32
This number is a composite.
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]
32 = 3 + 29.
32 +/- 3^2 are both prime. [Homewood]
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]
The smallest Honaker
number is also a Happy number. [Gupta]
π(32) is the (3+2)th prime. The smallest prime-digit number of this
form. [Bajpai]
The number of primes consisting of all distinct odd digits
only. Note that a dozen of them (six pairs) are emirps. [Loungrides]
32-3^2 is prime. [Silva]
The smallest Honaker
number equals two to the power (3+2). [Ramsey]
The "minimal prime problem" in base-32 cannot be proven. [Xayah]
The book "The 32nd Mersenne Prime" by David Slowinski delves into the fascinating world of prime numbers and mathematical discoveries.
The smallest positive integer that has half the sum of digits as its prime factorization (2*2*2*2*2). [Gaydos]
32 is the smallest fifth power such that the sum of its digits is a prime number. [Schiffman]