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The smallest twodigit number such that phi(n) + sigma(n) is prime. [Russo] 32!  1 and (32 + 1)!  1 are primes. [Gallot] 2^{5} is the highest known power with all decimal digits being prime. [Kulsha] M_{32} 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. 2^{32}  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 number n such that all the positive values of n3^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 (^{3}2=16), while the index of that prime comes by turning the second digit (1st prime) into an exponent (3^{2}=9, with 23=p_{9}). [Merickel]
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