Re: Q: About number of primes with n digits?


Danny wrote:
The first 4 primes are single digits in length.
The next 21 primes are 2 digits in length.
The next 143 are 3 digits in length.
etc..

4, 21, 143, 1061, 8363, 68906, 586081, 5096876, 45086079,
404204977, 3663002302, 33489857205, 308457624821, 2858876213963,
26639628671867, 249393770611256, 2344318816620308,
22116397130086627, 209317712988603747, 1986761935284574233,
18906449883457813088, 180340017203297174362

Sequence is in OEIS as A006879.

Will the ratio between terms converge?

If the sequence is divergent then at any point can the next
ratio be < the previous ratio?

Dan

By the PNT, the nth term is asymptotically

0.9 * 10^n / (n log 10)

so the ratio converges to 10.

---
J K Haugland
http://home.no.net/zamunda

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