# Contradiction in F-test and t-test [duplicate]

I have generated a summary for a particular multiple linear regression

> mod1 <- lm(log(wage) ~ education + experience + age)
> summary(mod1)

Call:
lm(formula = log(wage) ~ education + experience + age)

Residuals:
Min       1Q   Median       3Q      Max
-2.03367 -0.33094  0.04165  0.31958  1.84066

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  0.84480    0.71884   1.175    0.240
education    0.13805    0.11791   1.171    0.242
experience   0.05353    0.11796   0.454    0.650
age         -0.04173    0.11786  -0.354    0.723

Residual standard error: 0.4699 on 530 degrees of freedom
Multiple R-squared:  0.2117,    Adjusted R-squared:  0.2072
F-statistic: 47.44 on 3 and 530 DF,  p-value: < 2.2e-16


Since the F-statistic = 47.44 is larger than the cut-off value qf(0.95, 3, 530) = 2.622, I can reject the null hypothesis that states the model is not significant. But on the other hand, I find that the p-values are larger than 0.05. What is the reason for this? Is there a way to solve this?