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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

+ The smallest two-digit number such that phi(n) + sigma(n) is prime. [Russo]

+ 32! - 1 and (32 + 1)! - 1 are primes. [Gallot]

+ 25 is the highest known power with all decimal digits being prime. [Kulsha]

+ M32 contains all known prime factors of form 2^2^k+1 in logical order, where k = 0 to 4. [Luhn]

+ It is not known if there exists a mean gap of exactly 32 between the first n successive primes.

+ 232 - 1 is the product of the first Fermat primes which are known (3, 5, 17, 257, 65537). [Capelle]

+ The only even number formed from two consecutive primes. [Silva]

+ The smallest Honaker number.

+ The smallest number n such that all the positive values of n-3^k are all primes, (i.e., k=0, 1, 2, 3). [Loungrides]

+ Half of this reversal of a prime may be had by turning its first digit (2nd prime) into a tetration superscript (32=16), while the index of that prime comes by turning the second digit (1st prime) into an exponent (32=9, with 23=p9). [Merickel]

+ pi(32) is the (3+2)th prime. The smallest prime-digit number of this form. [Bajpai]

+ 32-3^2 is prime. [Silva]

(There are 4 curios for this number that have not yet been approved by an editor.)

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