Talk:Carmichael numbers

1729

By the way, the Hardy-Ramanujan number, e.g. $\scriptstyle 1729\,=\,7\cdot 13\cdot 19\,$, is a Carmichael number!

• 1729 is the Hardy-Ramanujan number ($\scriptstyle 1729\,=\,1^{3}+12^{3}\,=\,9^{3}+10^{3}\,$ is smallest integer which is the sum of 2 cubes in 2 ways;)

• 1729 is the third Carmichael number (Cf. A002997;)

• 1729 is the third Zeisel number (Cf. A051015;)

• 1729 is the smallest Chernick's Carmichael number (Cf. A033502.) Product of 3 prime factors (6n+1)(12n+1)(18n+1) with n=1, (Cf. http://www.cs.uwaterloo.ca/journals/JIS/VOL5/Dubner/dubner6.pdf ;)

• 1729 is the smallest abolute Euler pseudoprime. (Cf. A033181;)

• 1729 is the product of 19 * 91 (since 7*13 = 91;)

• 1729 is some figurate number (e.g. the 19^th dodecagonal number, A051624.)

• $\scriptstyle {\frac {1729+9271}{11}}\,=\,10^{3}\,$

— Karsten Meyer 12:14, 14 November 2010 (UTC) — Edited by Daniel Forgues 22:13, 14 November 2010 (UTC)

Tables of Carmichael numbers

• Tabelle Carmichael-Zahlen
• Tabelle Carmichael-Zahlen nach Chernick

— Karsten Meyer 00:40, 15 November 2010 (UTC)

Chernick's Carmichael numbers

Ther exist some Carmichael numbers, which comply the form (6n+1)*(12n+1)*(18n+1), but one of the "factors" is not prime:

172081 = 31 * 61 * 91 5 M3(5)

1773289 = 67 * 133 * 199 11 M3(11)

4463641 = 91 * 181 * 271 15 M3(15)

1110400109 = 557 * 1153 * 1729 96 M3(96)

134642101321 = 2821 * 5641 * 8461 470 M3(470)

91 and 133 are Fermat pseudoprimes, and 1729 and 2821 are Carmichael numbers. Nevertheless the numbers fit in the form of Chernick's Carmichael numbers. — Karsten Meyer 01:52, 1 January 2011 (UTC)