(Soft Question) Largest known Fermat Pseudoprime to a particular base

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I am aware that Carmichael Numbers can produce 300-billion-digit long absolute Fermat Pseudoprimes, which are Fermat Pseudoprimes to all coprime bases k. I was wondering if there are larger known Fermat Pseudoprimes that are only pseudoprime to say one coprime base k, or if the largest known Fermat Pseudoprimes are simply Carmichael Numbers, regardless of whether they are absolute.







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    Every composite Fermat number $F_n=2^2^n+1$ is a pseudoprime base 2.
    – gammatester
    Aug 14 at 7:39














up vote
0
down vote

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I am aware that Carmichael Numbers can produce 300-billion-digit long absolute Fermat Pseudoprimes, which are Fermat Pseudoprimes to all coprime bases k. I was wondering if there are larger known Fermat Pseudoprimes that are only pseudoprime to say one coprime base k, or if the largest known Fermat Pseudoprimes are simply Carmichael Numbers, regardless of whether they are absolute.







share|cite|improve this question
















  • 1




    Every composite Fermat number $F_n=2^2^n+1$ is a pseudoprime base 2.
    – gammatester
    Aug 14 at 7:39












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I am aware that Carmichael Numbers can produce 300-billion-digit long absolute Fermat Pseudoprimes, which are Fermat Pseudoprimes to all coprime bases k. I was wondering if there are larger known Fermat Pseudoprimes that are only pseudoprime to say one coprime base k, or if the largest known Fermat Pseudoprimes are simply Carmichael Numbers, regardless of whether they are absolute.







share|cite|improve this question












I am aware that Carmichael Numbers can produce 300-billion-digit long absolute Fermat Pseudoprimes, which are Fermat Pseudoprimes to all coprime bases k. I was wondering if there are larger known Fermat Pseudoprimes that are only pseudoprime to say one coprime base k, or if the largest known Fermat Pseudoprimes are simply Carmichael Numbers, regardless of whether they are absolute.









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asked Aug 14 at 7:30









Tejas Rao

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  • 1




    Every composite Fermat number $F_n=2^2^n+1$ is a pseudoprime base 2.
    – gammatester
    Aug 14 at 7:39












  • 1




    Every composite Fermat number $F_n=2^2^n+1$ is a pseudoprime base 2.
    – gammatester
    Aug 14 at 7:39







1




1




Every composite Fermat number $F_n=2^2^n+1$ is a pseudoprime base 2.
– gammatester
Aug 14 at 7:39




Every composite Fermat number $F_n=2^2^n+1$ is a pseudoprime base 2.
– gammatester
Aug 14 at 7:39















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