A new study shows that next prime can be predicted.

Huge breakthrough in prime number theory— study from City University of Hong demonstrates primes can be predicted
Revolutionary breakthrough in prime number theory: according to new study from City University of Hong, primes can be predicted. Credit: City University of Hong Kong

Both arithmetic aficionados and the mathematically challenged will be equally captivated by new research that upends hundreds of years of popular belief about prime numbers.


Contrary to what just about every mathematician on Earth will tell you, prime numbers can be predicted, according to researchers at City University of Hong Kong (CityUHK) and North Carolina State University, U.S.

The research team comprises Han-Lin Li, Shu-Cherng Fang, and Way Kuo. Fang is the Walter Clark Chair Professor of Industrial and Systems Engineering at North Carolina State University. Kuo is a Senior Fellow at the Hong Kong Institute for Advanced Study, CityU.

This is a genuinely revolutionary development in prime number theory, says Way Kuo, who is working on the project alongside researchers from the U.S. The team leader is Han-Lin Li, a Visiting Professor in the Department of Computer Science at CityUHK.

We have known for millennia that an infinite number of prime numbers, i.e., 2, 3, 5, 7, 11, etc., can be divided by themselves and the number 1 only. But until now, we have not been able to predict where the next prime will pop up in a sequence of numbers. In fact, mathematicians have generally agreed that prime numbers are like weeds: they seem just to shoot out randomly.

"But our team has devised a way to predict accurately and swiftly when prime numbers will appear," adds Kuo.

The technical aspects of the research are daunting for all but a handful of mathematicians worldwide. In a nutshell, the outcome of the team's research is a handy periodic table of primes, or the PTP, pointing the locations of prime numbers. The research is available as a working paper in the SSRN Electronic Journal

Source= https://phys.org/news/2024-04-breakthrough-prime-theory-primes.html

This was announced yesterday and in time there will be more discoveries regarding the predictability of random processes.

A mathematician who developed formulas to make random processes more predictable and helped to solve an iconic model of complex phenomena has won the 2024 Abel Prize, one of the field’s most coveted awards. Michel Talagrand received the prize for his “contributions to probability theory and functional analysis, with outstanding applications in mathematical physics and statistics,” the Norwegian Academy of Science and Letters in Oslo announced on 20 March.

Assaf Naor, a mathematician at Princeton University in New Jersey, says it is difficult to overestimate the impact of Talagrand’s work. “There are papers posted maybe on a daily basis where the punchline is ‘now we use Talagrand’s inequalities’,” he says.

Thanks to Talagrand’s techniques, “many things that seem complicated and random turn out to be not so random,” says Naor. His estimates are extremely powerful, for example for studying problems such as optimizing the route of a delivery truck. Finding a perfect solution would require an exorbitant amount of computation, so computer scientists can instead calculate the lengths of a limited number of random candidate routes and then take the average — and Talagrand’s inequalities ensure that the result is close to optimal.

Source:   https://www.scientificamerican.com/article/mathematician-who-tamed-randomness-wins-abel-prize/

I have difficulties to understand the following results, can someone explain?

I have these keys
#1=

Code:

03f4bef7834ec36e40f1c007a4c27c2f7d2ded709fda3333fdd5801625736ed152

#2=

Code:

03389523df912b20e7f5b2223f50a3e074551d3859487701d9e6297b950c9a78ea

Adding two keys gives me this one
#3=

Code:

0390823e1bb57e0b3492019544a0b3d4fcdfe51e843b417becd3d3285c9c154d0d
Private_key= 
0x000000000000000000000000000000000000000000000200ddfe92f46681b20a

If I subtract #2 from #1, we'd have this
#4=

Code:

032b0d9abd02f210631ca0fdf138a19c6725f6b67f2dba6c22bf181c73e81abd08

Then if we subtract #4 from #3, it would give us double of #2.
But I'm going to make it much easier for you to understand by showing scalar instead of points.
We have these
#1=
0x1c16e0f93f27c98dfa5
#2=
0x3f6feeff01e9e8d265
#3=
0x200ddfe92f46681b20a
#4=
0x181fe2094f092b00d40

Everything I do with 4 keys above is related to key #3, but I can't solve any of the other 3 keys even though whatever I do always gives me correct points, where is my mistake?

Note that scalar 1, 2 and 4 result in different points than above points but they do behave similar when working with 3. Why is that?

Is it possible to plot the ECC equation on to the Mandelbrot set to explore more mathematical properties of such amazing equations? If you know of any useful sources please do let me know.
https://en.m.wikipedia.org/wiki/Mandelbrot_set