51
This number is a composite.
51 and its reversal (15) are each products of two Fermat primes. [Harari]
π(51) = 15. [Gupta]
51 = 2 + 3 + 5 + 41 . It's the smallest number which can be written with all the digits from 1 to 5 (without repetition) as a sum of primes. Note that the highest digit (5) and the lowest digit (1) are the digits of 51. [Capelle]
The first base not of the form n^x (where generalized repunits can be factored algebraically) for which there are no known generalized repunit primes.
Since 51 is the product of the distinct Fermat primes 3 and 17, a regular polygon with 51 sides is constructible with compass and straightedge.
The only two-digit number n such that the sum of the n-th power of all two-digit primes is also prime. [Bopardikar]
The larger term in the only pair of double-digit semiprimes (15, 51) whose the difference and the sum of digits of each of them, i.e., 4 and 6 are also semiprimes. [Loungrides]
The smallest semiprime that is the product of two primes
whose concatenation (in some order) produce the decimal
expansion of square root of 3, e.g., 51 = 17 *3, 346 = 173
* 2. The sequence begins 51, 346, 8660254037844386465,
9135637898642163233468659,
91356386175449607536090017841537606328361073633, .... . See the largest known. [Bajpai]
As of October 2020, the number of known Mersenne primes and
the number of known Fibonacci primes were equal at 51.
Are you sure 51 isn’t prime?
Prime numbers that end with "51" occur more often than any
other two-digit ending among the first ten billion (1010)
primes. [Keith]