- -------- Original Message --------

Subject: SEQ FROM Roger L. Bagula

Date: Mon, 29 Sep 2003 22:15:22 -0400 (EDT)

From: <njas@...>

Reply-To: tftn@...

To: njas@...

CC: tftn@...

The following is a copy of the email message that was sent to njas

containing the sequence you submitted.

All greater than and less than signs have been replaced by their html

equivalents. They will be changed back when the message is processed.

This copy is just for your records. No reply is expected.

Subject: NEW SEQUENCE FROM Roger L. Bagula

%I A000001

%S A000001 1,0,1,1,2,2,3,4,6,5,7,7,8,9,11,11,12,12,13,13,15,15,17,19,19,20,21,20,21,23,

24,26,26,28,29,29,30,31,32,33,33,34,35,35,35,37,40,41,41,42,43,42,44,46,47,48,

48,48,49,48,50,54,54,54,55,57,58,60,61,60,61,62,63,64,65,66,68,67,69,71,71,72,

72,73,74,75,77,76,76,77,79,81,82,83,84,84,86,86,90,90,92,92,93,93,94,95,96,96,

96,97,98,98,98,100,102,103,103,104,105,105,108,108,109,111,112,113,115,116,

117,117,118,119,120,121,122,122,124,125,127,127,129,129,130,130,132,134,135,

134,135,136,137,137,138,141,142,142,144,145,146,147,148,149,150,151,152,152,

153,155,156,157,157,158,158,159,160,161,162,161,162,165,165,165,166,167,168,

169,170,171,175,174,176,176,178,179,180,180,182,181,182

%N A000001 A primes distribution difference from asymtotic sequence

%C A000001 This sequence is extremely linear.

%F A000001 a[n_]=-PrimePi[n]+Floor[Prime[n]/Log[n]]-2

%t A000001 Digits=200

a[n_]=-PrimePi[n]+Floor[Prime[n]/Log[n]]-2

b=Table[a[n],{n,2,Digits}]

%O A000001 2

%K A000001 ,nonn,

%A A000001 Roger L. Bagula (tftn@...), Sep 29 2003

RH

RA 209.179.241.6

RU

RI

--

Respectfully, Roger L. Bagula

tftn@..., 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :

URL : http://home.earthlink.net/~tftn

URL : http://victorian.fortunecity.com/carmelita/435/

[Non-text portions of this message have been removed] - Russell sent me Phil's message with p=13 and p=17!

Here is this message with my editings

(sorry Phil!)

%%%%%%%

NMBRTHRY archives -- November 2001 (#9)

Date: Wed, 7 Nov 2001 09:17:30 -0500

Reply-To: Phil Carmody <fatphil@...>

Sender: Number Theory List <NMBRTHRY@...>

From: Phil Carmody <fatphil@...>

Subject: Prime-producing Linear Polynomials

The linear polynomial

f(X) = dX+q

can have at most q successive terms f(0)...f(q-1) prime, (and q must

be prime for f(0) to be prime, evidently). It remains an open

question, and one with few data-points, whether such maximal q-based

q-length Arithmetic Progressions exist for every q.

q=3, d=2 yield the primes 3,5,7;

q=5, d=6 yield the primes 5,11,17,23,29;

q=7, d=150 yield the primes 7,157,307,457,607,757,907.

In 1986, Löh discovered for q=11 d=1536160080, and for q=13

d=9918821194590.

[The above was a synthesis of what Paulo Ribenboim has in The New Book

of Prime Number Records]

At the start of 2001 I started tackling the q=17 problem, and I wrote

some brute force code to attack it. The code was peppered with bugs,

and despite finding a record Cunningham Chain with the broken code

http://listserv.nodak.edu/scripts/wa.exe?A2=ind0103&L=nmbrthry&P=R423

I gave up both on the project and the code.

However, I recently encountered other tasks which seemed like a good

target for the code, and easier than the Arithmetic Progression

problem, and resolved to de-mothball the code. Within a day of

thinking this, Tom Hadley posted the very result I thought I might

search for - a minimal 15-tuple ( http://www.ltkz.demon.co.uk/kt15.txt

). Rather than kill the idea, this encouraged me!

So I (think I) fixed the bugs, and started the search again. After

roughly 5 days on a single 533MHz Alpha (21164), I found the following

result, finally toppling the 15-year-old record.

The record is now

q=17 d=341976204789992332560

And the primes are

<skip>

q=19 anyone?

(The scaling factors indicate that it might be possible with a

collaborative effort, and my code parallelises)

Thanks go to Tom Hadley for giving me a massive kick up the arse last

week and to Paul Jobling who has been a useful resource on how to

apply intelligence to brute force problems since the project began.

Phil

%%%%%%%%%%%%5

--- In primenumbers@yahoogroups.com, "Zak Seidov" <seidovzf@y...>

wrote:> Yes, Richard and Ken,

wrote:

> there is mistake -

> on my side,

> my "d" is larger than yours...

> Zak

>

> --- In primenumbers@yahoogroups.com, "Ken Davis" <kraden@y...>

> > This is posted on behalf of

<seidovzf@y...>

> > richyfortythree

> > cheers

> > Ken

> > > By my calculation the smallest d for p=11 is

> > > 1536160080. Have I

> > > made a

> > > mistake?

> >

> > 1536160080 is also what I get. (Same mistake maybe?)

> >

> > Cheers

> >

> > richyfourtythree

> >

> >

> > --- In primenumbers@yahoogroups.com, "mad37wriggle"

> > <fitzhughrichard@h...> wrote:

> > >

> > > By my calculation the smallest d for p=11 is 1536160080. Have I

> > made a

> > > mistake?

> > >

> > > Richard

> > >

> > >

> > > --- In primenumbers@yahoogroups.com, "Zak Seidov"

> > > wrote:

P

> > > > This is copy of my post

> > > > (sorry for those reading this twice):

> > > >

> > > > For p=11,

> > > > minimal d = 4911773580 (OEIS A088430),

> > > > and AP contains maximal number, 11, primes.

> > > >

> > > > For p=13, d should be a factor of 2310.

> > > > Who first find it (and then try 17,19,...)?

> > > > Zak

> > > >

> > > >

> > > > BTW I guess that found d is indeed minimal not unique-

> > > > there is no reason of absense of other larger d's.

> > > >

> > > >

> > > > On 28 Sep 2003, Russell E. Rierson wrote

> > > > (http://www.mathforum.org/discuss/sci.math/m/133406/540774):

> > > > >Twin primes are prime numbers such as 5 and 7, 11 and 13, 17

> and

> > 19,

> > > > >etc. These twins are only one unit apart.

> > > > >

> > > > >There are strings of prime numbers that are n-units apart:

> > > > >

> > > > >3, 5, 7, [3 prime numbers, 2 units apart]

> > > > >

> > > > >5, 11, 17, 23, 29, [5, 6 units]

> > > > >

> > > > >7, 157, 307, 457, 607, 757, 907, [7, 150 units]

> > > > >

> > > > >11... ? ...? ...? ...

> > > > >

> > > > >The question becomes: For all odd prime numbers P, are there

> > > > number of

> > > > >primes that are the same numerical[equal] distance apart?