Wednesday, January 23, 2019

Carmichael Number



Primes are those which pass AKS primality test,
For pseudo-primes Carmichael raised the zest.

Integer factorization have some fundamental association,
Any prime factor of a Carmichael number have no repetition.

The search for pseudo-primes have various algorithms,
Because of RSA, Carmichael numbers obtain spatial attention.

It has been proved that all Carmichael numbers are odd,
The congruence relation makes this picture broad.

Alford et al. proved they are infinitely many ones,
The finding of smallest such number was a milestone.

At least three primes are always their factors,
The third Carmichael number is Hardy-Ramanujan number.

Their intimacy with prime is wondering Cryptographers,
Unlocking their secrets can open new prime chapters.







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