[seqfan] On the infinity of Sophie Germain primes

[Chris]

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