I completed the following GFNxGF range :
5600 <= N <= 5699  1,200,000,000 < K < 2,500,000,000
and found the following factors:
2491340445*2^5654+1 is a Factor of xGF(5652,11,10)!!!!
1755293137*2^5672+1 is a Factor of xGF(5671,8,3)!!!!
2004304135*2^5672+1 is a Factor of xGF(5671,7,2)!!!!
1982981535*2^5675+1 is a Factor of xGF(5674,8,7)!!!!
