primes(1000)
## Not run:
# ## Appendix: Logarithmic Integrals and Prime Numbers (C.F.Gauss, 1846)
#
# library('gsl')
# # 'European' form of the logarithmic integral
# Li <- function(x) expint_Ei(log(x)) - expint_Ei(log(2))
#
# # No. of primes and logarithmic integral for 10^i, i=1..12
# i <- 1:12; N <- 10^i
# # piN <- numeric(12)
# # for (i in 1:12) piN[i] <- length(primes(10^i))
# piN <- c(4, 25, 168, 1229, 9592, 78498, 664579,
# 5761455, 50847534, 455052511, 4118054813, 37607912018)
# cbind(i, piN, round(Li(N)), round((Li(N)-piN)/piN, 6))
#
# # i pi(10^i) Li(10^i) rel.err
# # --------------------------------------
# # 1 4 5 0.280109
# # 2 25 29 0.163239
# # 3 168 177 0.050979
# # 4 1229 1245 0.013094
# # 5 9592 9629 0.003833
# # 6 78498 78627 0.001637
# # 7 664579 664917 0.000509
# # 8 5761455 5762208 0.000131
# # 9 50847534 50849234 0.000033
# # 10 455052511 455055614 0.000007
# # 11 4118054813 4118066400 0.000003
# # 12 37607912018 37607950280 0.000001
# # --------------------------------------## End(Not run)
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