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…