Ellipses and hyperbolas of decompositions of even numbers into pairs of prime numbers
<|begin_of_text|><|start_header_id|>system<|end_header_id|> You are a research archivist expert in dataset metadata. Answer the question truthfully.  <|eot_id|><|start_header_id|>user<|end_header_id|> Here is the Description of a dataset. Description:'This is just an attempt to associate sums or differences of prime numbers with points lying on an ellipse or hyperbola.Certain pairs of prime numbers can be represented as radius-distances from the focuses to points lying either on the ellipse or on the hyperbola.The ellipse equation can be written in the following form: |p(k)| + |p(t)| = 2n.The hyperbola equation can be written in the following form: ||p(k)| - |p(t)|| = 2n.Here p(k) and p(t) are prime numbers (p(1) = 2, p(2) = 3, p(3) = 5, p(4) = 7,...),k and t are indices of prime numbers,2n is a given even number,k, t, n ∈ N.If we construct ellipses and hyperbolas based on the above, we get the following:1) there are only 5 non-intersecting curves (for 2n=4; 2n=6; 2n=8; 2n=10; 2n=16). The remaining ellipses have intersection points.2) there is only 1 non-intersecting hyperb' . Please return only a json list of at most 3 Keywords corresponding to the Description:.<|eot_id|><|start_header_id|>assistant<|end_header_id|> {"Answer" : ["number,  numbers, theory, prime, primes, decomposition, geometric, analytical"]} <|eot_id|>
 Here is the Description of a dataset. Description:'This is just an attempt to associate sums or differences of prime numbers with points lying on an ellipse or hyperbola.Certain pairs of prime numbers can be represented as radius-distances from the focuses to points lying either on the ellipse or on the hyperbola.The ellipse equation can be written in the following form: |p(k)| + |p(t)| = 2n.The hyperbola equation can be written in the following form: ||p(k)| - |p(t)|| = 2n.Here p(k) and p(t) are prime numbers (p(1) = 2, p(2) = 3, p(3) = 5, p(4) = 7,...),k and t are indices of prime numbers,2n is a given even number,k, t, n ∈ N.If we construct ellipses and hyperbolas based on the above, we get the following:1) there are only 5 non-intersecting curves (for 2n=4; 2n=6; 2n=8; 2n=10; 2n=16). The remaining ellipses have intersection points.2) there is only 1 non-intersecting hyperb' . Please return only a json list of at most 3 Keywords corresponding to the Description:.
This is just an attempt to associate sums or differences of prime numbers with points lying on an ellipse or hyperbola.Certain pairs of prime numbers can be represented as radius-distances from the focuses to points lying either on the ellipse or on the hyperbola.The ellipse equation can be written in the following form: |p(k)| + |p(t)| = 2n.The hyperbola equation can be written in the following form: ||p(k)| - |p(t)|| = 2n.Here p(k) and p(t) are prime numbers (p(1) = 2, p(2) = 3, p(3) = 5, p(4) = 7,...),k and t are indices of prime numbers,2n is a given even number,k, t, n ∈ N.If we construct ellipses and hyperbolas based on the above, we get the following:1) there are only 5 non-intersecting curves (for 2n=4; 2n=6; 2n=8; 2n=10; 2n=16). The remaining ellipses have intersection points.2) there is only 1 non-intersecting hyperb
number,  numbers, theory, prime, primes, decomposition, geometric, analytical