Ted,
I think you are wrong about which coil is the primary. I am
assuming that your transformer is from a microwave that does not have a
inverter in it .

For a conventional micrewave over transformer, the coil that only has a
few windings is for the filament of the magnetron ( F for filament ).
The coil with the very fine wire is the high voltage and the other
winding with maybe one or two hundred turns is the primary.

Since microwave oven transformers produce high voltages with the
ability to supply relatively lots of current, they are dangerous to
test with the full 115 volts on the primary. I would use a much lower
voltage on the primary( maybe 5 volts AC ) and then measure the
secondary voltage. And figure what the secondary voltage is. If you
put 115 volts on the primary, you are likely to fry your multimeter.

If you put 5 volts on the primary, that is about 1/23 of 115 volts. So
if you measure 50 volts on the secondary, the transformer will have
1150 volts on the secondary when connected to 115 volts on the primary.

Be careful.
Dan