**Simon Plouffe**, Montréal, Quebec, Canada

Articles: Primes as sums of irrational numbers

ArXiv (10)

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Homepage: Hyperleap

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Second email: 17 July 2022, 5:18 PM

Dear Prof. Dr. Simon Plouffe,

We are still alive-and-well and moving slowly ahead. Is this statement about your work okay? I said, “And, Simon Plouffe has through algorithmic programming identified over 215 million constants. There is nothing in the universe not touched by dimensionless constants.”

Also, I am sure you have seen the five-tetrahedral gap that Aristotle missed.

Have you ever seen a five-octahedral gap? It seems that we all missed it.

Combined, the two make a very sweet image: https://81018.com/15-2/

I am not sure if its analogue is to a gate in circuitry or to a Zen koan!

I propose that it is the first step in a geometry of the gaps, quantum geometry, squishy geometry, imperfect geometries or even perhaps the geometry of quantum fluctuations. Your comments?

Laughter is perfectly acceptable and understandable! Speaking of perfection: https://81018.com/perfection/

By the way, I have a page on our site about you and your work: https://81018.com/plouffe/ Any changes? Just say the word. Thanks so much.

Best wishes,

Bruce

Response: March 8, 2018

**Professor Simon Plouffe responded and gave us permission to post his answer:**

“There are many answers:

- Most of the numbers are irrationals.
- Every table has a name, from a to z with 3 digits, like a008, is the 8’th table of algebraic numbers.
- There is a category of rational numbers like q001, q002.
- It is widely believed that the number gamma (euler constant) is irrational but no proof of that exist. It is the case with most of the numbers in the tables, we have no proof that they are irrationals (but most likely to be). Proofs of irrationality are tough and difficult to make.
- In other words, we don’t know much about the very nature of many mathematical constants.
- It is widely believed that most of the real numbers are transcendental: https://en.wikipedia.org/wiki/Transcendental_number

First email: Monday, Feb 19, 2018 at 11:10 PM

Dear Professor Simon Plouffe:

Our work began in December 2011 within high school geometry classes where we followed the tetrahedron-octahedron, going within, by dividing the edges in half, deeper and deeper, 112 steps to the Planck scale and then we followed it out 90 steps by multiplying by 2, to the Observable Universe. We thought it was a good STEM tool. On further consideration, the first 67 notations to the CERN-scale began to intrigue us.

A few years later, we added Planck Time to our Planck Length chart, then two years later we added Planck Charge and Planck Mass. As we studied the numbers we began to think that we lived in an exponential universe and thought Euler might be pleased. Certainly the Hawking-Guth team were not. There was a natural inflation that did not defy all logic. Then we began looking for alternatives to absolute space and time.

To say that we are a bit idiosyncratic captures some of the flavor of this work.

Now, we have discovered your work and we are celebrating. What marvelous things you have done and are doing. You’ll be teaching us a lot!

We wrote a small summary about Hilbert’s sense of the infinite and made our first reference to your 11.3 billion mathematical constants. It is below and part of our website: https://81018.com/finite-to-infinite/#3

**Are all those 215 million non-ending, non-repeating numbers?** I hope so. Thank you.

Most sincerely,

Bruce

****************

Bruce Camber

http://81018.com

Austin, Texas

**Our reference to you is highlighted.**

**Excerpt from the homepage**:

What is infinite? In 1925, the great mathematician, David Hilbert wrote, “We have already seen that the infinite is nowhere to be found in reality, no matter what experiences, observations, and knowledge are appealed to.” Many scholars would agree even today, but maybe Hilbert and those scholars are mistaken. There are many non-ending and non-repeating numbers such as pi, Euler’s equation (e), and all the other dimensionless constants. Aren’t these numbers evidence or a manifestation of the infinite within the finite?

Yes, I believe access to the infinite is found in the primary dimensionless constants where the number being generated does not end and does not repeat. There are 26-to-31 such numbers that have been associated by John Baez and Frank Wilczek-and-others to be necessarily part of the definition of the Standard Model of Particle Physics. There are over another 300 such numbers defined by the National Institute for Standards and Technology (NIST). All are dimensionless constants that seemingly never-end and never-repeat. And, then there is Simon Plouffe; he has identified, through algorithmic programming, 215 million mathematical constants (as of August 2017) which includes pi, Euler’s number, and more. This use of “never-ending, never-repeating” as the entry to the infinite will be challenged. If it can be defended, then there are more connections between the finite and infinite than David Hilbert and most scholars had ever anticipated. *More…*