What does a P value of 0.000 mean in correlation matrix results?

 Prism reports the correlation matrix on two tables. One reports the correlation coefficient. The other reports the corresponding P value testing the null hypothesis that the population correlation coefficient is really 0.0. Prism reports these  P values using decimals, when they fit, or scientific notation when tiny. For example, "1.23e-14" means 1.23 times ten to the minus fourteenth power. 

When the P value is really tiny, less than 1.2e-38, it simply reports the P value as "0.000". If you formatted that column to always use scientific notation, then it shows as "0.0000e+000".