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The Cooper pairing mechanism that binds single electrons to form pairs in metals allows electrons to circumvent the exclusion principle and condense into a single superconducting or zero-resistance state. We present results from an amorphous bismuth film system patterned with a nanohoneycomb array of holes, which undergoes a thickness-tuned insulator-superconductor transition. The insulating films exhibit activated resistances and magnetoresistance oscillations dictated by the superconducting flux quantum h/2e. This 2e period is direct evidence indicating that Cooper pairing is also responsible for electrically insulating behavior.