THE RESULT
On January the 15 at 3 p.m. Manfred Toplic found 9 consecutive primes in AP for N=500996388736659. The first prime is p=99679432066701086484490653695853561638982364080991618395774048585529071475461114799677694651.
The primality of the nine numbers p, p+210, …, p+1680 was checked independently by François Morain using his ECPP program. The prime certificates are available from ftp://lix.polytechnique.fr/pub/submissions/morain/Tmp, files p1.certif to p9.certif.
Other results
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 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 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 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);
27 New 8 consecutive primes in AP
November 14: Paul Zimmermann N=221236230528997.
November 17: Paul Zimmermann N=220237184434352.
November 20: Sturle Sunde N=228862441305057.
November 21: Craig Stevenson N=321173808733695.
November 25: Robert Dubner N=404323275143576.
November 26: Nik Lygeros and Michel Mizony N=220458527093293. Harvey Dubner N=400088345825136.
November 27: Tony Forbes N=303360676324814.
November 28: Nik Lygeros and Michel Mizony N=238613448197617.
December 2: Hubert Fauque N=415357208288569. Nik Lygeros and Michel Mizony N=238913241290933.
December 4: Nik Lygeros and Michel Mizony N=239483501258984.
December 5: Torsten Metzner N=246740197360565.
December 7: Bruce Biavatti N=418462289354440.
December 8: Torsten Metzner N=246587533582294. Gerald Ruescher (Jerry) N=305619363859099. Ray Ballinger N=319020586663871 and N=319556796707163.
December 12: Luke Welsh N=312289387456697.
December 13: Sturle Sunde N=309562765212360. Harvey Dubner N=402745620694208.
December 15: Emily and Stephen Tholberg N=410756110351860. December 17: Rick Heylen N=438200741959258.
December 20: Harriet Dubner N=401826849053806.
January 5: Paul Nicholson N=268982504413218.
January 6 : Michel Quercia N=502838172308698.
January 13 : Rick Heylen N=438452017809603.
New 7 consecutive primes in AP
November 18: Stefan Wehmeier N=224374802946759.
November 19: Nik Lygeros and Michel Mizony N=223291875083584.
November 21: Paul Nicholson N=229852712354663.
November 25: Nik Lygeros and Michel Mizony N=238171496314162. Michel Quercia N=237124256640106, 237486571323214, 235751617004478. Toplic Manfred N=317082542086489.
November 26: Nik Lygeros and Michel Mizony N=220515158330332, 22053280254926,238318072926332. Bernard Landreau N=234493022159199. Dennis S. Kluk N=310033615940928, 310203750897302. James Buddenhagen N=313066470571199, 313113234174309, 313125156325843. Jean-Yves Canart N=314207627176991, 314221397333934, 314098758652665, 314537286876882, 314971655488468. Luke Welsh N=312031945063874, 312034598384398.
November 27: Jan Roger Sandbakken N=324022080051914, 324059591947553, 324161142429028. Nik Lygeros and Michel Mizony N=220803683973333, 223178601181162.
November 29: Cyril Aschenbrenner N=334007034387862. Michel Quercia N=241602067280004, 241075507294088.
December 1: Stefan Wehmeier N=242216730877382, 242346355413738.
December 2: Nik Lygeros and Michel Mizony N=221563724245086, Michel Quercia N=244176871265110, 244805638922005, 244902299006292, 223371806491697. Bernard Landreau N=245018768802318, N=245232136635788, N=245422776210452. Tony Forbes N=302676352566637. Jean-Yves Canart N=314551869345498, 314794106556640, 314817356723173.
December 3: Kevin Mulholland N=240317026505641. Elisha Peterson N=307101006764323.
December 4: Nik Lygeros and Michel Mizony N=239285250842075, 239421015331246, 239522450105014, and 223371806491697. Manfred Toplic N=242856400123097, N=242856779606354. Craig Stevenson N=321075416201788, 321175233135617, 321281642161020, 321428915963488,321586938968054, 321618931302225, 321778679343127.
December 5: Nik Lygeros and Michel Mizony N=225064673426187. Michael Taeschner N=320022630749104, 320524244474271, 320605133930729 and 320624769464193. Stefan Wehmeier N=260048426749963.
December 6: Lou Weinfurtner N=332222194931107. Michel Quercia N=248324532127784.
December 8: Michel Quercia N=249861788177577. Jan Roger Sandbakken N=324366672903699. Nik Lygeros andMichel Mizony N=225190518713535. Bernard Landreau N=245090253509345.
December 9: Manfred Toplic N=317545786555498. Craig S. Stevenson N=321934333505878.
December 10: Jan Roger Sandbakken N=324466096432206.
December 11: Alain and Hervé Groleau N=250016910221813. Craig Stevenson N=321075416201788, 321175233135617, 321281642161020, 321428915963488, 321586938968054, 321618931302225, 321778679343127 and 321934333505878. Luke Welsh N=312254794682126.
December 12: Manfred Toplic N=348502333003047.
December 13: Sturle Sunde N=309092082751974, 309144435051124, 309284809100092, 309456597285996, 309475490996231, 309866092069137.
December 14: Chad Davis N=423170393381008. Michel Quercia N=264266218468246, 264333292778392.
December 15: Alain and Hervé Groleau N=250016910221813. Cyril Aschenbrenner N=334173518110390, 334193626287646, 334198450087910, 334201578451904.
December 16: Michel Quercia N=269345758823235, 269359358129453, 269450368779724, 269040400197698, 269217651572060, 269574769874795. Jan Roger Sandbakken N=324607131928718.
December 17: Luke Welsh N=312329869067802. Manfred Toplic N=348067119885721.
December 18: Lou Weinfurtner N=332222194931107. Manfred Toplic N=348556502990749. Bernard Landreau for N=245018768802318, 245232136635788, 245422776210452, 245090253509345, 245848082651377.
December 19: Manfred Toplic N=348594013042624. Ray Ballinger N=340009621006365, 340431150512728, 340460360378817. Chad Davis N=423203413238072. Keith Briggs N=227092546159946.
December 20: James Buddenhagen N=313572738058281, 313591613883251, 313636645094200, 313210775588722, 313320621593239, Cyril Banderier N=243009439045719, 243039272347154 and 270634338425169.
December 22: Toplic Manfred N=348116814727389.
December 23: Jean-Yves Canart N=335153877733529, 335333226909944, 335383015992567, 335497987326844, 335618565776047, 335883235198068 and 335904842676187.
December 26: Rick Heylen N=437837918353382.
December 29: Sturle Sunde N=263091607297737, 263663442620467.
January 2: Kevin O’Hare N=449005010972020. Jan Roger Sandbakken N=324773963579207, 324988356596358.
January 5 : Vilmar Trevisan N=266950782320918.
January 6 : Michael Taeschner N=320022630749104, 320524244474271, 320605133930729, 320624769464193, 320829397783191 and 320862143309957.
January 7 : Ray Ballinger N=352148596532302, 352149496793744, 352271328184946, 352371277932969, 352489030177472, 352749744874863, 352806823884291, 352848822787215.
January 9 : Torsten Metzner N=265936818259956.
January 12 : Jan Roger Sandbakken N=356090783143575.
January 14 : DENNIS S KLUK N=310523497582061.