*** SEARCH FOR NINE CONSECUTIVE PRIMES IN ARITHMETIC PROGRESSION ***

*** NEWSLETTER/4 ***

23 December 1997

Hello once again. This is Newsletter/4.

*** PROGRESS: Nine primes in Arithmetic Progression ***

Thanks to everybody for reporting your results and welcome 
to those who have joined recently. We now have 72 people 
(including the five of us) working on the problem. 

We have had 58 near misses, exceeding the expected number for 
a successful solution. Given that the probability that a 'k=9' 
solution is a 'hit 0' (or an ap=9 is a cp=9) is about 0.02, 
then the probability of no success for k near misses is 0.98^k. 
For k=58 (now), we get 31%, for k=100: 13%, for k=200: 2%. 

Ray Ballinger <root@ballingerr.xray.ufl.edu>
R 9 340547692363079 ap=9 cp=2 [P.P*P*P*P.P*P*P.P] 
R 9 340746891396007 ap=9 cp=5 [P.P.P.P.P*P*P*P.P] 

Bruce Biavatti
R 9 418190976673878 ap=9 cp=5 [P.P.P.P.P*P*P.P.P] 

James Buddenhagen
R 9 313551943553863 ap=9 cp=3 [P.P.P*P*P.P*P*P.P]

Stan Cohen
R 9 409107650676672 ap=9 cp=5 [P.P.P.P.P*P.P*P*P] 
R 9 409128886042763 ap=9 cp=4 [P.P.P.P*P.P.P*P*P] 

Harvey Dubner
R 9 400000508797243 ap=9 cp=5 [P*P.P.P.P.P*P.P.P] 
R 9 402224283386010 ap=9 cp=5 [P.P.P.P.P*P.P*P*P] 

Robert Dubner
R 9 404775492601035 ap=9 cp=3 [P*P*P.P*P*P.P.P*P] 
R 9 405901153999470 ap=9 cp=4 [P*P.P*P*P.P.P.P*P] 

Hubert Fauque
R 9 415050637639089 ap=9 cp=4 [P*P.P.P.P*P.P.P.P] 
R 9 415637612777076 ap=9 cp=2 [P.P*P*P.P*P.P*P*P] 

Tony Forbes
R 9 302582092752805 ap=9 cp=3 [P*P*P.P*P.P.P*P.P] 
R 9 302692436524493 ap=9 cp=4 [P.P.P.P*P.P*P.P.P] 
R 9 302906898816005 ap=9 cp=5 [P.P.P.P.P*P.P*P*P] 
R 9 304756042373705 ap=9 cp=3 [P.P*P.P.P*P*P*P.P] 
R 9 343094143543694 ap=9 cp=4 [P.P.P.P*P.P.P.P*P] 

Alain and Herve/ Groleau
R 9 250057630392811 ap=9 cp=2 [P.P*P*P*P*P.P*P.P]

Rick Heylen
R 9 438177862643515 ap=9 cp=4 [P.P*P.P.P.P*P*P*P] 

Becky & Greg Jaxon
R 9 328069176725833 ap=9 cp=5 [P.P*P*P*P.P.P.P.P] 

Mr Dennis S. Kluk
R 9 310541396835457 ap=9 cp=7 [P.P.P.P.P.P.P*P*P]

Paul Leunissen
R 9 428232431642070 ap=9 cp=2 [P.P*P.P*P*P*P*P.P] 

Torsten Metzner
R 9 226139828468252 ap=9 cp=5 [P*P.P*P*P.P.P.P.P] 
R 9 246861452584371 ap=9 cp=4 [P.P*P.P.P.P*P*P.P] 

Michel Mizony and Nik Lygeros
R 9 238560839501648 ap=9 cp=2 [P*P.P*P.P*P.P*P*P] 
R 9 225068386194867 ap=9 cp=4 [P.P.P.P*P.P.P*P*P] 
R 9 222870863019614 ap=9 cp=7 [P.P.P.P.P.P.P*P.P] 
R 9 255207304947344 ap=9 cp=2 [P*P.P*P*P.P*P*P*P]

Paul Nicholson
R 9 229588936903020 ap=9 cp=3 [P.P.P*P.P.P*P*P.P] 
R 9 240056180976390 ap=9 cp=2 [P.P*P*P.P*P*P*P*P] 
R 9 240614403401390 ap=9 cp=5 [P*P*P*P*P.P.P.P.P] 
R 9 261426734802900 ap=9 cp=2 [P*P.P*P*P*P.P*P*P]

Michel Quercia
R 9 233009952168708 ap=9 cp=5 [P.P.P.P.P*P*P*P*P] 
R 9 233319609748154 ap=9 cp=4 [P.P.P.P*P*P.P.P*P] 
R 9 233571893912031 ap=9 cp=2 [P.P*P.P*P*P.P*P.P] 
R 9 241383633852070 ap=9 cp=4 [P.P.P*P.P.P.P*P*P] 
R 9 241956398131452 ap=9 cp=4 [P*P*P*P.P.P.P*P.P] 
R 9 244034072310109 ap=9 cp=4 [P.P.P.P*P.P*P*P*P] 
R 9 248257374524554 ap=9 cp=6 [P*P.P.P.P.P.P*P.P] 
R 9 249472882024720 ap=9 cp=5 [P.P.P.P.P*P*P.P*P] 
R 9 264759565388846 ap=9 cp=7 [P.P.P.P.P.P.P*P*P] 
R 9 264458872928557 ap=9 cp=4 [P.P*P*P*P.P.P.P*P]
R 9 264811612305811 ap=9 cp=4 [P.P.P.P*P*P*P.P.P] 
R 9 269119298521119 ap=9 cp=4 [P*P*P.P.P*P.P.P.P] 
R 9 269930400869489 ap=9 cp=7 [P*P.P.P.P.P.P.P*P] 
R 9 271465920603158 ap=9 cp=2 [P.P*P*P.P*P.P*P.P] 
R 9 273957527123509 ap=9 cp=3 [P.P*P.P*P.P*P.P.P]
R 9 274048495127979 ap=9 cp=5 [P.P.P.P.P*P*P*P.P]

Gerald Ruescher 
R 9 305108859507098 ap=9 cp=4 [P.P.P*P.P.P.P*P*P] 
R 9 305307938469663 ap=9 cp=5 [P*P.P.P.P.P*P.P*P] 

Craig Stevenson
R 9 347054054201954 ap=9 cp=3 [P*P*P.P.P*P.P*P.P] 

Sturle Sunde
R 9 349188552182008 ap=9 cp=3 [P.P.P*P*P.P.P*P.P] 

Stefan Wehmeier
R 9 242650800387366 ap=9 cp=7 [P*P*P.P.P.P.P.P.P] 
R 9 242695575523580 ap=9 cp=8 [P.P.P.P.P.P.P.P*P] 
R 9 260644082004922 ap=9 cp=3 [P.P.P*P*P.P*P*P*P] 

Lou Weinfurtner
R 9 332241656305753 ap=9 cp=3 [P*P.P.P*P.P.P*P.P] 

Paul Zimmermann 
R 9 220214727578475 ap=9 cp=4 [P.P.P.P*P*P.P*P.P] 
R 9 221153832755059 ap=9 cp=7 [P.P.P.P.P.P.P*P*P] 
 
The asterisks denotes the presence of unwanted primes.

*** PROGRESS: Eight consecutive primes in Arithmetic Progression ***

Ray Ballinger
R 8 319020586663871 ap=8 cp=8 [C.P.P.P.P.P.P.P.P] 
R 8 319556796707163 ap=8 cp=8 [C.P.P.P.P.P.P.P.P] 

Bruce Biavati
R 8 418462289354440 ap=8 cp=8 [P.P.P.P.P.P.P.P.C] 

Harriet Dubner
R 8 401826849053806 ap=8 cp=8 [P.P.P.P.P.P.P.P.C]

Harvey Dubner
R 8 400088345825136 ap=8 cp=8 [C.P.P.P.P.P.P.P.P] 
R 8 402745620694208 ap=8 cp=8 [P.P.P.P.P.P.P.P*C] 

Robert Dubner
R 8 404323275143576 ap=8 cp=8 [C.P.P.P.P.P.P.P.P] 

Hubert Fauque
R 8 415357208288569 ap=8 cp=8 [P.P.P.P.P.P.P.P*C] 

Tony Forbes
R 8 303360676324814 ap=8 cp=8 [C*P.P.P.P.P.P.P.P] 

Rick Heylen
R 8 438200741959258 ap=8 cp=8 [P.P.P.P.P.P.P.P.C] 

Torsten Metzner
R 8 246740197360565 ap=8 cp=8 [P.P.P.P.P.P.P.P.C] 
R 8 246587533582294 ap=8 cp=8 [P.P.P.P.P.P.P.P.C] 

Michel Mizony and Nik Lygeros
R 8 220458527093293 ap=8 cp=8 [P.P.P.P.P.P.P.P*C] 
R 8 238613448197617 ap=8 cp=8 [P.P.P.P.P.P.P.P.C] 
R 8 238913241290933 ap=8 cp=8 [P.P.P.P.P.P.P.P.C] 
R 8 239483501258984 ap=8 cp=8 [P.P.P.P.P.P.P.P*C] 

Gerald Ruescher 
R 8 305619363859099 ap=8 cp=8 [P.P.P.P.P.P.P.P.C] 

Craig Stevenson
R 8 321173808733695 ap=8 cp=8 [C.P.P.P.P.P.P.P.P] 

Sturle Sunde
R 8 228862441305057 ap=8 cp=8 [P.P.P.P.P.P.P.P.C] 
R 8 309562765212360 ap=8 cp=8 [C*P.P.P.P.P.P.P.P] 

Emily & Stephen Tholberg
R 8 410756110351860 ap=8 cp=8 [P.P.P.P.P.P.P.P.C] 

Stefan Wehmeier
R 9 242695575523580 ap=9 cp=8 [P.P.P.P.P.P.P.P*P] 

Luke Welsh
R 8 312289387456697 ap=8 cp=8 [P.P.P.P.P.P.P.P.C] 

Paul Zimmermann
R 8 221236230528997 ap=8 cp=8 [P.P.P.P.P.P.P.P.C] 
R 8 220237184434352 ap=8 cp=8 [P.P.P.P.P.P.P.P.C] 

More details can be found at 

   http://www.loria.fr/~zimmerma/records/progress.html

*** NEW VERSION FOR PC/LINUX ***

Paul Zimmermann has released a new version of his program 
for Linux only, with 50% to 60% improvement for 586 and 686 
(up to 1650M/h on a K6-200), just changing by one line in the 
C source code (thanks to Paul Nicholson)!

The new program is primesAP.ppro.new.z and it can be 
downloaded from 

    ftp://ftp.loria.fr/pub/loria/eureca/tmp/9primes/

*** NEW VERSION OF CP09 ***

Sharp-eyed people may have noticed I have put CP09v221.ZIP 
online. I haven't advertised it; it was put there to solve a 
'no clock' problem reported by Manfred Toplic. There is no 
performance improvement, but it does allow you to set up the 
next range in advance and may be worth downloading for this 
reason. Go to

    http://www.ltkz.demon.co.uk/ar2/cp09v220.zip

*** TEN PRIMES ***

What about 10 primes after we are successful? Nik Lygeros 
and Michel Mizony have already started to investigate the 
optimum parameters, and the programs require only trivial 
modifications. We will need about 250 years on a Pentium 
120. Here are my [TF] thoughts: 

(i) 250 years is a long time but the project is certainly 
feasible.

(ii) Expect to spend six months with 500 computers. If we 
get more, so much the better. Gathering sufficient helpers 
will take several months and a lot of creative advertising. 
The whole project could easily span a year.

(iii) I'm sure we can squeeze a little more out of the 
computers. I have yet to investigate true Protected Mode 
on the PC. 

(iv) Finaly, the most persuasive argument for pushing ahead 
is that there is a natural boundary at 10. The extra 
constraint on 11 primes in arithmetical progression - the 
common difference must be a multiple of 2310 - means that 
11 will be extremely difficult with current technology. 
So, once we find it, the 10 primes record will hopefully 
stand for a long time to come. 

***

Happy hunting and Best Wishes,

Merry Christmas, 

Joyeux Noel, 

Harvey Dubner <70372.1170@compuserve.com>
Tony Forbes <tonyforbes@ltkz.demon.co.uk>
Paul Zimmermann <paul.zimmermann@loria.fr>
Nik Lygeros <lygeros@desargues.univ-lyon1.fr>
Michel Mizony <mizony@desargues.univ-lyon1.fr>