Nayan Hajratwala wrote:
>
> problem; I need to find the largest known prime of the form:
> (2^2^n)+1
> congratulations by the way on finding the largest Mersenne prime!!!
These are Fermat numbers, Fermat conjectured that all numbers of this form
would be prime and proved it for
F_0=3, F_1=5, F_2=17, F_3=257,F4=65537.
However, not a single prime beyond those 5 has been found so far, all 4 < n
<31, and many >31, are proved composite. It is commonly believed that indeed
there is not a single Fermat prime except the first five. Find another one
and you'll be famous!
See http://www.perfsci.com/prizes.html for a Fermat factoring contest,
www.mersenne.org/ecmg.htm for current ECM factoring limits on Fermat numbers,
and http://vamri.xray.ufl.edu/proths/fermat.html for overall status of Fermat
numbers (prime, genuine composites, some factors known, completely factored)
Ciao,
Alex.
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