Prime Curios!: 84

84
(another Prime Pages' Curiosity)

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Its digits are composite. Yet each digit minus 1, the sum of the digit minus 1 and the absolute value of the difference of the digits minus 1 is prime. [Russo]

The product of its digits minus 1 is prime. [Wolfe]

84 is the smallest number that can be expressed as the sum of 3 distinct primes raised to distinct prime exponents (2⁵ + 3³ + 5²). [Russ]

84!₂ + prime(48) is prime. [Firoozbakht]

84 = prime(prime(8))+prime(prime(4)). It is the only such number. [Firoozbakht]

(There are 2 curios for this number that have not yet been approved by an editor.)

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