Integer partitions detect the primes

A remarkable new paper:

Integer partitions detect the primes, by William Craig, Jan-Willem van Ittersum, Ken Ono

https://arxiv.org/abs/2405.06451

Florian Richter: Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative actions

Topic: Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative actions 

Speaker: Florian Richter, Northwestern University

June 4, 2020

Peter Sarnak on Möbius Disjointness

The Patterns in the Primes, with Andrew Granville

 

The Search for Randomness | Jean Bourgain

 

More teaching chalkboards

Chinese Remainder Theorem...

Number theory and cryptography class - chalkboard pictures

Today, the topic was the Euclidean algorithm...

Just before erasing this number theoretic Tibetan mandala :)

Mobius Randomness and Dynamics - Peter Sarnak

First group of 6 consecutive integers with exactly 6 prime factors each

 

My Top 100 book as a jazz of numbers

Sequential Experiments with Primes got into the 100 Best Number Theory Books of All Time @ https://bookauthority.org/books/best-number-theory-books As an undergraduate college faculty member, I am happy. Thank you! :-)

I believe the attractiveness of the book lies not only on the novelty of certain ideas, but also in the style in which said novelty is attained. It's a sort of "jazz" with numbers (unfolding as a sustained creative piece not unlike the free development of a jazz gig).  A jazz with no particular rigid/studied reverence to other established theoretical approaches. Just free self-sustained jazz discovering new facts. In its way, it's structured as a sort of "dessins d'enfants" leading to a different look on the mystery of prime numbers.

Sequential Experiments with Primes - SpringerVideos

Computer Scientists Attempt to Corner the Collatz Conjecture

Quanta Magazine: Computer Scientists Attempt to Corner the Collatz Conjecture

"A powerful technique called SAT solving could work on the notorious Collatz conjecture. But it’s a long shot."

ONU-SOLVE photo (raw class discussion leading to solving AMM 12126)

 

Stirring the pot

 

On a related note, a page on patterns with primes, with contributors including Charles W. Trigg and Martin Gardner:

PRIME PATTERNS

All primes in terms of one: non-associative algebra and Google cloud computing

Under addition, the positive integers 1, 1+1, 1+1+1,.... form a cyclic (semigroup) structure generated by 1. We will explore a way of representing prime numbers in terms of the single generator g = 2, under a non-associative, non-commutative binary operation "o" on the set A of all primes, defined by setting x o y:=P(2x+y) where P is the greatest prime factor function. For example, 3 = 2 o 2, 5 = 2 o (2 o (2 o (2 o 2)))), etc. In a joint work with Paul A. Vicol from Simon Fraser University, we managed to verify that all primes up to 7259167 can be expressed as non-associative products involving the symbols 2, o, and parentheses ),(. This computational evidence points towards a cyclicity conjecture for the (magma) structure (A, o). Moreover, we searched for other similar non-associative algebraic structures on A (prime magmas) that might be cyclic, established a set of fairly restrictive necessary conditions for cyclicity, formulated a more general cyclicity conjecture for special prime magmas, and found computational evidence (after days of running Julia programs on a GCE platform) for the cyclicity of the structures in a representative set. (October 24, 2014 - MAA Ohio Fall Meeting)

The Singular Mind of Terry Tao

The Singular Mind of Terry Tao 
A prodigy grows up to become one of the greatest mathematicians in the world. 
New York Times
By GARETH COOK, July 24, 2015

Mihai Raileanu - o amintire

De fapt una dintre multele amintiri ce nu se pot sterge. M-a introdus in lumea congruentelor si a lucrului cu 'numere mari'. In stilul problemelor ce le primeam la inceput de clasa a IX-a, sa se afle toate numerele naturale N astfel incat 1249^N  ≡ 1948441249 (mod 311920921441)...

OEIS - The Movie!

N. J. A. Sloane Article

'On Ducci Sequences with Primes' - Fibonacci Quarterly

http://www.fq.math.ca/Abstracts/52-1/caragiu.pdf
Mihai Caragiu, Alexandru Zaharescu, and Mohammad Zaki 
On Ducci Sequences with Primes 
Fibonacci Quart. 52 (2014), no. 1, 32-38.

An analogue of the Proth-Gilbreath conjecture (new paper)

O fenomenologie a numerelor prime - in gen fantasy cu demonstratii plus "experiment" (computer).

Far East Journal of Mathematical Sciences (FJMS)

Volume 81, Issue 1, Pages 1 - 12 (October 2013)
AN ANALOGUE OF THE PROTH-GILBREATH CONJECTURE 
Mihai Caragiu, Alexandru Zaharescu and Mohammad Zaki
Communicated by Juliusz Brzezinski