Prime Curios!: 85

85
(another Prime Pages' Curiosity)

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GIMPS has discovered a new largest known prime number: 2^82589933-1 (24,862,048 digits)

(85¹¹ - 85)/11 ± 1 are twin primes. [Luhn]

Between 641 and 114689 (the second smallest Fermat divisor) there exist 85 prime numbers that could conceivably be Fermat divisors.

There are 85 five-digit primes that begin with 85. [Bopardikar]

The only composite number resulting from the sum of three double-digit consecutive emirps, 17, 31, 37. Note that the concatenation in order of these emirps, i.e., 173137 is prime. [Loungrides]

The only known Smith number n such that the aliquot sum of n = (n). [Gupta]

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