Home » Subject » Number Theory » Computational N.T.
Importance: Medium ✭✭
Author(s): Michon, Gérard P.
Subject: Number Theory
» Computational Number Theory
Keywords:
Recomm. for undergrads: yes
Posted by: maxal
on: August 5th, 2007
Conjecture   Every odd number coprime to its Euler totient divides some Carmichael Number.

In December 2007 Joe Crump discovered the following Carmichael multiples (of the numbers with previously unknown Carmichael multiples):

    \item $ 24354644805191195265 $ is a Carmichael multiple of $ 885 $; \item $ 174470770903594881 $ is a Carmichael multiple of $ 2391 $; \item $ 12832546007164521 $ is a Carmichael multiple of $ 2517 $; \item $ 435262925087145321 $ is a Carmichael multiple of $ 2571 $; \item $ 291226428348047343201 $ is a Carmichael multiple of $ 2589 $; \item $ 947087538769733505 $ is a Carmichael multiple of $ 2595 $; \item $ 114593508055911048606465 $ is a Carmichael multiple of $ 2685 $; \item $ 13053581557039793157 $ is a Carmichael multiple of $ 2949 $.

Bibliography

Gérard P. Michon. "Least Carmichael Numbers with Given Divisors (up to 2999)."

Gérard P. Michon and Joseph K. Crump. "Carmichael Multiples of Odd Cyclic Numbers."

W. R. Alford, A. Granville, and C. Pomerance. "There are Infinitely Many Carmichael Numbers." Ann. Math. 139, 703-722, 1994.

Günter Löh and Wolfgang Niebuhr. "A new algorithm for constructing large Carmichael numbers." Math. Comp. 65 (1996), 823-836.


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