343

This number is a composite.

343 = (3 + 4)³ is palindromic, along with the fact that 3⁴³ + 34³ is prime. Note that 342³⁴³ + 343³⁴² is prime also. [Kulsha]

Ever since the Willow Grove Exit of the Pennsylvania Turnpike has existed, its exit number has been 27, the cube of an odd prime (3³ = 27). Now, the turnpike exit numbers are being changed, and the exit number for Willow Grove will soon be 343 - another cube of an odd prime (7³ = 343). [Litman]

The sum of the first five odd Fibonacci primes. [Silva]

7 cubed can be expressed using the first six odd primes: 7(3+5+11+13+17). [Silva]