## Calculating Carmichael numbers

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• Using Korselt s original criterion as suggested by Peter Kosinar, to simply my calculation of Carmichael numbers, I have written function subroutines to
Message 1 of 1 , Dec 18, 2010
Using Korselt's original criterion as suggested by Peter Kosinar,
to simply my calculation of Carmichael numbers,

I have written function subroutines to calculate Carmichael numbers with
middle prime between two given primes.

Here is result with middle prime between 3 and 101.

Carmichael numbers with middle prime <= 101
[[3, 11, 17, 561]]
[[5, 13, 17, 1105], [7, 13, 19, 1729], [7, 13, 31, 2821]]
[[5, 17, 29, 2465]]
[[7, 19, 67, 8911]]
[[7, 23, 41, 6601]]
[[5, 29, 73, 10585]]
[[7, 31, 73, 15841]]
[[13, 37, 61, 29341], [13, 37, 97, 46657], [13, 37, 241, 115921]]
[[17, 41, 233, 162401]]
[[19, 43, 409, 334153]]

[[13, 61, 397, 314821], [31, 61, 211, 399001], [31, 61, 271, 512461],
[31, 61, 631, 1193221], [41, 61, 101, 252601]]
[[7, 73, 103, 52633], [37, 73, 109, 294409], [37, 73, 181, 488881], [37,
73, 541, 1461241], [41, 73, 137, 410041]]
[[53, 79, 599, 2508013]]
[[13, 97, 421, 530881]]
[[41, 101, 461, 1909001]]
['Carmical numbers with middle prime <= ', 101]

Notice that 47 is not the middle prime of any Carmichael number which is
the product of exactly three different primes.

Kermit
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