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Douglas Harper's Etymology Dictionary
unprovable

early 15c., from un- (1) "not" + provable (adj.).

Wiktionary
unprovable

a. That cannot be proved or verified by any test

WordNet
unprovable

adj. not provable; "it was both unproved and unprovable"

Usage examples of "unprovable".

Worst of all, RSA depends upon the unprovable mathematical hypothesis that there is no polynomial time bounded algorithm for factoring numbers.