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172 is the only byte whose binary representation contains a 1 at bit n iff n is prime (172_{10} = 10101100_{2}). [Thoms]
Seventeen 2's followed by two 17's is prime. [De Geest] 172 = (1+7+2) * prime(1*7*2). It is the only known number (up to 10^8) with this property. [Firoozbakht] 172 = phi(1+7+2) * prime(1*7*2). It is the only known number (up to 10^8) with this property. [Firoozbakht]
(There is one curio for this number that has not yet been approved by an editor.)
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