From cnn: For many people, prime numbers have faded into the background since distant grade school days. However, for Luke Durant, a 36-year-old former Nvidia programmer, prime numbers became an all-consuming passion. He devoted nearly one year and invested a considerable sum of his own money to uncover the world’s largest known prime number. A prime number is a whole number that can only be divided by 1 and itself, such as 2, 3, 5 and 7. Durant’s remarkable discovery, officially called M136279841, consists of an astounding 41,024,320 digits and marks the first prime breakthrough in almost six years. 

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Durant’s feat is notable as the first of its kind uncovered through graphics processing units, or GPUs, according to GIMPS. GPUs are known for performing mathematical equations at high speeds and processing many pieces of data simultaneously; they are in everyday devices such as smartphones or laptops, rendering high-quality graphics or training artificial intelligence networks to process extensive amounts of information efficiently.

Unlike previous successful Mersenne prime searches that used central processing units, or CPUs, the primary component of a computer that serves as its control center to run the machine’s operating system and apps, Durant’s use of graphics processing units transformed his experience.

The professional-grade GPUs that Durant employed are known for their efficiency in handling repetitive math calculations in seconds. Durant’s supercomputer also included thousands of server GPUs, crossing 24 data center regions over 17 countries, according to a statement GIMPS released.

Woltman predicts that more primes will be discovered using GPUs in the future.

“GPUs are so good at tackling difficult number crunching compared to CPUs which are suited to a wide variety of problems,” he said. “That said, don’t count CPUs out, they will still be an important part of GIMPS and may well find the next prime number.”

Durant credits much of his success to the education he received at the Alabama School of Mathematics and Science in Mobile and its supportive environment. “My interests and technical abilities are in no small part due to my fellow students and faculty at ASMS,” he said.

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The Infinite Monkey Theorem is a famous thought experiment that states that a monkey pressing random keys on a typewriter would eventually reproduce the works of the Bard if given an infinite amount of time and/or if there were an infinite number of monkeys.

However, in the study published in the peer-reviewed journal Franklin Open, two mathematicians from Australia’s University of Technology Sydney have rejected this theorem as “misleading” within the confines of our finite universe.

They challenged it by looking at the Finite Monkeys Theorem, in which there is a finite amount of time and a finite number of monkeys. They took the assumption that the current population of around 200,000 chimpanzees would remain the same over the lifespan of the universe of one googol years (that’s 1 followed by 100 zeros). They also assumed that each chimpanzee would type one key per second for every second of the day, with each monkey having a working lifespan of just over 30 years.

Using these assumptions, the researchers calculated that among these randomly-typing monkeys, there is just a 5% chance that a word as simple as “bananas” would occur in the lifespan of one chimpanzee.

They found that a short sentence such as “I chimp, therefore I am” will “almost certainly never be produced by any currently living chimp,” study co-author and mathematician Stephen Woodcock, an associate professor at the University of Technology Sydney, told CNN on Friday. “By the time you’re at the scale of a full book, you’re billions of billions of times less likely,” he continued.

Woodcock and co-author Jay Falletta, a senior research consultant at the university, concluded in the study that, even with more chimpanzees or quicker typing, it is “not plausible” that monkey labor will ever be a viable tool for “developing written works of anything beyond the trivial.”

“Even if every atom in our known universe were its own universe on the scale of ours, we would still have pretty much no chance of ever seeing something as long as even a short book,” such as “Curious George,” which is around 1,800 words, “before the end of the universe,” Woodcock told CNN. (and he’s no chimp).

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It is only a short exchange is a rather long novel, but noteworthy – from page 134 in “A Gentleman in Moscow” by Amor Towels. It might lead you down a rabbit hole to discover if Amor is mathematically inclined. Meanwhile, here is the extract:

“Here,” he said in the tone of one chipping in. “This number is not prime.”

Nina looked up with an expression of disbelief.
“Which number?”

He laid the paper in front of her and tapped a figure circled in red.
“One thousand one hundred and seventy-three.”

“How do you know it’s not prime?”

“If a number’s individual digits sum to a number that is divisible by three, then it too is divisible by three.”

There you have it – a well known math tidbit, wrapped in a conversation in a totally non-mathematical novel. Use “Prime Numbers” in the search box for more on these fascinating numbers.

The swirls in Vincent van Gogh’s famous painting “The Starry Night” might well be from his observation of how eddies flow in a stream and, if so, he captured a piece of the math that governs our universe? The dappled starlight and swirling clouds of Vincent van Gogh’s painting are usually thought to reflect the artist’s tumultuous state of mind when he painted the work in 1889.

from CNN): Now, a new analysis by physicists based in China and France suggests the artist had a deep, intuitive understanding of the mathematical structure of turbulent flow.

As a common natural phenomenon observed in fluids — moving water, ocean currents, blood flow, billowing storm clouds and plumes of smoke — turbulent flow is chaotic, as larger swirls or eddies, form and break down into smaller ones.

It may appear random to the casual observer, but turbulence nonetheless follows a cascading pattern that can be studied and, at least partially, explained using mathematical equations.

“Imagine you are standing on a bridge, and you watch the river flow. You will see swirls on the surface, and these swirls are not random. They arrange themselves in specific patterns, and these kinds of patterns can be predicted by physical laws,” said Yongxiang Huang, lead author of the study that published Tuesday in the scientific journal Physics of Fluids. Huang is a researcher at State Key Laboratory of Marine Environmental Science & College of Ocean and Earth Sciences at Xiamen University in southeastern China.

“The Starry Night” is an oil-on-canvas painting that, the study noted, depicts a view just before sunrise from the east-facing window of the artist’s asylum room at Saint-Rémy-de-Provence in southern France. Van Gogh had admitted himself to an asylum there after mutilating his left ear.

Using a digital image of the painting, Huang and his colleagues examined the scale of its 14 main whirling shapes to understand whether they aligned with physical theories that describe the transfer of energy from large- to small-scale eddies as they collide and interact with one another.

‘The Starry Night’ and turbulence theories

The atmospheric motion of the painted sky cannot be directly measured, so Huang and his colleagues precisely measured the brushstrokes and compared the size of the brushstrokes to the mathematical scales expected from turbulence theories. To gauge physical movement, they used the relative brightness or luminance of the varying paint colors.

They discovered that the sizes of the 14 whirls or eddies in “The Starry Night,” and their relative distance and intensity, follow a physical law that governs fluid dynamics known as Kolmogorov’s theory of turbulence.

Jim Willard wrote an article back in 2019 on his fascination with numbers – and it makes for nice reading too. If you love numbers too, then enjoy:

“For as long as I can remember (many decades) I have been fascinated with numbers.

I see patterns in many things. I arrange items in order, place silver in parallel and other (sometimes) annoying habits. My phone number at my former place of gainful employment was a numeric palindrome, 6792976, a rarity for that phone system.

Naturally, I was not the first. The Babylonians of Mesopotamia beat me to it by about 5,000 years.

Hanging out between the Tigris and Euphrates rivers at that time they began a numbering system.

It is one of the oldest numbering systems known.

Following in that vein, the first mathematics can be traced to Babylonia during the third millennium B.C. They used tables to help them in problem calculations.

One of their tablets — perhaps similar to one used in my high school math — dates to the period 1900 to 1600 B.C.  It contains tables of Pythagorean triples for the equation a-squared plus b-squared = c-squared.

The Babylonians developed an advanced number system, base of 60 (sexagesimal). The decimal system is what we all grew up with.

Then in my computer days I had to learn binary and hexadecimal. In analyzing core dumps — yes, that’s what we called it when the computer threw up and refused to execute the program — the dumps were in hexadecimal, 0-9 then A-F for 10 through 15.

In those Dark Ages of Computerdom this allowed me to alter core storage using addresses and 0-F, very useful to resume printing checks when the printer burped. However, I digress.

Let us return to the Greek philosopher Pythagoras (he of the theorem).

He believed that the meaning of the universe lay in numbers.

He and his pals assigned symbolic meaning to numbers. This, of course, was more mystical than mathematical but it made them feel good.

They considered all even numbers as feminine and the odd ones as masculine.

They proceeded with the Number 1 identifying with reason, God, unity and the sun (don’t ask me).

Number 2 meant divisibility, opinion, sociability and the moon.

Number 3 had many meanings while 4 stood for solidity and foundation, points of the compass, the seasons and the Evangelists.

Number 5 was associated with fire, love and marriage (an interesting combination).

The “perfect” number was 6 being the sum of 1, 2 and 3 representing Creation (accomplished in six days?).

These guys obviously had time on their hands as they considered two numbers “friendly” if each were the sum of the divisors of the other (220 and 284 for instance).

Some “real believers” bought into this to the extent that they considered some so friendly that they were positively aphrodisiac; they wrote them on digestible tablets and swallowed them. I have no data on their effectiveness.

Well, this began as a quick review of numbers and devolved into human physiology; such is the way of writing columns about trivia.

Numbers are fun so perhaps I’ll return to them.”

Answer is in Post Support – More on Rubik here

The official Rubik Cube website

From cnn: Scientists from Oxford University’s physics department have developed a micro-thin, light-absorbing material flexible enough to apply to the surface of almost any building or object — with the potential to generate up to nearly twice the amount of energy of current solar panels.

The technology comes at a critical time for the solar power boom as human-caused climate change is rapidly warming the planet, forcing the world to accelerate its transition to clean energy. Here’s how it works: The solar coating is made of materials called perovskites, which are more efficient at absorbing the sun’s energy than the silicon-based panels widely used today. That because its light-absorbing layers can capture a wider range of light from the sun’s spectrum than traditional panels. And more light means more energy.

The Oxford scientists aren’t the only ones who have produced this type of coating, but theirs is notably efficient, capturing around 27% of the energy in sunlight. Today’s solar panels that use silicon cells, by comparison, typically covert up to 22% of sunlight into power.

The researchers believe that over time, perovskites will be able to deliver efficiency exceeding 45%, pointing to the increase in yield they were able to achieve during just five years of experimenting, from 6% to 27%.

Subash Chandar has been awarded the National Excellence in Education Award (NZ) for his inspiring work as a Mathematics and Statistics teacher. You can check out his youtube channel here at ‘infinityplusone’:

https://www.youtube.com/@infinityplusone

An interesting article from the BBC, written by Kit Yates, Director of the Centre for Mathematical Biology at the University of Bath and the author of The Maths of Life and Death, and How to Expect the Unexpected