it apears in the first 3 posts both myself and JayDeeKay made a slight error by not including 2^2002 in our calculations.

Doing so results in

2^1994(1+2^4+2^5+2^6+2^8)+2^p

369*2^1994+2^p

2^1994*(369+2^(p-1994))

and so far the only solution I can find is with p-1994=8 thus

p=2002