My question is this, is there a known convergence of the sum of primes divided by the square of the sample size?(adsbygoogle = window.adsbygoogle || []).push({});

I've just been looking at it, admittedly with only the first 50,000 primes, and it looks as if it is converging on a number near 6. If you plot the points below, you might see what I mean:

5000 ... 4.57821036

10000 ... 4.96165411

15000 ... 5.18540836

20000 ... 5.344388313

25000 ... 5.466979301

30000 ... 5.567297328

35000 ... 5.651915416

40000 ... 5.725362149

45000 ... 5.789698869

50000 ... 5.84735752

Is this a known phenomenon, and if so, what is it called?

If not, and someone has access to a greater number of primes, it would be interesting to see if the trend continues. Is there a ceiling at 6 (I doubt it, it would be a little too neat), or at 2pi (which would be rather cool), or does it just keep increasing (but at an ever decreasing rate, thus being a prime example of Xeno's Arrow!)

I am happy to do the finger work, if someone can direct me to, or send me the primes above 50,000 in a useable format (actually I mean by that the primes above the 50,000th prime, so primes above 611,953).

cheers,

neopolitan

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# Question about sum of primes and sample size

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