The shortest way of doing this is by using the package Hmisc:

Code:

require(Hmisc)
## Assuming you only have numeric values in your data
cortests <- rcorr(as.matrix(data1), type="pearson")

Use cortest$r for the correlation matrix and cortest$p to get a matrix with p-values.

As you do multiple comparisons here, note that a significant p-value must be Bonferroni corrected (or it's equivalent): significance p = 0.05 / number of tests.