Prime Curios!: 81

81
(another Prime Pages' Curiosity)

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81 is the third smallest prime power of a prime power of a prime. [Petersen]

81 is the smallest (and only known) square such that 81*2^81-1 is prime. [Gupta]

81 = (prime(8)+8) * (prime(1)+1). Note that 81 is the only known number (less than 10000000) with this property. [Firoozbakht]

(There is one curio for this number that has not yet been approved by an editor.)