This number is a prime.

+ If we place 11 in the formula 2^p-1, we get the composite Mersenne number 2047, but if we place 11 in the formula (2^p+1)/3 [p is an odd prime], we get the prime number 683.

+ 683 = prime(6*8*3) - 6*8*3. Note that the prime 683 is the smallest number greater than one with this property. Note that the next such number is also prime. [Firoozbakht]

+ The smallest number with complexity of height 5: 683 -1-> 22 -2-> 10 -3-> 7 -4-> 6 -5-> 5. [Beedassy]

+ Regarding light, the maximum possible efficacy is 683 lumens per watt which corresponds to an efficiency of 100%. [Homewood]

+ The smallest prime whose the square consists of all the composite digits, i.e., 683^2=466489. [Loungrides]

+ There are 683 six-digit squares. [Gaydos]

+ Smallest Wagstaff prime p such that (2^p+1)/3 is not prime.

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

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