If you don't mind a smidge of obsolescence, 'imperscrutable' (adj.) or 'imperscrutableness' (n.) might work for you:
adjective: Not to be searched out; unsearchable, inscrutable, or
noun: unsearchableness, inscrutableness.
["† imperˈscrutable, adj.". OED Online. September 2015. Oxford University Press. http://www.oed.com/view/Entry/92319 (accessed November 03, 2015).]
If, on the other hand, you want some common coin, then 'inscrutable' (adj.), might be the ticket:
That cannot be searched into or found out by searching; impenetrable or unfathomable to investigation; quite unintelligible, entirely mysterious.
["inscrutable, adj. and n.". OED Online. September 2015. Oxford University Press. http://www.oed.com/view/Entry/96667 (accessed November 03, 2015).]
Also possible is 'inscrutability' (n.):
The quality of being inscrutable; transf. something inscrutable.
["inscrutability, n.". OED Online. September 2015. Oxford University Press. http://www.oed.com/view/Entry/96666 (accessed November 03, 2015).]
Other words along the same lines that you might find useful include
unsearchableness = That cannot be searched into, so as to be ascertained or exactly estimated; inscrutable.
unconceivableness = inconceivable.
impenetrability = The quality or condition of being impenetrable; incapability of being penetrated, entered, or pierced; inscrutability; unfathomableness; ‘unsusceptibility of intellectual impression’.
(All from OED Online.)
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