Programming contest: Prime generating polynomials

Max maxale at gmail.com
Mon Mar 27 08:39:07 CEST 2006


On 3/26/06, Dean Hickerson <dean at math.ucdavis.edu> wrote:
> > 2) In some russian book (not that old) I have read that the existence> > of p other than 2, 3, 5, 11, 17, 41 such that f(x) generates primes> > for x=0,...,p-2 is an open problem, and it is proved that there is no> > other p for p<10^9.>> > This was really confusing to me. It is not an open problem for almost> > a hundred years already, and the answer to it is negative. It is very> > sad that such unjustified things somehow get published.>> The problem hasn't been solved for that long.  In 1952, Kurt Heegner proved> that only nine imaginary quadratic number fields exist with class number 1,> but his proof was not accepted as complete at the time.  For some discussion> of the history, see postings 123, 125, 127, 129, 131, 136, and 165 at:>>   http://www.maa.org/scripts/WA.EXE?A1=ind9812&L=math-history-list&D=0&O=D&T=0
Thanks for the correction and links.
> When was the Russian book published?
It was published in 1998. The actual title is
Школьные олимпиады. Международные математические олимпиады / Сост.А.А.Фомин, Г.М.Кузнецова. - М.: Дрофа, 1998.
(direct translation: School olympiads. International mathematicalolympiads. / Editors A.A.Fomin and G.M.Kuznetsov. Drofa, Moscow 1998.)
Note also that year 1998 is a computer era, so if it were a real openproblem it would have been verified for much greater bound than 10^9.It takes about 10 minutes here to check up all primes p<10^9. So thestatement about an open problem looks like someone's fantasy.
Max





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