I would run 1/0 gauge.
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A 100 amp residential service requires a size #8 copper wire, it should be insulated in green.
A 100 amp service requires that you use AWG 4 copper wire or AWG 2 aluminum wire.
2 copper
A #3 copper wire with an insulation factor of 75 and 90 degrees C is rated at 100 and 105 amps respectively.
AWG # 4 copper.