Pearson's correlation coefficient between two variables is defined as the covariance of the two variables divided by the product of their standard deviations. (from http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient)
foo <- c(1e154, 1, 0)
sd(foo)
## [1] 5.773503e+153
foo <- c(1e155, 1, 0)
sd(foo)
## [1] Inf
And, even more fundamental, to calculate sd()
you need to take the square of x:
1e154^2
[1] 1e+308
1e155^2
[1] Inf
So, your number is indeed at the boundary of what is possible to calculate using 64 bits.
Using R-2.15.2 on Windows I get:
cor(c(1e555, 1, 0), 1:3)
[1] NaN