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[QUOTE="cpatrocks, post: 1798160, member: 1710"]
The [URL='https://en.wikipedia.org/wiki/Goldbach%27s_conjecture'][U]Goldbach conjecture[/U][/URL] verification project reports that it has computed all primes below 4×1018.[URL='https://en.wikipedia.org/wiki/List_of_prime_numbers#cite_note-2'][U][2][/U][/URL] That means 95,676,260,903,887,607 primes[URL='https://en.wikipedia.org/wiki/List_of_prime_numbers#cite_note-3'][U][3][/U][/URL] (nearly 1017), but they were not stored. There are known formulae to evaluate the [URL='https://en.wikipedia.org/wiki/Prime-counting_function'][U]prime-counting function[/U][/URL] (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 [URL='https://en.wikipedia.org/wiki/Riemann_hypothesis'][U]Riemann hypothesis[/U][/URL] is true.[URL='https://en.wikipedia.org/wiki/List_of_prime_numbers#cite_note-Franke-4'][U][4][/U][/URL]
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