It's an interesting heuristic, but I think your limitation that it be less than the square of the Nth prime is a case of overfitting.
Here's a list of results for the first N primes, for different Ns:
3: 7
4: 11
5: 13
6: 17
7: 107
8: 41
9: 157
10: 1811
11: 1579
12: 18859
13: 95533
14: 310469
15: 1995293
16: 208303
17: 2396687
18: 58513111
19: 299808329
20: 2933961157
21: 3952306763
22: 33298242781
23: 115405393057
I just wrote a script to brute force all combinations here, so the 24th iteration got very slow, but of all those the nonprime ones are n=23, 19, 18, 16, 14, and 13.
So, your rule appears to hold true as long as N is less than the cube of the Nth prime. The actual rule is probably more complex than a simple power, considering 83^5 is far less than the result in N=23.
I think I'll play with this a bit more this evening then ping some mathematician friends about it. They always love playing with weird properties of primes.
You shouldn't be outraged, but your justification for their pay is a little simplified.
People aren't paid based on the value they create, strictly speaking. They're paid whatever is necessary to get them to work.
The value of a good executive is, I'd argue, far higher than their pay reflects. A truly bad executive can put a company on the path to ruin, and a decent executive making bad choices can do the same. What companies are paying for in good/great executives isn't some N times multiplier on that salary in new income, they're paying for reduced chances of catastrophe.
The supply of good/great executives is small, and the potential loss from putting a dunce in charge of AAPL/GOOG is obscene, so is it any wonder the price lands where it does?
>By contrast, 3D XPoint works by changing the properties of the material that makes up its memory cells to either having a high resistance to electricity to represent a one or a low resistance to represent a zero.
Which sounds a lot like memristors: https://en.wikipedia.org/wiki/Memristor to me. If it's memristor memory, the main advantages are that it's cheap, uses hugely less power than flash, takes up less space, and has far lower latencies.
We're probably a long ways from replacing DRAM with memristors because it's still much higher latency, but if this stuff scales up well you could do something like put the whole page file on it and get even faster loads than current top of the line SSDs.
Here's a list of results for the first N primes, for different Ns: 3: 7 4: 11 5: 13 6: 17 7: 107 8: 41 9: 157 10: 1811 11: 1579 12: 18859 13: 95533 14: 310469 15: 1995293 16: 208303 17: 2396687 18: 58513111 19: 299808329 20: 2933961157 21: 3952306763 22: 33298242781 23: 115405393057
I just wrote a script to brute force all combinations here, so the 24th iteration got very slow, but of all those the nonprime ones are n=23, 19, 18, 16, 14, and 13.
So, your rule appears to hold true as long as N is less than the cube of the Nth prime. The actual rule is probably more complex than a simple power, considering 83^5 is far less than the result in N=23.
I think I'll play with this a bit more this evening then ping some mathematician friends about it. They always love playing with weird properties of primes.