transformer resistances

I have an transformer from a old power supply.
It has 2 red wires and 2 yellow wires.
I think the red wires are the high voltage (mains) in and the yellow
the low voltage (12v ?) out,
To check this I touched a 6V battery across the yellow wires and got a
high voltage across the red wires (enought to spark across a 3mm gap)
But when I measure the resistance across the red wires I get 31.1ohms
and across the yellow 10.4ohms.
This is not what I expected.
I thought the high voltage winding would be thicker wire and less
turns than the low voltage winding and so would have a lower
resistance.
Could anyone explain where I am going wrong?
.

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