That's weird, are you looking only at the top 10 countries?
I've reproduced dwaltrib's results using World Bank data on 251 countries, and I get a Pearson's r of 0.82 and a p value of 5.6e-61 (!). I.e. a strong correlation, with high confidence. It makes sense too -- larger countries generally have more people, and more people generally generate more economic activity.
Code if you want to try yourself:
import pandas as pd
gdp = pd.read_csv("~/Downloads/API_NY.GDP.MKTP.CD_DS2_en_csv_v2_5551501.csv").set_index("Country Name")
datamash gave me 0.52 for Pearson. Which is "eh, maybe".