2007-03-18, 03:22 | #1 |
May 2004
2^{2}×79 Posts |
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 |
2007-03-19, 04:53 | #2 |
May 2004
2^{2}×79 Posts |
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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