SP: "the known values are still the references in seq. A006988, unless someone has a greater value than 10^24 ?" I think A006988(25), the (10^25)-th prime, should be a little more than 6*10^26 and someone has calculated the number of primes < 10^27 (see A006880) so it certainly seems do-able with today's hardware/software. Using Kim Walisch's program, Tom Rokicki needed 6 hours to do the number of primes < 10^23. On my 6-core 2018 Mac mini it took 14 hours. I think the time required scales by four or five for each power of ten. So by the time Tom is doing the number of primes < 6*10^26, he's looking at a couple of months or so. I'm looking at half a year. Also, while Walisch's program does the n-th prime directly, there appears to be a built-in limit: ./primecount 1e18 -n primecount: nth_prime(n): n must be <= 216289611853439384 So while A006988 states that the (10^23)-th and (10^24)-th primes were calculated using Walisch's program (in 2015), I assume they used a version without the limit. Otherwise one is manually playing high-low with the reverse procedure.