Problems & Puzzles:
Problems
Problem
24. Carmichael Numbers
A number C
is a 'Carmichael number' if and only if:
a) C is odd
b) C is a composite, having
more than two prime factors
c) C is squarefree
(C = (product of)(p_{i}^a_{i}), a_{i}
= 1 for all i)
d) C is such that (C1)@(p1)
= 0 for all its p.
Questions:

Does exist a Carmichael Number that is the product of 3
or more consecutive primes?
 101101 is the first Carmichael palindrome. Find 5 more of these
numbers.
On feb. 2007 Anton Vrba pointed out that the second
Carmichael palindrome ( 127665878878566721, author? ) was published
here.
So after 127665878878566721 we need only two more
terms to finish the homework.
BTW see
WON 124 to
discover another sequence where 127665878878566721 is the 4th term.
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