correlations with significance levels

I want to calculate how significant a correlation is

I use this code for the correlation. How can I see if this correlation is statistically significant?
I guess I can use this code, but I have to add something.

x <- c(6,7,8,17,12,16)
y <- c(33.46,50.68,87.92, 98.84, 63.6, 107.3)
cor(x, y, method = c("pearson"))
cor.test(x, y, method=c("pearson"))

The result is a 2 tailed p value. Take half of it. If the half is less than your significance level alpha, then the null hypothesis of no correlation is rejected/


should do the job too, right?

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