- #1
Playdo
- 88
- 0
What is the value of the simple continued fraction [1;2,3,5,7,11,13,...,nth prime] as n goes to infinity?
What is the value of this infinite continued fraction?
- Context: Graduate
- Thread starter Playdo
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- Fraction
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SUMMARY
The value of the infinite continued fraction [1;2,3,5,7,11,13,...,nth prime] converges as n approaches infinity, but it cannot be expressed in a simpler form. Calculations can yield results to numerous decimal places, confirming the complexity of this constant. The discussion emphasizes the importance of verifying any discovered patterns with the original poster before sharing them publicly.
PREREQUISITES- Understanding of continued fractions
- Familiarity with prime numbers and their sequence
- Basic knowledge of numerical computation techniques
- Experience with mathematical convergence concepts
- Research the properties of continued fractions in number theory
- Explore numerical methods for calculating continued fractions
- Investigate the distribution of prime numbers and their significance
- Learn about mathematical constants and their representations
Mathematicians, number theorists, and anyone interested in advanced mathematical concepts related to continued fractions and prime number sequences.
- #2
g_edgar
- 606
- 0
You can compute it to as many decimals as you like. There is absolutely no reason to think this constant can be written in any simpler way.
- #3
The Chaz
- 206
- 0
g_edgar said:
...but if you find a pattern, you'd better run it by my before telling anyone else!
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