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If we place 11 in the formula 2^p1, 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]
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