- http://arxiv.org/abs/1305.6289

Very readable and nice.

Also claims a result I had conjectured here before (I had

outlined a proof using Zhang, but never checked that the proof plan could

really be carried through)

is indeed true: there are infinitely many "de Polignac numbers."

One of the most impressive claims in Pintz's paper is this. Let a "near twin"

prime p be a prime p such that p,q are two primes with p<q<p+70000000.

Then: the near-twin primes contain arbitrarily long arithmetic progressions. > http://arxiv.org/abs/1305.6289

--So those of you who keep finding long APs with prime entries only, might

> One of the most impressive claims in Pintz's paper is this. Let a "near twin"

> prime p be a prime p such that p,q are two primes with p<q<p+70000000.

>

> Then: the near-twin primes contain arbitrarily long arithmetic progressions.

instead seek long APs with twin-prime entries only (a task which

ought to be accomplishable using similar methods).- WarrenS wrote:
> seek long APs with twin-prime entries only

Paul Jobling found 10 twin primes in AP in 2000:

https://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0001&L=NMBRTHRY&F=&S=&P=8002

http://www.primepuzzles.net/puzzles/puzz_121.htm

I don't know whether his record has been broken.

--

Jerns Kruse Andersen - --- In primenumbers@yahoogroups.com, "Jens Kruse Andersen" <jens.k.a@...> wrote:
>

--oh. I was about to mention the following twin-prime arithmetic progressions

> WarrenS wrote:

> > seek long APs with twin-prime entries only

>

> Paul Jobling found 10 twin primes in AP in 2000:

> https://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0001&L=NMBRTHRY&F=&S=&P=8002

> http://www.primepuzzles.net/puzzles/puzz_121.htm

> I don't know whether his record has been broken.

>

> --

> Jerns Kruse Andersen

which however are shorter than Jobling's:

start=3, gap=2, #terms=2

start=5, gap=6, #terms=3

start=5, gap=12, #terms=4

start=11, gap=13222650, #terms=5

start=17, gap=6930, #terms=5

start=11, gap=569460150, #terms=6

start=311, gap=1667820, #terms=6

start=1049, gap=643896330, #terms=7

start=191339, gap=16170, #terms=7

start=451277, gap=15248310, #terms=8

start=1767419, gap=5897430, #terms=8

start=3005291, gap=1517670, #terms=8

which I found in about 30 minutes using a very stupid search.

Jobling finds 10 APs with 10 twin primes each,

and conjectures there is a maximum length of such an AP.

But Pintz's theorem (if believe him) now disproves Jobling's conjecture

at least if the definition of "twin" prime is no longer (p, p+2) but rather

(p, p+SuitableAbsoluteConstant).

I do not think it would be too difficult to break Jobling's "10" record,

if anybody were willing to put in the effort. Jobling's search took 40 days

on a 233 MHz machine. Finding one of length 11 ought to be only

about 50 times harder using his method, but I would think there might be

better search methods partly based on sieving. > > Paul Jobling found 10 twin primes in AP in 2000:

--and after a few hours:

> > https://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0001&L=NMBRTHRY&F=&S=&P=8002

> > http://www.primepuzzles.net/puzzles/puzz_121.htm

> --oh. I was about to mention the following twin-prime arithmetic progressions

> which however are shorter than Jobling's:

>

> start=3, gap=2, #terms=2

> start=5, gap=6, #terms=3

> start=5, gap=12, #terms=4

> start=11, gap=13222650, #terms=5

> start=17, gap=6930, #terms=5

> start=11, gap=569460150, #terms=6

> start=311, gap=1667820, #terms=6

> start=1049, gap=643896330, #terms=7

> start=191339, gap=16170, #terms=7

> start=451277, gap=15248310, #terms=8

> start=1767419, gap=5897430, #terms=8

> start=3005291, gap=1517670, #terms=8

>

> which I found in about 30 minutes using a very stupid search.

start=14471111, gap=156791250, #terms=9

it looks like my stupid search method actually is comparable in efficiency to Jobling's search method. (Rather to my surprise, since his seemed less stupid on the face of it.)