51