After his recent work on Taxicab(6) confirming the number found as an upper bound by Randall Rathbun in 2002, Uwe Hollerbach (USA) confirmed this week that my upper bound 933528127886302221000 = 8387730^3 + 7002840^3 (1) = 8444345^3 + 6920095^3 (2) = 9773330^3 - 84560^3 (3) = 9781317^3 - 1318317^3 (4) = 9877140^3 - 3109470^3 (5) = 10060050^3 - 4389840^3 (6) = 10852660^3 - 7011550^3 (7) = 18421650^3 - 17454840^3 (8) = 41337660^3 - 41154750^3 (9) = 77480130^3 - 77428260^3 (10) constructed in Dec 2006 is really Cabtaxi(10). See his announcement at http://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0805&L=nmbrthry&T=0&P=1284 See also http://cboyer.club.fr/Taxicab.htm, with updated tables of Taxicab and Cabtaxi numbers. You can also freely access to my paper published in Journal of Integer Sequences, with explanations on how this number was constructed, before to be proved the real Cabtaxi(10) number. Reminder: -Taxicab(n) is the smallest number expressible as a sum of two cubes in n different ways. -Cabtaxi(n) is the smallest number expressible as a sum or difference of two cubes in n different ways. Christian.