[seqfan] Re: On the infinity of Sophie Germain primes

[Benoît Jubin]

I do not see how this follows from Motohashi's (not Hiratoshi) result
http://matwbn.icm.edu.pl/ksiazki/aa/aa17/aa1736.pdf
However, a weaker result that follows from Motohashi's and is enough to
produce prime partitionable numbers with the same recipe as in the
Trotter-Erdos article is the following, if I'm not mistaken:
there exist infinitely many prime pairs p_1, p_2 with p_2 = 1 (mod p_1) and
p_1 < p_2 < p_1^2 -p_1.

Best regards,
Benoît

On Fri, Aug 14, 2015 at 3:37 PM, Chris <cgribble263 at btinternet.com> wrote:

> Dear Seqfans,
>
>
>
> https://en.wikipedia.org/wiki/Sophie_Germain_prime and
> http://mathworld.wolfram.com/SophieGermainPrime.html both refer to
> Hoffman,
> P. The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search
> for Mathematical Truth.
> <http://www.amazon.com/exec/obidos/ASIN/0786863625/ref=nosim/weisstein-20>
> New York: Hyperion, p. 190, 1998 in which it is stated that the conjecture
> that there are infinitely many Sophie Germain primes remains unproven.
>
>
>
> However, in W. T. Trotter, Jr. and Paul Erdős,
> <https://www.renyi.hu/~p_erdos/1978-49.pdf> When the Cartesian product of
> directed cycles is Hamiltonian, J. Graph Theory 2 (1978) 137-142
> DOI:10.1002/jgt.3190020206, p. 141, it is proved that there are infinitely
> many prime-partitionable numbers.  The proof relies on a theorem by
> Hirotashi from which follows that there exist infinitely many prime pairs
> p1, p2 with p1 > 3 for which p2 = 2p1 + 1.  Doesn't this imply that there
> are infinitely many Sophie Germain primes?
>
>
>
> Best regards,
>
> Chris Gribble
>
>
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