PRP Records

Probable Primes Top 10000

(280932 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 ?
25115^328574+328574^15386434Serge Batalov05/2014
2522^1280078+1885099385342Enzo Doria08/2017
2532^1274941+1880717383796Enzo Doria10/2016
2542^1272632+383431383101Enzo Doria01/2017
2552^1271346+1889839382714Enzo Doria08/2017
256(10^380976-7)/3380976Leonid Durman01/2012
2572^1257787+1447761378632Makoto Morimoto10/2013
258(2^1257787+32270)/(2*233*281*2207*3011)378620Makoto Morimoto12/2016
259(77^200657-1)/76378536Paul Bourdelais08/2020
260(98^189619+1)/99377573Paul Bourdelais02/2021
261F(1803059)376817Henri Lifchitz06/2009
2627^442674+4374103Paul Bourdelais02/2021
263(97^187393-1)/96372306Paul Bourdelais09/2020
2642^1234709+883127371685Enzo Doria12/2016
2652^1231466+283819370709Enzo Doria07/2017
2662^1220335+1881263367358Enzo Doria11/2016
2672^1216694+1884769366262Enzo Doria02/2017
2682^1215889-3366020Paul Bourdelais06/2019
2692^1215296+1885441365841Enzo Doria03/2017
270(80^192133+1)/81365645Paul Bourdelais01/2021
2712^1214307+1888115365543Enzo Doria05/2017
2722^1213815+3365395Paul Bourdelais06/2019
273(80^191953+1)/81365302Paul Bourdelais01/2021
2742^1207345+1882577363448Enzo Doria12/2016
2752^1207073+883727363366Enzo Doria03/2017
2763^761457-2363308Ryan Propper07/2015
277(2^1200912+274110)/2361511Stefano Morozzi01/2021
278(2^1200887+344126)/2361503Stefano Morozzi10/2020
279(2^1200856+305790)/2361494Stefano Morozzi10/2020
280(2^1200768+380458)/2361467Stefano Morozzi01/2021
2812^1200672+1880881361439Enzo Doria10/2016
282(2^1200603+356030)/2361418Stefano Morozzi10/2020
283(2^1200590+275854)/2361414Stefano Morozzi03/2021
284(2^1200456+320526)/2361373Stefano Morozzi10/2020
285(2^1200289+348366)/2361323Stefano Morozzi10/2020
286(2^1200284+273162)/2361322Stefano Morozzi10/2020
287(2^1200250+364230)/2361311Stefano Morozzi10/2020
288(2^1200209+305990)/2361299Stefano Morozzi10/2020
289(2^1200210+376278)/2361299Stefano Morozzi10/2020
290(2^1200182+274462)/2361291Stefano Morozzi01/2021
291(2^1200162+275910)/2361285Stefano Morozzi03/2021
292(2^1200131+360150)/2361276Stefano Morozzi10/2020
293(2^1200118+290718)/2361272Stefano Morozzi01/2021
294(64*10^360173-1)/243360173Serge Batalov09/2014
2952^1195093+1882577359759Enzo Doria12/2016
296(6^461108-11)/5358812Paul Bourdelais04/2019
2972^1191375+8543358640Phil Moore06/2008
2982^1190972+1880191358519Enzo Doria11/2016
299(45^216551-1)/44358004Paul Bourdelais08/2020
300(50^210319-1)/49357324Paul Bourdelais08/2020
301(531^131072+25^131072)/2357184Kellen Shenton03/2021
3022^1179836+1885021355167Enzo Doria02/2017
30320^271951+3353817Paul Bourdelais01/2021
304(63^195893-1)/62352477Paul Bourdelais08/2020
305numbpart(100000135540)352269Serge Batalov04/2017
306(10^352237-1)/9/10567111/950335427352221Maksym Voznyy01/2015
3072^1168554+783529351770Enzo Doria01/2017
308(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
3092^1166152+1882411351047Enzo Doria12/2016
3102^1162154+1890207349844Enzo Doria08/2017
311(7*10^348724-61)/9348724Erik Branger09/2016
312(127^165601-1)/126348390Alexander Zhirkov09/2015
3132^1153083+1883693347113Enzo Doria04/2017
314(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
3152^1145882+80779344945Enzo Doria09/2016
3162^1136462+1887289342110Enzo Doria05/2017
317F(1636007)341905Henri Lifchitz03/2009
3182^1133678+782569341272Enzo Doria11/2016
319(11^327001+1)/12340536Paul Bourdelais09/2013
320(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
321Tau(907^20848)339132Nik Lygeros / Olivier Rozier01/2016
3222^1126380-3339075Paul Bourdelais06/2019
3232^1125446+1885099338794Enzo Doria08/2017
324(63^188147+1)/64338539Paul Bourdelais12/2020
3252^1124549+143807338523Enzo Doria10/2016
3262^1121187+1886783337511Enzo Doria04/2017
327(48^200443-1)/47336992Paul Bourdelais08/2020
328(94^170371-1)/93336162Paul Bourdelais09/2020
3292^1116184+1883521336005Enzo Doria02/2017
3302^1114517+1880087335504Enzo Doria10/2016
331(101^166849+1)/102334418Paul Bourdelais12/2020
332(3^700897+1)/4334413Paul Bourdelais04/2010
3332^1104408-114539332460Enzo Doria03/2015
3342^1101921+82085331712Enzo Doria10/2016
3352^1100655+683513331331Enzo Doria01/2017
336(10^330906+71)/9330906Serge Batalov07/2015
3372^1098346+482899330636Enzo Doria11/2016
3382^1095679+1878713329833Enzo Doria09/2016
3392^1094740-1851539329550Enzo Doria08/2015
3402^1091469-379369328565Enzo Doria03/2014
341(69^178093-1)/68327485Paul Bourdelais08/2020
3422^1085750+582349326844Enzo Doria11/2016
3432^1083596+483061326195Enzo Doria12/2016
344(2^541456-1)*10^162995+2^541455-1325990paolo galliani01/2019
3452^1082908+583561325988Enzo Doria05/2017
34630^220411-29^220411325574Jean-Louis Charton10/2018
3472^1078242+1881649324584Enzo Doria11/2016
3482^1077737+1880117324432Enzo Doria10/2016
3492^1075425+1880117323736Enzo Doria10/2016
350(28^223381+1)/29323267Paul Bourdelais12/2020
35110^322999+187071323000Stefano Morozzi03/2019
35210^322999-143151322999Patrick De Geest05/2020
3532^1072146+1886869322749Enzo Doria04/2017
3542^1072118-7321953322740Enzo Doria02/2015
3552^1071026+1886869322411Enzo Doria04/2017
3562^1070539+1880633322265Enzo Doria10/2016
3572^1069293-1147195321890Enzo Doria05/2015
3582^1065968+1880941320889Enzo Doria10/2016
3592^1065897-1147195320867Enzo Doria05/2015
3602^1063427+1882103320124Enzo Doria12/2016
3612^1061095-1061095319422Henri Lifchitz10/2013
3622^1060950+653119319378Enzo Doria12/2016
3632^1060363+782753319202Enzo Doria11/2016
364(71^172259-1)/70318895Paul Bourdelais08/2020
3652^1054736+483061317508Enzo Doria12/2016
3662^1053965+1879667317276Enzo Doria10/2016
367(43^194119-1)/42317086Paul Bourdelais08/2020
3682^1052186-458165316740Enzo Doria03/2015
3692^1046613-114685315062Enzo Doria04/2015
3702^1045625-459373314765Enzo Doria06/2015
371(7*10^314564-61)/9314564Erik Branger09/2016
372(7^371669-1)/6314096Paul Bourdelais02/2010
373(53^181981-1)/52313784Paul Bourdelais08/2020
3742^1041944+283051313657Enzo Doria12/2016
3752^1041153-114391313419Enzo Doria02/2015
376(74^167311+1)/75312742Paul Bourdelais12/2020
3772^1038871+1866983312732Enzo Doria04/2016
378(55^179573-1)/54312521Paul Bourdelais08/2020
3792^1037647+1881263312363Enzo Doria11/2016
3802^1037226+1879699312237Enzo Doria10/2016
3812^1036867+1865843312129Enzo Doria02/2016
382(76^165947+1)/77312114Paul Bourdelais01/2021
3832^1036020-114539311874Enzo Doria02/2015
384(90^159463-1)/89311628Paul Bourdelais08/2020
3852^1032240+1883431310736Enzo Doria01/2017
3862^1030352+1870021310167Enzo Doria06/2016
3872^1030046+1882843310075Enzo Doria11/2016
3883^648872+16309591Robert Price04/2020
3895^442281+2309142Paul Bourdelais01/2021
390(11^293831-1)/10305993Paul Bourdelais03/2010
391(67^167449-1)/66305773Paul Bourdelais08/2020
392(62^170539+1)/63305671Paul Bourdelais12/2020
3932^1015321-1015321305643Henri Lifchitz08/2013
3942^1014224-2791229305312Enzo Doria01/2016
3952^1010751-107709304267Enzo Doria03/2014
396(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
3972^1009577+1869587303913Enzo Doria06/2016
3988^336419-7^336419303817Jean-Louis Charton01/2008
3992^1008301+1869377303529Enzo Doria06/2016
400(2^1007838+5)/3303389Serge Batalov08/2015
4016^389756+5303290Paul Bourdelais02/2021
4022^1005326+383059302634Enzo Doria12/2016
4032^1004929+1877567302514Enzo Doria08/2016
4042^1003494+1874899302082Enzo Doria06/2016
4052^1003046+60529301947Enzo Doria04/2016
406(23^221411-1)/22301501Paul Bourdelais08/2020
4072^1000647+1881353301225Enzo Doria11/2016
4082^1000000+821751301030Tony Prest / Never Odd Or Even10/2015
4092^999646+1874029300924Enzo Doria06/2016
410(59^169777-1)/58300649Paul Bourdelais08/2020
41110^300476+3300477Ed Trice10/2012
41210^300476-530913300476Patrick De Geest03/2016
4132^998053+1879667300444Enzo Doria09/2016
414314738^9+9^314738300337Anatoly F. Selevich02/2011
4157^355039-6^355039300043Jean-Louis Charton05/2011
41610^300000+287389300001Patrick De Geest10/2019
41710^300000-83657300000Patrick De Geest10/2019
418numbpart(72526161452)299999Serge Batalov04/2017
4192^996182-114431299881Enzo Doria02/2015
4202^995214-2788361299590Enzo Doria12/2015
4212^994791-114319299462Enzo Doria01/2015
4222^994490-1863791299372Enzo Doria01/2016
4232^993322+1885729299020Enzo Doria03/2017
4242^992711-2788807298836Enzo Doria12/2015
4252^992525-114199298780Enzo Doria12/2014
4262^992329+1884707298721Enzo Doria02/2017
427(2^986191+1)/3296873Vincent Diepeveen06/2008
4282^985217-114553296580Enzo Doria03/2015
429(76^157649-1)/75296507Paul Bourdelais07/2019
4302^984131-1828009296253Enzo Doria01/2015
4312^983620+60451296100Phil Moore03/2008
4322^982721-2683295829Yves Minet02/2016
4332^981298-2788421295401Enzo Doria12/2015
4342^981163-2790967295360Enzo Doria12/2015
4352^979594+1865839294888Enzo Doria02/2016
4362^976760+1885021294035Enzo Doria02/2017
4372^974441+1878407293336Enzo Doria08/2016
4382^974180+1876831293258Enzo Doria07/2016
4392^974170+453319293255Enzo Doria01/2017
4402^972744-114419292826Enzo Doria03/2015
44111^281143+6292781Paul Bourdelais03/2021
442CopelandErdos(292447)292447Mark Rodenkirch12/2015
4432^970911+1873373292274Enzo Doria07/2016
4442^970670+383059292201Enzo Doria12/2016
4452^970141-100363292042Enzo Doria02/2014
4462^969945+1874717291983Enzo Doria06/2016
4472^969384+1880701291814Enzo Doria10/2016
448(3^611333-2^611333)/(99035947*87109884549431)291659Mike Oakes02/2017
4492^962194+60139289650Enzo Doria02/2016
4502^959307-1861507288781Enzo Doria11/2015
45114^251797-3288592Paul Bourdelais12/2020
4522^957372+283531288198Enzo Doria02/2017
4532^957192-1864049288144Enzo Doria01/2016
4542^956446+1875199287919Enzo Doria06/2016
455(17^233689+1)/18287542Paul Bourdelais09/2013
4562^955178+1883587287538Enzo Doria12/2016
4572^954127-954127^2287221Henri Lifchitz01/2021
4582^954001+1875257287183Enzo Doria07/2016
459(23891^65536+1)/2286932Serge Batalov03/2018
4602^952268+1878601286662Enzo Doria09/2016
4612^950801+81557286220Enzo Doria08/2016
46222845^65536+22844^65536285658Kellen Shenton03/2021
463(11*2^948635-13)/15285568Renaud Lifchitz11/2011
464(54^164839+1)/55285565Paul Bourdelais07/2019
4652^948510+782569285530Enzo Doria10/2016
4662^948374-114137285490Enzo Doria01/2015
4672^947739+1872923285298Enzo Doria06/2016
4682^942533+82067283731Enzo Doria09/2016
4692^940950+1874989283255Enzo Doria06/2016
4702^940426-2786141283097Enzo Doria11/2015
4712^939881-114115282933Enzo Doria12/2014
47210^282493+632551282494Patrick De Geest02/2017
47410^282493-9^282493282493Jean-Louis Charton03/2007
47310^282493-132327282493Patrick De Geest02/2017
4753^591827-2^591827282374Mike Oakes08/2009
476Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
4772^936716-1835519281980Enzo Doria04/2015
4782^936588+79411281942Enzo Doria06/2016
4792^936047+1877423281779Enzo Doria08/2016
4802^935713+1869377281678Enzo Doria05/2016
4812^933082+1877059280886Enzo Doria08/2016
482(5*10^280710+1)/3280711Serge Batalov10/2014
483(42^172663+1)/43280274Paul Bourdelais07/2019
484(10^279978+11)/3279978Serge Batalov07/2015
4852^929524-1864829279815Enzo Doria01/2016
4862^929152+60181279703Enzo Doria02/2016
4872^928621-2787883279543Enzo Doria11/2015
488(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
4892^927429+1882277279184Enzo Doria12/2016
490(71^150697-1)/70278978Paul Bourdelais07/2019
491(33^183661-1)/32278891Paul Bourdelais12/2018
492(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
4932^925330-1301278553Yves Minet06/2015
494(21^210599+1)/22278457Paul Bourdelais08/2013
4952^923261-69175277930Enzo Doria11/2015
496757^96487-756^96487277796Jean-Louis Charton12/2012
497((((((((((((((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
498(5^396413-1)/4277081Paul Bourdelais06/2010
4992^920318+2792299277044Enzo Doria02/2016
5002^918596-2786939276525Enzo Doria11/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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