Elimination of possible primes to 11^2, 13^2 and 17^2


Here are some more tabular representations of the step-wise removal of possible primes within 11 x 11, 13 x 13 and 17 x 17 blocks. First, 11 x 11:

The first table shows remaining primes (plus “1,” and recalling of course that the lower primes, 2, 3, 5 and 7 are all prime but now show as “non-prime” for subsequent repetitions of this primorial) in primorial number notation, and all eliminated candidate primes are shown with the lowest prime factor indicated. In the second table, the highest prime factor of each composite number is shown, for contrast. The positions removed by the most recent round of sieving (i.e. by 11) are shown in red. I will use this same format for the remaining representations of 13 x 13 and 17 x 17.

In the next graph, I’ve used the other table format, with the tops of successive lower primorials (i.e. 0 to 209, 210 to 419 etc) shown, listing the first 30 rows of each:

The following series of tables present precisely the same information, in the same format, for 13 x 13 after sieving by 13, and 17 x 17 after sieving by 17:

sieving by 13:


sieving by 17:


I continue to mull this all over. No breakthroughs to report yet,😉, just posting some progress…

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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