Here's a full list of knowable parities based on the parities of our known variables, d and e.

-even e even d

-x – even

-a – even

-b – even

-f – odd

-c – even

-even e odd d

-x – even

-a – odd

-b – odd

-f – odd

-c – odd

-odd e even d

-x – odd

-a – odd

-b – odd

-f – even

-c – odd

-odd e odd d

-x – odd

-a – even

-b – even

-f – even

-c – even

The parity of n will be the same as BigN, which you can calculate from ((d^2+e+1)/2)-d. You can't, however, find the parity of n or N based solely on other parities. You have to calculate it based on BigN. So, for example, some odd e even d examples have odd BigNs and some have even BigNs. You also have to use calculation to find the parity of t, but this is a calculation based on unknowns, so it's a little harder than finding n's parity.

Choose a prime number that is a factor of any value of a in a cell in the first row (e,1).

In (e,1), p will be a factor of a in elements:

t+p, t+2p, t+3p,..

and

p+1-t, 2p+1-t, 3p+1-t,..

E.g. 5

E.g. (1,1)

5 appears as a factor of a in the second element (1,1,2,3,5,13) 5x13=65

5 will be a factor of the 2nd,7th,12th,17th value of a in (1,1) - t+p, t+2p, etc

5+1 is 6. 5 will be a factor of a in the (6-2) element at (1,1) - p+1-t, 2p+1-t, etc

The fourth element is 25.

Five will be a factor of the fourth, ninth, fourteenth, nineteenth element of (1,1).

This is true of any factor p in any cell in row (e,1).