Sieving to 19, shown in 19 x 19 table


Following on from the previous graphs, I’ve done the same for sieving by 19, and present, below, the results to 19^2 in a 19 x 19 table, only showing the results in wrapping format.

For this example I’ve eliminated the primorial number representation of the remaining possible primes (which are by definition now confirmed to be prime in this box) and replaced it with a simple “P” to indicate confirmed prime.

This series of tables also highlights the values eliminated by prior rounds of sieving by 2, 3, 5, 7, 11, 13 and 17.

Sieving by 19 with first 4 (2^2) places highlighted:

Sieving by 19 with first 9 (3^2) places highlighted:

Sieving by 19 with first 25 (5^2) places highlighted:

Sieving by 19 with first 49 (7^2) places highlighted:

Sieving by 19 with first 121 (11^2) places highlighted:

Sieving by 19 with first 169 (13^2) places highlighted:

Sieving by 19 with first 289 (17^2) places highlighted:

Sieving by 19:

Still nothing brilliant to offer. 🙂 Just using this space as a big white board, documenting the ongoing thought process…

About petequinn

I'm a Canadian geotechnical engineer specializing in the study of landslides. I started this page to discuss some mathematical topics that interest me, initially this involved mostly prime numbers, but more recently I've diverted focus back to a number of topics of interest in geotechnique, geographic information systems and risk. I completed undergraduate training in engineering physics at Royal Military College (Kingston, Ontario), did a masters degree in civil (geotechnical) engineering at University of British Columbia (Vancouver), and doctorate in geological engineering at Queen's University (Kingston). I was a military engineer for several years at the beginning of my career, and did design and construction work across Canada and abroad. I've worked a few years for the federal government managing large environmental clean up projects in Canada's arctic, and I've worked across Canada, on both coasts and in the middle, as a consulting geotechnical engineer. My work has taken me everywhere in Canada's north, to most major Canadian cities and many small Canadian towns, and to Alaska, Chile, Bermuda, the Caribbean, Germany, Norway, Sweden, Bosnia, and Croatia. My main "hobby" is competitive distance running, which I may write about in future.
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