Conjecture: this sequence is finite.  Carlos Rivera
Rivera's conjecture that this sequence is finite conflicts with heuristics; the next entry is almost certainly 6205, since floor((Pi3)*10^6205) is (very) probably prime, though its proof may take decades.  David Broadhurst, Nov 08 2000
Floor((Pi3)*10^6205) is a strong pseudoprime to all (1229) prime bases a < 10000 (the test took 45 minutes).  Joerg Arndt, Jan 16 2011
Terms for n>=5 are only probable primes.  Dmitry Kamenetsky, Aug 03 2015
Floor((Pi3)*10^16350) is a probable prime, checked with 25 iterations of the MillerRabin test.  Dmitry Kamenetsky, Aug 05 2015
The next term is greater than 65400.  Dmitry Kamenetsky, Aug 09 2015
