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Old 2007-03-18, 03:22   #1
devarajkandadai
 
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May 2004

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Default Carmichael Numbers-Upper bounds

An interesting corollary of the Devaraj-Pomerance (Maxal) Theorem
(published in this forum a couple of years back) is that we can fix upperbounds for the number of possible Carmichael Numbers with k factors.

Let k=3.

(p_1-1)(N-1)/(p_2-1)(P_3-1) is asymptotic to the integer on the rhs.,
when we keep one of the factors fixed and allow the other two to
increase indefinitely.

UB - for 3, the fixed factor: 1

UB- for 11, the fixed factor: 65

A.K.Devaraj
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Old 2007-03-19, 04:53   #2
devarajkandadai
 
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Default Carmichael Numbers-UBs

The actual number of 3-factor Carmichael numbers, with 11 as one of
the factors, may be much less than 65.
Devaraj
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