The 1st prime is 2, the 10th prime is 29, the 100th prime is 541, the 1000th prime is 7919, the 10000th...
arithmetic/nth.prime New
New entry, edited from material collected for the archive and not yet in a released version.
Problem
The 1st prime is 2, the 10th prime is 29, the 100th prime is 541, the 1000th prime is 7919, the 10000th prime is 104729, the 100000th prime is 1299709, and the 1000000th prime is 15485863. How far can this be extended by computation? -- Phil Gibbs <gibbs@eurocontrol.fr>
Show solution
Phil, How far would you like? the 10000000th prime is 179424671 the 100000000th prime is 2038074743 the 1000000000th prime is 22801763489 the 10000000000th prime is 252097800611 the 100000000000th prime is 2760727302517 [ See Lagarias, Miller and Odlyzko, "Computing pi(x): the Meissel-Lehmer method" [Editor: "Calculating pi(x)" in the original] in Math. Comp. 1985. ] -- Victor S. Miller <victor@harder.ida.org>, April 1994 [ Editor: two of these values are off. Counting primes with a sieve gives pi(179424671) = 9999999 and pi(179424673) = 10000000, so the 10000000th prime is 179424673; and pi(252097800611) = 9999999999, pi(252097800623) = 10000000000, so the 10000000000th prime is 252097800623. The other values check. ]