# 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.