Crop factor Vs shutter speed

Should we take into account the crop factor when calculating hand held shutter speeds to avoid camera shake?

If I shoot 35mm with the Bigma at 500mm, rule of thumb says I should keep my shutter speed above 1/500th, so assuming I dont use SR on A DSLR do I still keep the shutter speed at 1/500th or do I have to allow for the crop factor and shoot at 1/750th

This is in the manual where it does confirm that we use the higher speed.

This is borne out in general with formats, so a medium format camera can in theory be used at slower shutter speeds than a 35mm one and the one ironically most in need of a firm tripod is the 110 or other submin format.

Whenever you crop AND enlarge heavily, every little thing will show up. So, something that look sharp as a 5 X 7 might show traces of motion blur, either camera shake or subject movement, when seen at 17 X 22. So, it is wise to err on the safe side.

I thought so too, just wanted confirmation. dont remember reading it in the manual though.