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?