Jan 7 2013
I came across the following site tonight http://www.abovetopsecret.com/forum/thread503088/pg1
His non-prime rays obviously screen out numbers with 2 or 3 as factors. The N%24 != {1,5,7,11,13,17,19,23} replaces the "visual" even and N%3 tests in a single computer-based command. His Ray 1 observations are interesting, but encapsulates the known (p2^2-p1^2)%8=0 condition, which includes many false positives.
His 2nd (p^2-1)%24=0 also includes many false positives, and tosses products of 3 already xcluded.
35 required 1 (mod 34)
1397 required 667 (mod 730)
730-16 = 34 * 21 (21,16) bracketed 17&19 (twin primes) and X&Y differ by 5 (21-16)
11193 - X = 34 * Y . we know 11193/34 =329+. so we seek TPs just below that.
we know we have 311,313 but 11193-313*34 = 551> 311 so no TP pair is possible (N was composite)
But N=34*315+309=10953 is also composite, as is 34*309+315 and 34*310+315
Our trial conjecture immed fails.