Prime Curios!: 81

81
(another Prime Pages' Curiosity)

Curios:

Curios Search: Participate:

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]

3^4 = 1 + 2^4 * 5 is an identity with first three primes and first 5 naturals only. [Zschorn]