683
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.
The Isle of Lewis has a total area of 683 square miles. [MacLeod]