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]

(There is one curio for this number that has not yet been approved by an editor.)

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