RoseCode

Problem #405

Carmichael chains
 Public ★(x8) 06/29/17 by Philippe_57721 6xp Programming 72.7%

A Carmichael number is a chain if when we remove repeatedly its largest factor, we still obtain a Carmicheal number.

$174470590282430768272287350512321$ is a Carmichael chain of length 10 (it has 10 factors).

$174470590282430768272287350512321 = 7 . 13 . 31 . 61 . 181 . 541 . 2161 . 187921 . 3570481 . 7140961$
$24432368456070656074481761 = 7 . 13 . 31 . 61 . 181 . 541 . 2161 . 187921 . 3570481$
$6842878720281848881 = 7 . 13 . 31 . 61 . 181 . 541 . 2161 . 187921$
$36413592521761 = 7 . 13 . 31 . 61 . 181 . 541 . 2161$
$16850343601 = 7 . 13 . 31 . 61 . 181 . 541$
$31146661 = 7 . 13 . 31 . 61 . 181$
$172081 = 7 . 13 . 31 . 61$
$2821 = 7 . 13 . 31$
All these numbers are Carmichael numbers.

Of course, we stop at 3 factors, as a Carmichael number can't have less than 3 factors.

Find the next Carmichael chain of length 10. We assume that no factor is greater than $10^{7}$.

[My timing: 60 sec]

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