Table of Chebyshev's Theta Function for Large-ish Values of x?

Question

Chebyshev's Theta Function is defined as $\vartheta(x)=\sum_{p\le x} \log p$

I am trying to find a table of this function for large-ish values of $x$, preferably in a form I could download to a spreadsheet. By "large-ish" I mean for $x$ over 16000.

I have found a table in a 1962 paper by J.Rosser and L.Schoenfeld, titled "Approximate Formulas for Some Functions of Prime Numbers". Page 91 lists values of $\vartheta(x)$ for $x$ from 500 to 16000 in steps of 500. My search has not turned up any similar table thus far.

If anyone knows of such a table I would be grateful for the reference.

Answer 1

It's easy enough to compute with a computer algebra system. For example, in Maple:

Primes:= select(isprime,[$1..30000]):
Theta:= x -> convert(map(evalf@ln,select(`<=`,Primes,x)),`+`);
for i from 16000 by 1000 to 30000 do
  print(i,Theta(i))
od:

                   16000, 15886.79251
                   17000, 16838.47253
                   18000, 17854.57508
                   19000, 18777.95241
                   20000, 19805.30968
                   21000, 20778.19314
                   22000, 21815.61079
                   23000, 22817.63579
                   24000, 23864.33160
                   25000, 24814.24553
                   26000, 25808.63562
                   27000, 26837.34886
                   28000, 27798.29406
                   29000, 28803.55793
                   30000, 29750.34194

(the last 3 digits or so of each of these may be off due to roundoff error).