Tables of best known results (in May 2007) on Taxicab and Cabtaxi numbers

Tables of best known results on Taxicab and Cabtaxi numbers, in May 2007
(Tables built when the JIS & PLS articles were written in 2007. Today, better bounds are known: see the updated tables.)

We knew in November 2006:

Taxicab(n) for any n ≤ 5, and the upper bound of Taxicab(6) proposed by Randall L. Rathbun in 2002 which was probably^(*) Taxicab(6)
Cabtaxi(n) for any n ≤ 9, including the biggest and latest of them, Cabtaxi(9), found by Duncan Moore in 2005

Nothing seemed to be known on bigger n. I proposed to extend the range of known information on these numbers, with:

Upper bounds of Taxicab(n) for any n within 7 ≤ n ≤ 19
Upper bounds of Cabtaxi(n) for any n within 10 ≤ n ≤ 30

The upper bounds of Taxicab(7) and Cabtaxi(10) may have a chance of being the correct Taxicab and Cabtaxi numbers. But the probability decreases when n increases, and is close to 0 for Taxicab(19) and Cabtaxi(30).

(*) probability greater than 99.8%, according to a paper of 2005 by C. S. Calude - E. Calude - M. J. Dinneen, http://www.cs.auckland.ac.nz/CDMTCS/researchreports/261cris.pdf

Taxicab(2)	= 1729	Bernard Frenicle de Bessy (France)	1657
Taxicab(3)	= 87539319	John Leech (UK)	1957
Taxicab(4)	= 6963472309248	Edwin Rosenstiel, John A. Dardis, Colin R. Rosenstiel (UK)	1989
Taxicab(5)	= 48988659276962496	John A. Dardis (UK)	1994
Taxicab(6)	≤ 24153319581254312065344	Randall L. Rathbun (USA)	2002
Taxicab(7)	≤ 24885189317885898975235988544	: - ) (France)	Dec. 2006
Taxicab(8)	≤ 50974398750539071400590819921724352
Taxicab(9)	≤ 136897813798023990395783317207361432493888
Taxicab(10)	≤ 7335345315241855602572782233444632535674275447104
Taxicab(11)	≤ 2818537360434849382734382145310807703728251895897826621632
Taxicab(12)	≤ 73914858746493893996583617733225161086864012865017882136931801625152
Taxicab(13) ... Taxicab(19)	see List 3 in the Appendix of the JIS paper or the downloadable file at the end of this web page		May 2007

Cabtaxi(2)	= 91	François Viète (France), Pietro Bongo (Italy) indep.	1591
Cabtaxi(3)	= 728	Edward B. Escott (USA)	1902
Cabtaxi(4)	= 2741256	Randall L. Rathbun (USA)	~1992
Cabtaxi(5)	= 6017193
Cabtaxi(6)	= 1412774811
Cabtaxi(7)	= 11302198488
Cabtaxi(8)	= 137513849003496	Daniel. J. Bernstein (USA)	1998
Cabtaxi(9)	= 424910390480793000	Duncan Moore (UK)	2005
Cabtaxi(10)	≤ 933528127886302221000	: - ) (France)	Dec. 2006 - Feb. 2007
Cabtaxi(11)	≤ 8904950890305189093226944
Cabtaxi(12)	≤ 1912223147184127402358643000
Cabtaxi(13)	≤ 23266019031789278104497609381000
Cabtaxi(14)	≤ 567434938166308703690592195193209000
Cabtaxi(15)	≤ 31136289927061691188910174934641764248000
Cabtaxi(16)	≤ 1577146493675455843791867090964409284453944000
Cabtaxi(17)	≤ 23045156159180392847591977008030799542699242304000
Cabtaxi(18)	≤ 181609634582880844694340486417510510845396106201660096000
Cabtaxi(19)	≤ 298950477236981197723488725070538575992924211134299879660632000
Cabtaxi(20)	≤ 2149172021033860338362430683389430843511963750524516489973424104024000
Cabtaxi(21) ... Cabtaxi(30)	see List 4 in the Appendix of the JIS paper or the downloadable file at the end of this web page		May 2007

Warning! These numbers are no more the best known bounds! See the updated tables of Taxicab and Cabtaxi numbers.

Decompositions of these upper bounds:

Taxicab.txt (from 7 to 12)
Cabtaxi.txt (from 10 to 20)

And list of bigger upper bounds:

Taxibig.txt (Taxicab from 13 to 19, Cabtaxi from 21 to 30)

Warning! Several numbers in the above lists of 2007 are no more the best known bounds! See the updated lists.