The
Goldbach conjecture verification project reports that it has computed all primes below 4×1018.
[2] That means 95,676,260,903,887,607 primes
[3] (nearly 1017), but they were not stored. There are known formulae to evaluate the
prime-counting function (the number of primes below a given value) faster than computing the primes. This has been used to compute that there are 1,925,320,391,606,803,968,923 primes (roughly 2×1021) below 1023. A different computation found that there are 18,435,599,767,349,200,867,866 primes (roughly 2×1022) below 1024, if the
Riemann hypothesis is true.
[4]