Modified Erasthmus's Sieve Demo

 I wrote before, asking if the modification on Erasthmus's Sieve I discovered was still Erasthmus's Sieve.

I am convinced it is not the Sieve of Erastosthenes, since the odd numberline is not a geometric progression. I allude to it as a Modified Erasthmus's Sieve, while open to correction.

Earlier I demonstrated n < 100. Although it took me a long time to present the current entry, I did understand that n < 100 was not sufficient. Below I present a clearer picture of how it develops, using n<=361, or 19^2. I don't know enough Number Theory to offer Proof.



In the first slide, I enumerate 2 literal, and develop the odd number line up to 361. I then start with 3 as the next unstruck number, and blindly strike by 3s. The result leaves NO MULTIPLES OF 3 UNSTRUCK.


In the second slide, I start with the next unstruck number (5) and blindly strike by that number. The result leaves NO MULTIPLES OF 5 UNSTRUCK. By observation of experiment, multiples of 3 x 5 (15) are double struck, starting with 15 x 1, then 15 x 2 etc.


In the third slide I advance to the next unstruck number, 7, and strike by sevens, annotating double strikes with a legend. NO MULTIPLES OF 7 WERE UNSTRUCK.


In the fourth slide, I present the result after advancing next unstruck to next unstruck, striking by the relevant number, until I reached 19, the square root of 361. This resulted in a computation by hand of all primes <= 361. 

By observation, can be implemented just as easily as Erasthmus's Sieve and in a computer algorithm is less RAM intensive. Reduced double striking suggests it is also faster. By building a List method in Python of all odds < 2^32, I was able to develop a file with all primes <= 2^32 on an Intel Core i5 12600K, with 128GB of Gskill RipJaws RAM, and write it to a PCIe3 M.2 drive (using Anaconda3 Python 3 on a Linux Mint Mate OS,)

...in 829 seconds.

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