Newsletter 1, Newsletter 2, Newsletter 3 and Newsletter 4 from Tony Forbes.

News

Ranges of 10^12 values which are finished: 220-226, 229, 233-235, 237-241, 243-246, 249, 251, 253-259, 261-264, 267-268, 270-275, 277-283, 287-288, 293-294, 300-302, 304-305, 314, 317, 319-321, 324, 332, 335, 347-349, 352, 401-405, 411, 421, 437, 438, 500-507.

9 primes in AP found (not necessarily consecutive)

Remark: The expected number of such "near misses" is about 50 for one solution with no bad intermediate prime. The following table gives the expected number (and what we got so far) of "near misses" for one true solution (hit 0) for each "hit" value from 1 to 10.
k=9 hit 0 hit 1 hit 2 hit 3 hit 4 hit 5 hit 6 hit 7 hit 8 hit 9 hit 10 Total
expected 1 4 8 10 10 8 5 3 1 0.5 0.2 51
got 1 2 11 22 20 17 8 4 0 2 1 87
November 4: Harvey Dubner found 9 primes in AP, with only two bad intermediate primes (p+100 and p+1212), for N=400000508797243.

November 12: Paul Zimmermann found 9 primes in AP, with two bad intermediate primes (p+1348 and p+1566), for N=221153832755059. Torsten Metzner from Paderborn (Germany) found 9 primes in AP, with six bad intermediate primes (p+i for i=12, 598, 730, 792, 816, 838) for N=226139828468252.

November 14: Paul Zimmermann found 9 primes in AP, with three bad intermediate primes (p+730, p+856 and p+1368) for N=220214727578475.

November 17: Michel Quercia from Dijon (France) found 9 primes in AP, with five bad intermediate primes for N=233009952168708 (p+i for i=1008, 1108, 1236, 1332, 1632) and for N=233571893912031 (p+i for i=220, 730, 990, 1408, 1368).

November 19: Michel Quercia from Dijon (France) found 9 primes in AP, with three bad intermediate primes (p+732, p+918 and p+1582) for N=233319609748154. Harvey Dubner found 9 primes in AP, with six bad intermediate primes for N=402224283386010. Hubert Fauque, a PC helper from Montpellier (France), found 9 primes in AP with three bad intermediate primes for N=415050637639089.

November 23: Paul Nicholson reports 9 primes in AP with three bad intermediate primes for N=229588936903020.

November 24: Stan Cohen reports two 9-uples in AP with three bad intermediate primes for N=409107650676672 and N=409128886042763. Bruce Biavatti reports 9 primes in AP with three bad intermediate primes for N=418190976673878.

November 26: Michel Quercia reports 9 primes in AP with five bad intermediate primes for N=241956398131452. Becky and Greg Jaxon from Champaign (Illinois) report 9 primes in AP with three bad intermediate primes for N=328069176725833.

November 28: Michel Mizony and Nik Lygeros report 9 primes in AP with ten bad intermediate primes for N=238560839501648. Michel Quercia reports 9 primes in AP with four bad intermediate primes for N=241383633852070. Tony Forbes reports 9 primes in AP with five bad intermediate primes for N=302582092752805.

December 1: Paul Nicholson reports 9 primes in AP with seven bad intermediate primes for N=240056180976390, and with four bad intermediate primes for N=240614403401390. Stefan Wehmeier from Paderborn (Germany) reports 9 primes in AP with two bad intermediate primes for N=242650800387366, and with only one bad intermediate prime (p+1488) for N=242695575523580; the second one is also a new solution (11th one) to the 8-primes problem.

December 2: Michel Quercia reports 9 primes in AP with four bad intermediate primes for N=244034072310109. Tony Forbes reports 9 primes in AP with two bad primes for N=302692436524493.

December 4: Gerald Ruescher (alias Jerry) from Paderborn (Germany) reports 9 primes in AP with three bad intermediate primes for N=305108859507098, and with four bad intermediate primes for N=305307938469663.

December 5: Michel Quercia reports 9 primes in AP with two bad intermediate primes for N=248257374524554, Michel Mizony and Nik Lygeros 9 primes in AP with four bad intermediate primes for N=225068386194867. Torsten Metzner reports 9 primes in AP with four bad intermediate primes for N=246861452584371.

December 7: Michel Quercia reports 9 primes in AP with three bad intermediate primes for N=249472882024720, and Lou Weinfurtner from Ashland, Kentucky (USA) reports 9 primes in AP with three bad intermediate primes for N=332241656305753.

December 10: Stefan Wehmeier reports 9 primes in AP with five bad intermediate primes for N=260644082004922, Tony Forbes found 9 primes in AP with six bad intermediate primes for N=302906898816005, and Ray Ballinger found 9 primes in AP with nine bad intermediate primes for N=340547692363079.

December 11: Robert Dubner reports 9 primes in AP with six bad intermediate primes for N=404775492601035, and Paul Leunissen found 9 primes in AP with seven bad intermediate primes for N=428232431642070.

December 12: Michel Quercia found 9 primes in AP with two bad intermediate primes for N=264759565388846, and with three bad intermediate primes for N=264811612305811. Michel Mizony and Nik Lygeros found 9 primes in AP with only one bad intermediate prime (p+1410) for N=222870863019614 (too bad!), Tony Forbes 9 primes in AP with seven bad intermediate primes for N=304756042373705, Craig Stevenson 9 primes in AP with four bad intermediate primes for N=347054054201954, Robert Dubner found 9 primes in AP with five bad intermediate primes for N=405901153999470, and Hubert Fauque found 9 primes in AP with seven bad intermediate primes for N=415637612777076. What a lucky day !

December 13: Michel Quercia found 9 primes in AP with three bad intermediate primes for N=269930400869489.

December 14: Michel Quercia found 9 primes in AP with five bad intermediate primes for N=264458872928557.

December 15: Alain and Hervé Groleau found 9 primes in AP with six bad intermediate primes for N=250057630392811, and Paul Nicholson with six bad intermediate primes too for N=261426734802900.

December 16: Michel Quercia found 9 primes in AP with four bad intermediate primes for N=269119298521119.

December 17: Rick Heylen found 9 primes in AP with five bad intermediate primes for N=438177862643515.

December 18: Sturle Sunde found 9 primes in AP with four bad intermediate primes for N=349188552182008.

December 19: Michel Quercia found 9 primes in AP with six bad intermediate primes for N=271465920603158, Tony Forbes with two for N=343094143543694, Ray Ballinger with three for N=340746891396007 and Michel Mizony and Nik Lygeros with nine for N=255207304947344.

December 20: James Buddenhagen found 9 primes in AP with four bad intermediate primes for N= 313551943553863.

December 22: Michel Quercia found 9 primes in AP with five bad intermediate primes for N=273957527123509 and Nik Lygeros and Michel Mizony from Lyon (France) with two for N=255831931845191.

December 23: Michel Quercia found 9 primes in AP with three bad intermediate primes for N=274048495127979.

December 26: Michel Quercia found 9 primes in AP with three bad intermediate primes for N=275600537160456.

December 29: Michel Quercia found 9 primes in AP with five bad intermediate primes for N=279197288985660.

December 30: Michel Quercia found 9 primes in AP with four bad intermediate primes for N=279490711670429.

January 2: Craig Stevenson found 9 primes in AP with three bad intermediate primes for N=347759162806947, Michel Quercia with five bad intermediate primes for N=280890562451594, and Nik Lygeros and Michel Mizony with four for N=258593388104416.

January 3: Michel Quercia found 9 primes in AP with five bad intermediate primes for N=501078823074479.

January 5: Tony Forbes found 9 primes in AP with six bad intermediate primes for N=399816269077893 and Torsten Metzner with three bad intermediate primes for N=265744173727017 and Paul Nicholson with four for N=268583530908596.

January 6: Craig Stevenson found 9 primes in AP with five bad intermediate primes for N=347807968092117 and Sturle Sunde with three bad intermediate primes for N=349958760073914.

January 7 : Michel Quercia found 9 primes in AP with four for N=505003529654063.

January 9 : Nik Lygeros and Michel Mizony found 9 primes in AP with three bad intermediate primes for N=507382929206040, Michel Quercia with four for N=506025780283914, Craig Stevenson with two for N=358067348924929 and Jon Kierkegaard with three for N=290958736460603.

January 10 : Michel Quercia found 9 primes in AP with three bad intermediate primes for N=506433637675866, with four for N=293253744319118 and Jon Kierkegaard with four for N=290017561629624.

January 12 : Michel Quercia found 9 primes in AP with five bad intermediate primes for N=293576472812961 and Stefan Wehmeier with five for N=260644082004922 and Toplic Manfred with two for N=500814679548574.

January 13 : Heylen found 9 primes in AP with four bad intermediate primes for N=438917221194258 and Bernard Landreau with five for N=291245407253784.

January 14 : DENNIS S KLUK found 9 primes in AP with two bad intermediate primes for N=310541396835457.

January 15 : Nik Lygeros and Michel Mizony found 9 primes in AP with four bad intermediate primes for N=508331721014703 and with five for N=508343030687139. Robert Dubner found 9 primes in AP with four for N=445489240925339.

January 15 : at 15h. Toplic Manfred found 9 primes in AP (with null bad intermediate primes) for N=500996388736659, (i.e.p=996794320667010864844906536958535616389823640809916183957740485 85529071475461114799677694651);

January 17 : Vilmar Trevisan found 9 primes in AP with four bad intermediate primes for N=90017561629624.

Some 8 primes in AP found (not necessarily consecutive)

November 13: Paul Nicholson near from Manchester (UK) found 8 primes in AP, with six bad intermediate primes (p+i for i=310, 562, 1008, 1368, 1390, 1488) for N=229021132339400. Stefan Wehmeier from Paderborn (Germany) found 8 primes in AP, with two bad intermediate primes (p+46 and p+1566) for N=224207430775447.

November 14: Nik Lygeros and Michel Mizony from Lyon (France) found 8 primes in AP, with four bad intermediate primes (p+880, p+1302, p+1356, p+1642) for N=223501197073747. Paul Zimmermann found 8 primes in AP, with no intermediate prime, for N=221236230528997. This is the second known solution for 8 consecutive primes in arithmetic progression.

November 17: Paul Zimmermann found 8 primes in AP, with no intermediate prime, for N=220237184434352.

November 18: Sturle Sunde, a student at the University of Oslo (Norway), found 8 primes in AP, with two intermediate primes (p+492 and p+1108), for N=309261492595406. Paul Nicholson found 8 primes in AP with four intermediate primes for N=229379063220138, and with three intermediate primes (p+792, p+1356 and p+1360) for N=229336460744798. What a lucky day for him !

November 19: Nick Gorham from Leeds (UK), a colleague of Paul Nicholson, found 8 primes in AP with three intermediate primes for N=229267875976928.

November 20: Paul Nicholson found 8 primes in AP with two intermediate primes for N=229392402078958. Sturle Sunde from Norway found 8 primes in AP with no intermediate prime for N=228862441305057. This is the 4th known solution to the 8-primes problem.

November 21: Nik Lygeros and Michel Mizony from Lyon (France) found 8 primes in AP with three intermediate primes for N=225720432463328. Bernard Landreau from Bordeaux (France) found 8 primes in AP with two intermediate primes for N=234174882485574.

Craig Stevenson from Socorro, New Mexico (USA) reports 8 primes in AP with no intermediate prime for N=321173808733695; this is the 5th known solution to the 8-primes problem.

November 23: Tony Forbes reports some hits from PC helpers: Jean-Yves Canart from Silly (Belgium) found 8 primes in AP with three intermediate primes for N=314240589608328, and Luke Welsh from Sunnyvale, California (USA) found 8 primes in AP with only one intermediate prime (p+792) for N=312013123453568.

November 25: Toplic Manfred from Austria reports 8 primes in AP with 4 intermediate primes for N=317082542086489; please note that the first 7 primes are consecutive! Robert Dubner (Harvey's son) reports 8 primes in AP with no intermediate prime for N=404323275143576. This is the 6th known solution to the 8-primes problem.

November 26: Michel Mizony and Nik Lygeros report 8 primes in AP with no intermediate prime for N=220458527093293, and similarly Harvey Dubner for N=400088345825136. These are the 7th and 8th solutions to the 8-primes problem. Dennis S. Kluk reports 8 primes in AP with four intermediate primes for N=310174534321206, James Buddenhagen with one intermediate prime for N=313097064121256, and Toplic Manfred with three intermediate primes for N=317030494157387.

November 27: Tony Forbes found 8 consecutive primes in AP with N=303360676324814 (9th solution to the 8-primes problem).

November 28: Michel Mizony and Nik Lygeros report 8 primes in AP with no intermediate prime for N=238613448197617 (10th solution for 8 primes).

December 2: Michel Mizony and Nik Lygeros report 8 primes in AP with no intermediate prime for N=238913241290933 (12th solution for 8 primes). Hubert Fauque reports 8 consecutive primes in AP for N=415357208288569 (13th solution).

December 4: Michel Mizony and Nik Lygeros report 8 consecutive primes in AP for N=239483501258984 (14th solution).

December 5: Torsten Metzner reports 8 consecutive primes in AP for N=246740197360565 (15th solution).

December 7: Bruce Biavatti from Byack (New York) found 8 consecutive primes in AP for N=418462289354440 (16th solution).

December 8: Torsten Metzner reports 8 consecutive primes in AP for N=246587533582294 (17th solution), Gerald Ruescher (Jerry) for N=305619363859099 (18th), and Ray Ballinger for N=319020586663871 and 319556796707163 (19th and 20th). Cyril Aschenbrenner from Lyon (France) found 8 primes in AP with five bad intermediate primes for N=334133981208577 and N=334121938039256.

December 11: Alain and Hervé Groleau from Lyon (France) found 8 primes in AP with three bad intermediate primes for N=250012996718998, and with seven bad intermediate primes for N=250027066979226.

December 12: Luke Welsh found 8 consecutive primes in AP for N=312289387456697.

December 13: Sturle Sunde found 8 consecutive primes in AP for N=309562765212360, as did Harvey Dubner for N=402745620694208.

December 15: Emily and Stephen Tholberg, from Pagosa Springs (Colorado, USA) found 8 consecutive primes in AP for N=410756110351860. Jon Kierkegaard from Denmark reports 8 primes in AP with four bad intermediate primes for N=267024719778317. Francoise and Laurent Spagnesi from France report 8 primes in AP with two bad intermediate primes for N=232213211399336.

December 17: Rick Heylen found 8 consecutive primes in AP for N=438200741959258.

December 18: Bernard Landreau (Bordeaux) reports 8 primes in AP with one bad intermediate prime for N=245666455923468, 245719624775643. With two intermediate primes for N=245404027799115. With three bad intermediate primes for N=245598639390559, 245020108880246, 245728189153025. With five intermediate primes for N=245304468107831, 245109634770486.

December 19 : Chad Davis reports 8 primes in AP with three bad intermediate primes for N=423120008991892, with four bad intermediate primes for N=423151028531518 and five bad intermediate primes for N=423190249214800.

December 20: Harriet Dubner found 8 consecutive primes in AP for N=401826849053806. Cyril Banderier reports 8 primes in AP with one bad intermediate prime for N=243851833231955, with two bad intermediate primes for N=243325755778771, 243591960164191 and with three bad intermediate primes for N=243169577887257, 243924622209843.

December 24: Michael Taeschner reports 8 primes in AP with two bad primes for N=320764402657829 and three bad primes for N=320798912067448.

January 5: Paul Nicholson found 8 consecutive primes in AP for N=268982504413218.

January 6 : Michel Quercia found 8 consecutive primes in AP for N=502838172308698.

January 13 : Heylen found 8 consecutive primes in AP for N=438452017809603.

Other near misses

November 13: P. Zimmermann found N=221204904583321. If p+7*210 had been prime, this would have been a solution. By the way, this number seems to have very large factors.

November 25: M. Mizony and N. Lygeros found N=220515158330332. If p+7*210 had been prime, this would have been a solution.

December 22: M. Mizony and N. Lygeros found N=255812161211463. If p+7*210 had been prime, this would have been a solution.

December 23: Jean-Yves Canart found N=335805445305144. If p+210 had been prime, this would have been a solution.

January 7: Toplic Manfred found N=500507171112423. If p+210 had been prime, this would have been a solution.

January 15: Cyril Banderier found N=243009439045719. If p+7*210 had been prime, this would have been a solution.

New 7 consecutive primes in AP found

November 18: Stefan Wehmeier from Paderborn (Germany) found 7 consecutive primes in AP for N=224374802946759.

November 19: Michel Mizony and Nik Lygeros from Lyon (France) found 7 consecutive primes in AP for N=223291875083584.

November 21: Paul Nicholson found 7 consecutive primes in AP for N=229852712354663.

November 25: Michel Mizony and Nik Lygeros found 7 consecutive primes in AP for N=238171496314162. Michel Quercia found new solutions for N=237124256640106, N=237486571323214, N=235751617004478.

November 26: Michel Mizony and Nik Lygeros found 7 consecutive primes in AP for N=220515158330332, N=220532802549262 and N=238318072926332, Bernard Landreau also for N=234493022159199, Dennis S. Kluk for N=310033615940928 and N=310203750897302, James Buddenhagen for N=313066470571199, N=313113234174309 and N=313125156325843, Jean-Yves Canart for N=314207627176991, N=314221397333934, N=314098758652665, N=314537286876882 and N=314971655488468, Luke Welsh for N=312031945063874 and N=312034598384398.

November 27: Jan Roger Sandbakken found 7 consecutive primes in AP for N=324022080051914, N=324059591947553 and N=324161142429028, Michel Mizony and Nik Lygeros for N=220803683973333 and N=223178601181162.

November 29: Cyril Aschenbrenner from Lyon (France) found 7 consecutive primes in AP for N=334007034387862, Michel Quercia for N=241602067280004 and N=241075507294088.

December 1: Stefan Wehmeier found 7 consecutive primes in AP for N=242216730877382 and N=242346355413738.

December 2: Michel Mizony and Nik Lygeros found 7 consecutive primes in AP for N=221563724245086, Michel Quercia for N=244176871265110, N=244805638922005, N=244902299006292 and N=223371806491697. Bernard Landreau reports 7 consecutive primes in AP for N=245018768802318, N=245232136635788 and N=245422776210452. Tony Forbes reports 7 consecutive primes in AP for N=302676352566637. Jean-Yves Canart found 7 consecutive primes in AP for N=314551869345498, 314794106556640 and 314817356723173.

December 3: Kevin Mulholland, a colleague of Paul Nicholson, found 7 consecutive primes in AP for N=240317026505641. Elisha Peterson found 7 consecutive primes in AP for N=307101006764323.

December 4: Michel Mizony and Nik Lygeros found 7 consecutive primes in AP for N=239285250842075, 239421015331246, 239522450105014, and 223371806491697. Manfred Toplic found 7 consecutive primes in AP for N=242856400123097 and N=242856779606354. Craig Stevenson found 7 consecutive primes in AP for N=321075416201788, 321175233135617, 321281642161020, 321428915963488,321586938968054, 321618931302225 and 321778679343127.

December 5: Michel Mizony and Nik Lygeros found 7 consecutive primes in AP for N=225064673426187. Michael Taeschner reports 7 consecutive primes in AP for N=320022630749104, 320524244474271, 320605133930729 and 320624769464193. Stefan Wehmeier found 7 consecutive primes in AP for N=260048426749963.

December 6: Lou Weinfurtner from Ashland (USA) found 7 consecutive primes in AP for N=332222194931107. Michel Quercia found 7 consecutive primes in AP for N=248324532127784.

December 8: Michel Quercia found 7 consecutive primes in AP for N=249861788177577, Jan Roger Sandbakken for N=324366672903699, and Michel Mizony for N=225190518713535. Bernard Landreau found 7 consecutive primes in AP for N=245090253509345.

December 9: Manfred Toplic found 7 consecutive primes in AP for N=317545786555498, and Craig S. Stevenson for N=321934333505878.

December 10: Jan Roger Sandbakken found 7 consecutive primes in AP for N=324466096432206.

December 11: Alain and Hervé Groleau from Lyon (France) found 7 consecutive primes in AP N=250016910221813, Craig Stevenson for N=321075416201788, 321175233135617, 321281642161020, 321428915963488, 321586938968054, 321618931302225, 321778679343127 and 321934333505878, and Luke Welsh for N=312254794682126.

December 12: Manfred Toplic found 7 consecutive primes in AP for N=348502333003047.

December 13: Sturle Sunde found 7 consecutive primes in AP for N=309092082751974, 309144435051124, 309284809100092, 309456597285996, 309475490996231 and 309866092069137.

December 14: Chad Davis reports 7 consecutive primes in AP for N=423170393381008, and Michel Quercia for 264266218468246 and 264333292778392.

December 15: Alain and Hervé Groleau found 7 consecutive primes in AP for N=250016910221813, and Cyril Aschenbrenner for N=334173518110390, 334193626287646, 334198450087910 and 334201578451904.

December 16: Michel Quercia reports 7 consecutive primes in AP for N=269345758823235, 269359358129453, 269450368779724, 269040400197698, 269217651572060, and 269574769874795 and Jan Roger Sandbakken for N=324607131928718.

December 17: Luke Welsh reports 7 consecutive primes in AP for N=312329869067802 and Manfred Toplic for N=348067119885721.

December 18: Lou Weinfurtner reports 7 consecutive primes in AP for N=332222194931107, Manfred Toplic for N=348556502990749 and Bernard Landreau for N=245018768802318, 245232136635788, 245422776210452, 245090253509345, 245848082651377.

December 19: Manfred Toplic reports 7 consecutive primes in AP for N=348594013042624, Ray Ballinger for N=340009621006365, 340431150512728, 340460360378817, Chad Davis for N=423203413238072 and Keith Briggs for N=227092546159946.

December 20: James Buddenhagen reports 7 consecutive primes in AP for N=313572738058281, 313591613883251, 313636645094200, 313210775588722, 313320621593239, Cyril Banderier reports 7 consecutive primes in AP for N=243009439045719, 243039272347154 and 270634338425169.

December 22: Toplic Manfred reports 7 consecutive primes in AP for N=348116814727389.

December 23: Jean-Yves Canart reports 7 consecutive primes in AP for N=335153877733529, 335333226909944, 335383015992567, 335497987326844, 335618565776047, 335883235198068 and 335904842676187.

December 26: Rick Heylen reports 7 consecutive primes in AP for N=437837918353382.

December 29: Sturle Sunde found 7 consecutive primes in AP for N=263091607297737 and N=263663442620467.

January 2: Kevin O'Hare reports 7 consecutive primes in AP for N=449005010972020 and Jan Roger Sandbakken for N=324773963579207 and N=324988356596358.

January 5 : Vilmar Trevisan reports 7 consecutive primes in AP for N=266950782320918.

January 6 : Michael Taeschner reports 7 consecutive primes in AP for N=320022630749104, 320524244474271, 320605133930729, 320624769464193, 320829397783191 and 320862143309957.

January 7 : Ray Ballinger reports 7 consecutive primes in AP for N=352148596532302, 352149496793744, 352271328184946, 352371277932969, 352489030177472, 352749744874863, 352806823884291, 352848822787215.

January 9 : Torsten Metzner reports 7 consecutive primes in AP for N=265936818259956.

January 12 : Jan Roger Sandbakken reports 7 consecutive primes in AP for N=356090783143575.

January 14 : DENNIS S KLUK reports 7 consecutive primes in AP for N=310523497582061.

January 20 : Bernard Landreau reports 7 consecutive primes in AP for N=291243173169631.