Difference in p-values between R and SPSS

My apologies for asking slightly about SPSS in addition to R...

Could not find an exact answer in the archives on whether R and SPSS may
give different p-vals when output for coeffs and conf-intervals are the
same.
Amyway, a colleague and I are doing a very simple coxreg analyses and
get the same results for the coefficient and confidence interval,

                  exp(coef) exp(-coef) lower .95 upper .95
age_at_entry      1.02       0.98      1.01      1.03


but in R we get p = 0.00011, and SPSS gives p < 0.0001

Should we worry about this difference in p-value or do R and SPSS
sometime differ?

All the best,
Kare