Riemann Hypothesis & Ulam's Spiral: Patterns & Relations

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In summary, the conversation discusses the similarities between Riemann hypothesis and Ulam's spiral, both of which demonstrate patterns within prime numbers. However, it is clarified that there is no known relation between the two and that any straight line on Ulam's spiral is simply a quadratic equation. The conversation also touches on the concept of number theory and the idea of searching for solutions in a limited space.
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Damidami
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Both Riemann hypothesis and Ulam's spiral (and http://en.wikipedia.org/wiki/Sacks_spiral" [Broken]) show some patterns emerge from the prime numbers.

I was wondering if there is some know relation between them, for example, if the RH is proven true does that imply something on Ulam's spiral?
 
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No. ANY straight line on such a spiral is simply a quadratic equation. Plot random numbers on Ulam's spiral, you'll get straight lines galore. They will mean nothing, of course. Don't look for the black cat in the dark room that isn't there.
 
  • #3
I think the whole point of number theory is that we're looking near the lamppost, even though we figure the black cat's in the dark room. :wink:
 

1. What is the Riemann Hypothesis?

The Riemann Hypothesis is a conjecture in mathematics that was first proposed by German mathematician Bernhard Riemann in 1859. It states that all nontrivial zeros of the Riemann zeta function, which encodes the distribution of prime numbers, lie on the critical line with a real part of 1/2.

2. Why is the Riemann Hypothesis important?

The Riemann Hypothesis is considered one of the most important unsolved problems in mathematics. It has far-reaching implications in number theory, as it would provide a better understanding of the distribution of prime numbers. It also has connections to other areas of mathematics, such as physics and computer science.

3. What is Ulam's Spiral?

Ulam's Spiral is a visual representation of the distribution of prime numbers on a two-dimensional plane. It was discovered by mathematician Stanislaw Ulam in 1963 and is created by plotting the natural numbers in a spiral pattern and highlighting the prime numbers. The spiral exhibits certain patterns and symmetries that have intrigued mathematicians for decades.

4. What is the relationship between the Riemann Hypothesis and Ulam's Spiral?

The Riemann Hypothesis and Ulam's Spiral are connected through the prime numbers. The Riemann Hypothesis is a conjecture about the distribution of prime numbers, while Ulam's Spiral is a visual representation of that distribution. Some mathematicians have proposed that the patterns and symmetries observed in Ulam's Spiral could provide insights into the truth of the Riemann Hypothesis.

5. Has the Riemann Hypothesis been proven?

No, the Riemann Hypothesis has not been proven, despite numerous attempts by mathematicians over the past 160 years. It remains one of the most famous unsolved problems in mathematics, and its proof would have a significant impact on the field. However, in recent years, there have been some breakthroughs and progress made towards solving the Riemann Hypothesis, giving hope that it may one day be proven.

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