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# Talk:Carmichael numbers

## 1729

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

• 1729 is the Hardy-Ramanujan number (${\displaystyle \scriptstyle 1729\,=\,1^{3}+12^{3}\,=\,9^{3}+10^{3}\,}$ is smallest integer which is the sum of 2 cubes in 2 ways;)
• 1729 is the product of 19 * 91 (since 7*13 = 91;)
• ${\displaystyle \scriptstyle {\frac {1729+9271}{11}}\,=\,10^{3}\,}$

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

## Tables of Carmichael numbers

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)