theorem Th35: :: NUMBER19:35

for k being Nat st k,1 are_congruent_mod ((2 |^ 32) - 1) * 641 & k, - 1 are_congruent_mod 6700417 & k > 6700417 holds
for n being positive Nat holds
( k + (2 |^ n) is composite & ( not not Fermat 0 divides k + (2 |^ n) & ... & not Fermat 4 divides k + (2 |^ n) or 641 divides k + (2 |^ n) or 6700417 divides k + (2 |^ n) ) )