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.
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?