13176Re: [PrimeNumbers] Re: Prime Number Progresions
- Aug 5, 2003
> > Perhaps 2x^2 + 29 generates the longest sequenceIf we restrict to two term equations then it can't be
> of consecutive
> > primes of any two term equation.
> If you believe the first Hardy-Littlewood Conjecture
> (also known
> as the k-tuple Conjecture), there exist arbitrarily
> long sequences
> of primes from two term equations.
of the form 2x^2+p since of a proof (referred to on
Wolfram site) which shows that this type of sequence
can only yield 29 primes.
This implies we must look at ax^2+p for a>2. What
would be interesting is to rule out some more values
for a. I might look at this if I get some spare time.
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