Almost through with 1000 < n < 2000 for 30 digits:
Code:
25 30 hex (hex digits)
21181,1148 ok ok N=0x52BD000 (292)
21181,1172 ok ok N=0x52BD000 (298)
10223,1181 ok ok N=0x4FDE000 (302)
27653,1257 ok ok N=0xD80A000 (319)
21181,1268 ok ok N=0x52BD000 (322)
33661,1320 ok ok N=0x837D000 (335)
10223,1517 ok ok N=0x4FDE000 (384)
10223,1529 ok ok N=0x4FDE000 (387)
24737,1543 ok ok N=0x3050800 (391)
24737,1567 ok stage1 complete N=0x3050800 (397)
55459,1666 ok ok N=0x3628C00 (422)
55459,1894 ok ok N=0x3628C00 (479)
55459,1966 ok ok N=0x3628C00 (497)
No new factors at that level.
I found out something strange:
As you can see at the end of each line, the numbers in hex always start the same for same k's, they only differ in the (hex) digit count.
That means that the n's of these numbers differ by a multiple of 4.
Is that
a) coincidence,
b) natural (due to some obvious implication) or
c) a phenomenon unknown so far?