In a medium bowl, stir together the warm water and corn syrup. Sprinkle the yeast over the top, and let stand until foamy, about 5 minutes.
Add 2 1/2 cups of the rye flour to the yeast mixture, and beat until smooth.
Stir in the salt. Set bowl in a warm place, and cover with a cloth or towel.
Let rise for 30 minutes.
Stir in more flour 1/2 cup at a time, until the dough is stiff. Turn the dough out onto a floured surface and knead in more flour by hand as needed to form a stiff but slightly sticky dough. You may use less or more flour. Form dough into a ball. Clean the mixing bowl, and lightly grease it. Place the dough in the bowl, and cover with a towel. Place in a warm place to rise until doubled. This may take as long as 2 hours.
Turn the risen dough out onto a floured surface, and press out the air bubbles. Roll dough into a loaf, and place into a greased 9x5 inch loaf pan.
Turn the loaf so that the seam is on the bottom. Cover the pan with plastic wrap, and let rise in a warm place until doubled, about 1 hour.
Preheat oven to 350 degrees F (175 degrees C). Remove plastic wrap from loaf pan.
Bake for 30 to 35 minutes in the preheated oven, or until the loaf sounds hollow when tapped on the bottom. Bread will not brown very much.