This article was written is a reflective mode after visiting the Grand Pyramid of Giza on January 02, 2025. Prime numbers and pyramid constructions are poles apart, yet an effort is made to build a bridge over them. In life, a bridge is only known for its one of the longest spans.

Let me first demystify the title of this reflection as I do not want to turn off any one of my loyal readers. The word ‘Primes’ in the title is obviously the plural of ‘Prime’. The mathematical meaning of primes refers to those natural numbers (1, 2, 3, 4 ……….), which have only two different divisors -1 and the number itself. Under this definition, 1 is not a prime! Thus, primes are individually and theoretically understood. (Googlable for more information)

The word ‘Pyramids’ in the title is generally well understood by everyone: a structure having four triangular faces jutting out from the four base lines of a square foundation. The top vertices meet at a point, the highest point of a pyramid. However, ‘pyramids’ in the title refers only to the large pyramids of Egypt. Yes, small pyramids have been built by many ancient civilizations. My focus is on the Egyptian pyramids - especially on the Grand Pyramid (GP) of Giza. The reasons: I saw it, touched it, and overly felt it for the first time in my life - thus fulfilling a desire since boyhood. This happened only two days ago - during an Egypt sightseeing tour that I am currently undertaking in a travel group. Here are some of the questions that have cropped up in my interdisciplinary mind:

1. The rudimentary knowledge of primes and structural knowledge of pyramids are a part of our human DNA. Anyone claiming to have known them first has a myopic outlook.

2. There is no question of discovering a prime - they are there on the landscape of human minds (I have no idea about the minds of other entities though). Yes, one may undertake a research project of discovering and unearthing pyramids in a specific geographical region. Archaeological research is relatively very expensive, and complex due to regulations of a nation.

3. A conjugate question to the #2 above is about their largeness. In the case of pyramids, a specific pyramid is the largest as long as a larger one is not built. In fact, irrespective of the material resources, there is a limit to the number of pyramids that can be built on the Earth. Anyways, the GP of Giza (on the outskirts of Cairo) has been a winner in this category for a few millennia. This tells a lot about it.

The story of primes is very different. It is proven that the number of primes cannot be finite - they are infinitely many. However, finding the largest prime is very complicated - though probably not that challenging as compared to building a pyramid bigger than the GP. It requires both mathematical skill and the power of a supercomputer. (Googlable)

1. Usefulness. Large primes have far flung applications in high-level security codes - about which the general public has no clue (Googlable). I have heard of some esoteric properties of pyramids, but homes are never built in the form of pyramids. On the other hand, primes are the building blocks of all natural numbers. (Unique Factorization)

2. The ordered listing of primes looks like: 2, 3, 5, 7, 11, 13,……. One of the numerous questions involving primes is the Goldbach Conjecture, which simply states: every even number (divisible by 2) greater than 2 is the sum of two primes (not necessarily different; a few examples are the following: 4 = 2 + 2; 10 = 5 + 5 = 7 + 3, so on). This conjecture is nearly 300 years old - though still unproven. It has not been disproven either by finding an even number that is not the sum of two primes. However, it has been verified to be true for many even numbers. But verification of a statement is no proof in the world of mathematics! However, verification of physical principles works all the time in science.
3. In the context of the GP, the questions of who, why and how have been raised. The answers are murky. Since the 18th century, the colonization and/or occupation of this land, had given rise to a new discipline of Egyptology, which subsequently emerged in large universities of many affluent countries of the West. In the context of my research interest, I don’t care about the names of the dynasties of ancient Egyptian kings (called pharaohs), who financed this pyramid in various stages. Likewise, their motivation for its expansion is not of much interest either.

Sidebar. The bottom line of human ambition is to stay in political power, no matter what the political system is - a lesson of history. Moreover, the rulers want the political power to stay in the family modulo fratricidal wars, intrigues, and coups. It seems pharaohs went a few steps further in ensuring their rulership in their next births and other worlds. It was because of their strong belief in reincarnation.

A. For me, the most pertinent question is as to how the GP was built (engineering aspect). To the best of my knowledge, no one has been able to figure it out (Googlable). There are all sorts of guesses. In mathematics, they are considered wrong proofs. Yes, a few mathematicians too have announced proofs of the Goldbach Conjecture, but they all have been found wrong after careful scrutiny.

B. Aliens built the GP. Of course, this is absurd. Nevertheless, it tells that its architecture and engineering are of a high level of ingenuity.

C. Thousands of slaves built it. This suggestion reminds me of an elementary math problem - say, one cook can prepare a dish in 60 minutes. How long would it take for 60 cooks to prepare the same dish? One minute is correct. But can one figure out the logistics of 60 persons standing in a kitchen- forget about working on a dish.

D. There are several videos showing failure after failure of building a pyramid, even one-third the size of the GP.

E. A general misconception about a pyramid is the hollowness of its interior. But it is not fully solid either. According to one estimate, 2.3 million blocks of stones, each weighing 2.5-15 tons, have been placed precisely to build the GP alone. Egyptian pyramids have withstood every fury of nature and vandalism of man for 4000 years. They are the ultimate man-made wonders in the world.

F. Just like an MRI or CT-Scan can look at any interior part of the human body, the latest technology has been developed that can scan the interiors of solids too - including pyramids to a certain depth or distance. The GP has all kinds of rooms filled with objects, and perhaps it has miles of labyrinths. (Googlable). How were they placed there in the first place?

G. In order to have some perspective of its interior, I crawled double down for 10 minutes, but at the end stood up inside a room, 20’x12’x15’, which had an emptied out stone coffin. Walking back to the same exit/entrance was so challenging that the stiffness in my upper thighs didn’t leave until three days after. Of course, during this short excursion, I noted two other pathways branching away.

H. The pyramids must be serving other purposes besides housing tombs of the royalties. That’s my conjecture.

G. The pyramids are perfect examples that repudiate the far-fetched generalization of the 1859 findings of Charles Darwin (1809 - 1882). They were based upon his long-term biological-geological experiments, which became the bases of his Theory of Evolution. Human curiosity, intelligence and stupidity are constant. I tell my students to be open to this non-linear thinking. Darwinian thinking is linear. There is absolutely no such thing as the human race becoming more intelligent with the passage of time.

I. There must have been architectural maps and engineering designs of the GP needed and used during its planning, construction, expansion, and maintenance. They must have been saved in a chamber of the GP. If stored in the ancient library of Alexandria, then they might have been destroyed by the Mighty Time or during its holocaust twice perpetrated by the Arab invaders of Egypt. Anyways, finding some blueprints of the GP is also an ongoing research problem.

That is enough on the Grand Pyramid of Cairo (Egypt) and Goldbach (German) Conjecture for the time being.