PrimePi(10^23): A006880 and MathWorld disagreement

[Max Alekseyev]

Neil, Eric, SeqFans,

The values for pi(10^23) listed at
http://www.research.att.com/~njas/sequences/b006880.txt and at
http://mathworld.wolfram.com/PrimeCountingFunction.html differ
dramatically. Moreover, MathWorld claims that the exact value of
pi(10^23) is known only up to +/- 1.

So, I wonder which value is correct and what is the current status of
pi(10^23) ?

Regards,
Max