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#primenumbers

3 posts1 participant0 posts today
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ƧƿѦςɛ♏ѦਹѤʞ

@thepdog
P is a prime number greater than 3.
P^2 – 1 = (p – 1)(p + 1).
Since 3 must divide one of any three consecutive numbers, 3 must divide (p – 1), p or (p + 1).
It can’t divide p, so it must divide either (p – 1) or (p + 1).
But p = 2k + 1 for some k.
Hence (p – 1)(p + 1) = (2k)(2k + 2) = 4k(k + 1).
Therefore 4 divides p^2 – 1.
So, either k or k + 1 must itself be divisible by 2, meaning 8 divides p^2 – 1.
As 8 and 3 are relatively prime, 3x8 = 24 divides p^2 – 1.
#maths #PrimeNumbers

Continued thread
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MOULE

Update: New record! After appending random digit after random digit for two days, it eventually found this 31689-digit prime. It's larger than the 148091th number in the Fibonacci sequence, which is also prime.

The tiny white digits on the black background look like TV static when zoomed out!

Screenshot of the 31689-digit prime number in its entirety. The white digits on the black background are so numerous it appears like TV static when zoomed out.
#Math#Mathematics#PrimeNumbers
Continued thread
Public
MOULE

Update: overnight it found a 17828-digit prime number, a new personal best!

I can see why most primes found are found with easy-to-write formulae like (2^p)-1 or (k^2^n)+1. Ttrying to go backwards – coming up with a compact formula to represent a really huge prime made up of random digits like this one, is really tricky.

Screenshot of the 17828-digit prime number in its entirety. The white digits on the black background are so numerous it appears like a grey rectangle when zoomed out.
#Math#Mathematics#PrimeNumbers
Public
MOULE

Just for fun, I wrote a Python program to start with a random decimal digit, and keep adding the decimal digit until it reaches a prime number.

I'm excited to share it's found a 10997-digit long prime number, which is my new personal best largest prime! It's larger than the 37th factorial prime (3507!-1) which is 10912 digits.

I'll leave the program running overnight to see if it can find longer ones! :MOULE_Happy:

Screenshot of the 10997-digit prime number in its entirety. The white digits on the black background are so numerous it appears like a grey rectangle when zoomed out.
#Math#Mathematics#PrimeNumbers
Public
Tariq

in 2020 I started to write what I was learning about #primenumbers .. with the aim of reaching the foothills of the #RiemannHypothesis.

That is, at least understanding what the question was.

I learned about unique factorisation, the logarithmic distribution, Euler's product, twin primes, Goldbach conjecture, ...

A year later I paused the project as I needed to learn more maths.

youtube.com/watch?v=Ln6vWyQ4p3k

I'll be returning to it - writing more, doing more videos

fromprimestoriemann.blogspot.c

YouTube11a - Rotating Extended Riemann Zeta FunctionBy Primes To Riemann
#maths
Public
Soh Kam Yung

Easy to recite prime numbers. 🙂

"The number 12,345,678,910,987,654,321 is indeed prime. It consists of 20 digits and is really easy to remember: count to 10 and then count backward again until you get to 1. But it has been unclear whether other primes take the palindromic form of starting at 1, ascending to the number n and then descending again."

scientificamerican.com/article

Scientific American · These Prime Numbers Are So Memorable That People Hunt for ThemBy Manon Bischoff
#Mathematics#Numbers#PrimeNumbers
Public
Hari Tulsidas

A sensational proof has unveiled fresh insights into the mysterious world of prime numbers—the building blocks of mathematics. This breakthrough sheds light on patterns in primes, a question that has fascinated mathematicians for centuries. Could this discovery lead to cryptography, computing, or number theory advances? #Mathematics #PrimeNumbers #Innovation
quantamagazine.org/sensational

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