The Goldbach Conjecture and Dirichlet's Theorem

The Goldbach Conjecture says any even number greater than 2 can be written as the sum of 2 primes. 

Dirichlet's Theorem says that there are infinitely many primes of the form n*a + b, where a and b are coprime (have no factors in common) and n is any positive integer. 

Some examples:

17 + 3 = 20

2*2 + 3 = 7

2*991 + 977 = 2819 

991, 997, and 2819 are all prime, and 991 and 977 are coprime. 

Primes of arbitrary size can be made by using the conjecture and theorem together. 

I like to think of semiprimes as being rectangles made up of square blocks. To find the primes, fit the squares into square than is missing a square-shaped piece from a corner. 

Dirichlet's Theorem is the key to solving the integer factorization problem in my opinion. 

 

hard truths about publishing

https://www.psychologytoday.com/us/blog/curious/202506/the-participation-trophy-culture-of-adulthood

spirals, primes, conjectures, and theorems

I'm not sure how all these pieces fit together but it seems like they do. More on that here:

Derpetology: The Archimedes, Ulam, and Sacks Spirals, Euler's Prime Formula, and the Non-random Distribution of Prime Numbers

My country tis of thee?

Rammstein - Amerika (Official Video)

https://www.youtube.com/watch?v=Rr8ljRgcJNM

Who wore it better?

Putin - Woke Up This Morning

The tricks to becoming a charismatic leader are easy to learn. 

 

flags and the sincerest form of flattery

Great minds think alike. 

South Korea

Liberia

Malaysia 

UK

Russia

USA

Cuba

North Korea

France 

Cambodia

Thailand 

Norway

Army of Tennessee battle flag

how to support me

If you enjoy my content and live close to a Western Union, you can send me money that way. 

***

500,000 locations

Western Union has over 500,000 locations worldwide, with a combined network of approximately 455,000 agent locations in 200 countries and territories. In the United States alone, there are about 68,458 locations.

***

Donors will be anonymous unless they specify otherwise. Also, I'll take suggestions from donors about content (articles, illustrations, etc.). 

My email is: harty.thomas@gmail.com

I want to keep this blog ad free.