1.

1, 1, 1, 1, 1, 1, 1, 1, 1
1, 1, 1, 1, 1, 1
1, 1, 1, 1, 1
1, 1, 1
1
1
1


2.
pnk(151, 10) = 79811865


3.
[[6, 4, 2, 2, 2, 2, 2], 0]


4.
You get the same answer when you run pnFast(10000) and [seq(PnFast(i),i=1..10000)][10000]. 
pnFast(20000) = 252114813812529697916619533230470452281328949601811593436850314108034284423801564956623970731689824369192324789351994903016411826230578166735959242113097


5.

pnFastMod:=proc(n,m):
pn(n mod m):
end:

pnFastMod(10^5, 101) = 42