PRP Records

Probable Primes Top 10000

(271019 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
2512^1195093+1882577359759Enzo Doria12/2016
252(6^461108-11)/5358812Paul Bourdelais04/2019
2532^1191375+8543358640Phil Moore06/2008
2542^1190972+1880191358519Enzo Doria11/2016
255(45^216551-1)/44358004Paul Bourdelais08/2020
256(50^210319-1)/49357324Paul Bourdelais08/2020
2572^1179836+1885021355167Enzo Doria02/2017
258(63^195893-1)/62352477Paul Bourdelais08/2020
259numbpart(100000135540)352269Serge Batalov04/2017
260(10^352237-1)/9/10567111/950335427352221Maksym Voznyy01/2015
2612^1168554+783529351770Enzo Doria01/2017
262(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
2632^1166152+1882411351047Enzo Doria12/2016
2642^1162154+1890207349844Enzo Doria08/2017
265(7*10^348724-61)/9348724Erik Branger09/2016
266(127^165601-1)/126348390Alexander Zhirkov09/2015
2672^1153083+1883693347113Enzo Doria04/2017
268(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
2692^1145882+80779344945Enzo Doria09/2016
2702^1136462+1887289342110Enzo Doria05/2017
271F(1636007)341905Henri Lifchitz03/2009
2722^1133678+782569341272Enzo Doria11/2016
273(11^327001+1)/12340536Paul Bourdelais09/2013
274(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
275Tau(907^20848)339132Nik Lygeros / Olivier Rozier01/2016
2762^1126380-3339075Paul Bourdelais06/2019
2772^1125446+1885099338794Enzo Doria08/2017
2782^1124549+143807338523Enzo Doria10/2016
2792^1121187+1886783337511Enzo Doria04/2017
280(48^200443-1)/47336992Paul Bourdelais08/2020
281(94^170371-1)/93336162Paul Bourdelais09/2020
2822^1116184+1883521336005Enzo Doria02/2017
2832^1114517+1880087335504Enzo Doria10/2016
284(3^700897+1)/4334413Paul Bourdelais04/2010
2852^1104408-114539332460Enzo Doria03/2015
2862^1101921+82085331712Enzo Doria10/2016
2872^1100655+683513331331Enzo Doria01/2017
288(10^330906+71)/9330906Serge Batalov07/2015
2892^1098346+482899330636Enzo Doria11/2016
2902^1095679+1878713329833Enzo Doria09/2016
2912^1094740-1851539329550Enzo Doria08/2015
2922^1091469-379369328565Enzo Doria03/2014
293(69^178093-1)/68327485Paul Bourdelais08/2020
2942^1085750+582349326844Enzo Doria11/2016
2952^1083596+483061326195Enzo Doria12/2016
296(2^541456-1)*10^162995+2^541455-1325990paolo galliani01/2019
2972^1082908+583561325988Enzo Doria05/2017
29830^220411-29^220411325574Jean-Louis Charton10/2018
2992^1078242+1881649324584Enzo Doria11/2016
3002^1077737+1880117324432Enzo Doria10/2016
3012^1075425+1880117323736Enzo Doria10/2016
30210^322999+187071323000Stefano Morozzi03/2019
30310^322999-143151322999Patrick De Geest05/2020
3042^1072146+1886869322749Enzo Doria04/2017
3052^1072118-7321953322740Enzo Doria02/2015
3062^1071026+1886869322411Enzo Doria04/2017
3072^1070539+1880633322265Enzo Doria10/2016
3082^1069293-1147195321890Enzo Doria05/2015
3092^1065968+1880941320889Enzo Doria10/2016
3102^1065897-1147195320867Enzo Doria05/2015
3112^1063427+1882103320124Enzo Doria12/2016
3122^1061095-1061095319422Henri Lifchitz10/2013
3132^1060950+653119319378Enzo Doria12/2016
3142^1060363+782753319202Enzo Doria11/2016
315(71^172259-1)/70318895Paul Bourdelais08/2020
3162^1054736+483061317508Enzo Doria12/2016
3172^1053965+1879667317276Enzo Doria10/2016
318(43^194119-1)/42317086Paul Bourdelais08/2020
3192^1052186-458165316740Enzo Doria03/2015
3202^1046613-114685315062Enzo Doria04/2015
3212^1045625-459373314765Enzo Doria06/2015
322(7*10^314564-61)/9314564Erik Branger09/2016
323(7^371669-1)/6314096Paul Bourdelais02/2010
324(53^181981-1)/52313784Paul Bourdelais08/2020
3252^1041944+283051313657Enzo Doria12/2016
3262^1041153-114391313419Enzo Doria02/2015
3272^1038871+1866983312732Enzo Doria04/2016
328(55^179573-1)/54312521Paul Bourdelais08/2020
3292^1037647+1881263312363Enzo Doria11/2016
3302^1037226+1879699312237Enzo Doria10/2016
3312^1036867+1865843312129Enzo Doria02/2016
3322^1036020-114539311874Enzo Doria02/2015
333(90^159463-1)/89311628Paul Bourdelais08/2020
3342^1032240+1883431310736Enzo Doria01/2017
3352^1030352+1870021310167Enzo Doria06/2016
3362^1030046+1882843310075Enzo Doria11/2016
3373^648872+16309591Robert Price04/2020
338(11^293831-1)/10305993Paul Bourdelais03/2010
339(67^167449-1)/66305773Paul Bourdelais08/2020
3402^1015321-1015321305643Henri Lifchitz08/2013
3412^1014224-2791229305312Enzo Doria01/2016
3422^1010751-107709304267Enzo Doria03/2014
343(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
3442^1009577+1869587303913Enzo Doria06/2016
3458^336419-7^336419303817Jean-Louis Charton01/2008
3462^1008301+1869377303529Enzo Doria06/2016
347(2^1007838+5)/3303389Serge Batalov08/2015
3482^1005326+383059302634Enzo Doria12/2016
3492^1004929+1877567302514Enzo Doria08/2016
3502^1003494+1874899302082Enzo Doria06/2016
3512^1003046+60529301947Enzo Doria04/2016
352(23^221411-1)/22301501Paul Bourdelais08/2020
3532^1000647+1881353301225Enzo Doria11/2016
3542^1000000+821751301030Tony Prest / Never Odd Or Even10/2015
3552^999646+1874029300924Enzo Doria06/2016
356(59^169777-1)/58300649Paul Bourdelais08/2020
35710^300476+3300477Ed Trice10/2012
35810^300476-530913300476Patrick De Geest03/2016
3592^998053+1879667300444Enzo Doria09/2016
360314738^9+9^314738300337Anatoly F. Selevich02/2011
3617^355039-6^355039300043Jean-Louis Charton05/2011
36210^300000+287389300001Patrick De Geest10/2019
36310^300000-83657300000Patrick De Geest10/2019
364numbpart(72526161452)299999Serge Batalov04/2017
3652^996182-114431299881Enzo Doria02/2015
3662^995214-2788361299590Enzo Doria12/2015
3672^994791-114319299462Enzo Doria01/2015
3682^994490-1863791299372Enzo Doria01/2016
3692^993322+1885729299020Enzo Doria03/2017
3702^992711-2788807298836Enzo Doria12/2015
3712^992525-114199298780Enzo Doria12/2014
3722^992329+1884707298721Enzo Doria02/2017
373(2^986191+1)/3296873Vincent Diepeveen06/2008
3742^985217-114553296580Enzo Doria03/2015
375(76^157649-1)/75296507Paul Bourdelais07/2019
3762^984131-1828009296253Enzo Doria01/2015
3772^983620+60451296100Phil Moore03/2008
3782^982721-2683295829Yves Minet02/2016
3792^981298-2788421295401Enzo Doria12/2015
3802^981163-2790967295360Enzo Doria12/2015
3812^979594+1865839294888Enzo Doria02/2016
3822^976760+1885021294035Enzo Doria02/2017
3832^974441+1878407293336Enzo Doria08/2016
3842^974180+1876831293258Enzo Doria07/2016
3852^974170+453319293255Enzo Doria01/2017
3862^972744-114419292826Enzo Doria03/2015
387CopelandErdos(292447)292447Mark Rodenkirch12/2015
3882^970911+1873373292274Enzo Doria07/2016
3892^970670+383059292201Enzo Doria12/2016
3902^970141-100363292042Enzo Doria02/2014
3912^969945+1874717291983Enzo Doria06/2016
3922^969384+1880701291814Enzo Doria10/2016
393(3^611333-2^611333)/(99035947*87109884549431)291659Mike Oakes02/2017
3942^962194+60139289650Enzo Doria02/2016
3952^959307-1861507288781Enzo Doria11/2015
3962^957372+283531288198Enzo Doria02/2017
3972^957192-1864049288144Enzo Doria01/2016
3982^956446+1875199287919Enzo Doria06/2016
399(17^233689+1)/18287542Paul Bourdelais09/2013
4002^955178+1883587287538Enzo Doria12/2016
4012^954001+1875257287183Enzo Doria07/2016
402(23891^65536+1)/2286932Serge Batalov03/2018
4032^952268+1878601286662Enzo Doria09/2016
4042^950801+81557286220Enzo Doria08/2016
405(11*2^948635-13)/15285568Renaud Lifchitz11/2011
406(54^164839+1)/55285565Paul Bourdelais07/2019
4072^948510+782569285530Enzo Doria10/2016
4082^948374-114137285490Enzo Doria01/2015
4092^947739+1872923285298Enzo Doria06/2016
4102^942533+82067283731Enzo Doria09/2016
4112^940950+1874989283255Enzo Doria06/2016
4122^940426-2786141283097Enzo Doria11/2015
4132^939881-114115282933Enzo Doria12/2014
41410^282493+632551282494Patrick De Geest02/2017
41610^282493-9^282493282493Jean-Louis Charton03/2007
41510^282493-132327282493Patrick De Geest02/2017
4173^591827-2^591827282374Mike Oakes08/2009
418Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
4192^936716-1835519281980Enzo Doria04/2015
4202^936588+79411281942Enzo Doria06/2016
4212^936047+1877423281779Enzo Doria08/2016
4222^935713+1869377281678Enzo Doria05/2016
4232^933082+1877059280886Enzo Doria08/2016
424(5*10^280710+1)/3280711Serge Batalov10/2014
425(42^172663+1)/43280274Paul Bourdelais07/2019
426(10^279978+11)/3279978Serge Batalov07/2015
4272^929524-1864829279815Enzo Doria01/2016
4282^929152+60181279703Enzo Doria02/2016
4292^928621-2787883279543Enzo Doria11/2015
430(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
4312^927429+1882277279184Enzo Doria12/2016
432(71^150697-1)/70278978Paul Bourdelais07/2019
433(33^183661-1)/32278891Paul Bourdelais12/2018
434(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
4352^925330-1301278553Yves Minet06/2015
436(21^210599+1)/22278457Paul Bourdelais08/2013
4372^923261-69175277930Enzo Doria11/2015
438757^96487-756^96487277796Jean-Louis Charton12/2012
439((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2277369Serge Batalov07/2016
440(5^396413-1)/4277081Paul Bourdelais06/2010
4412^920318+2792299277044Enzo Doria02/2016
4422^918596-2786939276525Enzo Doria11/2015
4432^916639+60563275936Enzo Doria04/2016
4442^916385-2786383275860Enzo Doria11/2015
4452^915928+82081275722Enzo Doria09/2016
4462^915576-114137275616Enzo Doria01/2015
4472^914828+1876741275391Enzo Doria07/2016
4482^914757-2203275370Yves Minet12/2015
4492^911900+1871245274510Enzo Doria05/2016
4502^910490+283429274085Enzo Doria01/2017
4512^909988-1862249273934Enzo Doria12/2015
4522^909297+1879157273726Enzo Doria08/2016
4532^909257-1864423273714Enzo Doria01/2016
4542^908579-1861747273510Enzo Doria12/2015
4552^907635-2791597273226Enzo Doria01/2016
456(53^158341+1)/54273022Paul Bourdelais07/2019
4572^906594-113201272912Enzo Doria08/2014
4582^904773+1872167272364Enzo Doria06/2016
4592^904149-1862473272176Enzo Doria12/2015
460(7*10^271757-61)/9271757Erik Branger03/2012
4612^902497+1880117271679Enzo Doria09/2016
4622^901858+77689271487Enzo Doria06/2016
4632^901372+1875301271341Enzo Doria06/2016
4642^899121-115033270663Enzo Doria07/2015
4652^898900+883021270596Enzo Doria12/2016
4662^898762-251511270555Enzo Doria12/2013
4672^898589+47270503Lelio R Paula03/2016
468187322*10^270343-187321270349Danilo Nitsche09/2013
46948358*10^270343-48357270348Danilo Nitsche09/2013
470(10^270343-1)/9270343Maksym Voznyy07/2007
4712^897867-3217270285Yves Minet12/2016
4722^897849-115273270280Enzo Doria07/2015
4732^896616-114179269909Enzo Doria12/2014
4742^894928+583561269401Enzo Doria04/2017
4752^894673-39343269324Enzo Doria08/2015
476F(1285607)268676Henri Lifchitz11/2008
4772^892112+187663268553Enzo Doria08/2016
478(10^268207+1)/11268206Paul Bourdelais02/2010
4792^890957-69583268205Enzo Doria12/2015
48032841!^2+32840!^2+...+2!^2+1!^2268128Serge Batalov07/2017
4812^890122-351401267954Enzo Doria07/2015
482(19^209359-1)/18267718Paul Bourdelais08/2010
483(85^138647+1)/86267507Paul Bourdelais07/2019
484(485^99523-1)/484267291Michael Stocker05/2020
4852^886324+77791266811Enzo Doria06/2016
4862^884714+1880527266326Enzo Doria10/2016
48711^255426+255426^11265999Serge Batalov05/2014
4882^883462-343421265949Enzo Doria07/2015
4892^883442+1875019265943Enzo Doria06/2016
4902^883333-291583265910Enzo Doria07/2015
4912^880411+1882673265031Enzo Doria12/2016
4922^879530-2788031264765Enzo Doria12/2015
4932^878118+2793079264340Enzo Doria02/2016
494(37^168527-1)/36264283Paul Bourdelais08/2019
4952^875748-461129263627Enzo Doria07/2015
4962^875181-2789923263456Enzo Doria12/2015
4972^875101-350083263432Enzo Doria08/2015
4982^874684+1883587263307Enzo Doria01/2017
4992^874616+1872211263286Enzo Doria05/2016
5003^551491+16263129Robert Price04/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2020 15:45 (Time in France)

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