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 square-free (C = (product of)(p_i^a_i), a_i = 1 for all i)

d) C is such that (C-1)@(p-1) = 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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