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Old 2019-09-14, 13:11   #1
devarajkandadai's Avatar
May 2004

4748 Posts
Default Algorithm for combining Carmichael numbers

We can combine two Carmichael numbers to form another Carmichael number.
An example: 1729 = 7*13*19
294409 = 37*73*109
Both are of type (6m+1)(12m+1)(18m+1); we get the first by putting m = 1 and the second by putting m = 6.
First step: Check whether for any given value of m, 6m+1, 13m+1 and 18m+1 are primes.If for two given values of m, we get two Carmichael numbers by applying Korselt's criterion. If so their product will be a Carmichael number subject to satisfaction of Korselt's criterion.
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