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# 81

This number is a composite.

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 are 81 *Full House primes*, with the most advantageous
being 18181 and 81181 (where 1 is regarded as the Ace.) [Goelz]

The smallest square greater than 1 such that 81^(81+1) + π(81+1) is a prime. [Jha]

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