PRP Records

Probable Primes Top 10000

(288949 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 ?
2512^1386321+60299417325Enzo Doria02/2018
2522^1386320+184531417324Enzo Doria09/2017
2532^1382074+1883587416046Enzo Doria01/2017
2542^1379907+1885223415394Enzo Doria03/2017
2552^1375574+1886719414090Enzo Doria04/2017
2562^1373111+1884833413348Enzo Doria02/2017
2572^1368632+1889731412000Enzo Doria10/2017
258(89*10^411590+1)/9411591Serge Batalov09/2014
259F(1968721)411439Henri Lifchitz11/2009
2602^1366066+683749411227Enzo Doria02/2017
2612^1355790+1888939408134Enzo Doria07/2017
2622^1355635+1884203408087Enzo Doria01/2017
263(88^208739+1)/89405888Paul Bourdelais12/2020
264(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
2652^1347744-3405712Paul Bourdelais07/2019
26610^400000+1415223400001Patrick De Geest10/2020
26710^400000-339233400000Patrick De Geest10/2020
268Tau(863^24630)397727Nik Lygeros / Olivier Rozier01/2016
2692^1319770+1884949397291Enzo Doria06/2017
2702^1313062+1888849395272Enzo Doria08/2017
271(1073516^81920+1)/(1073516^16384+1)395236Serge Batalov01/2017
272(1059995^81920+1)/(1059995^16384+1)394875Serge Batalov01/2017
2732^1311618+783529394837Enzo Doria01/2017
2742^1308000+1883521393748Enzo Doria02/2017
275(1009565^81920+1)/(1009565^16384+1)393487Serge Batalov01/2017
276(995042^81920+1)/(995042^16384+1)393075Serge Batalov01/2017
277(988945^81920+1)/(988945^16384+1)392900Serge Batalov01/2017
278(988823^81920+1)/(988823^16384+1)392897Serge Batalov01/2017
279(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
280(978970^81920+1)/(978970^16384+1)392612Serge Batalov01/2017
2812^1303102+1866409392273Enzo Doria09/2017
2822^1302818+283429392188Enzo Doria01/2017
283(934422^81920+1)/(934422^16384+1)391286Serge Batalov01/2017
2842^1299181+1886867391093Enzo Doria04/2017
285(37^249341-1)/36391016Paul Bourdelais08/2020
2862^1298304+1882891390829Enzo Doria01/2017
28795196^12497+12497^95196390000Hans Havermann12/2021
288(874207^81920+1)/(874207^16384+1)389390Serge Batalov01/2017
28981650^54369+54369^81650386642Yusuf AttarBashi06/2021
29080565^62824+62824^80565386561Hans Havermann08/2021
29183747^41272+41272^83747386548Hans Havermann08/2021
29215^328574+328574^15386434Serge Batalov05/2014
2932^1280078+1885099385342Enzo Doria08/2017
2942^1274941+1880717383796Enzo Doria10/2016
2952^1272632+383431383101Enzo Doria01/2017
2962^1271346+1889839382714Enzo Doria08/2017
297(10^380976-7)/3380976Leonid Durman01/2012
2982^1257787+1447761378632Makoto Morimoto10/2013
299(2^1257787+32270)/(2*233*281*2207*3011)378620Makoto Morimoto12/2016
300(77^200657-1)/76378536Paul Bourdelais08/2020
301(98^189619+1)/99377573Paul Bourdelais02/2021
302F(1803059)376817Henri Lifchitz06/2009
3037^442674+4374103Paul Bourdelais02/2021
304(97^187393-1)/96372306Paul Bourdelais09/2020
30510^371696+7371697Alfred Reich05/2021
3062^1234709+883127371685Enzo Doria12/2016
307(67^203431+1)/68371479Paul Bourdelais09/2021
3082^1231466+283819370709Enzo Doria07/2017
3092^1220335+1881263367358Enzo Doria11/2016
3102^1216694+1884769366262Enzo Doria02/2017
3112^1215889-3366020Paul Bourdelais06/2019
3122^1215296+1885441365841Enzo Doria03/2017
313(80^192133+1)/81365645Paul Bourdelais01/2021
3142^1214307+1888115365543Enzo Doria05/2017
3152^1213815+3365395Paul Bourdelais06/2019
316(80^191953+1)/81365302Paul Bourdelais01/2021
3172^1207345+1882577363448Enzo Doria12/2016
3182^1207073+883727363366Enzo Doria03/2017
3193^761457-2363308Ryan Propper07/2015
320(10^363030+7)/337/443363025Alfred Reich12/2021
321(2^1200924+324730)/2361514Stefano Morozzi06/2021
322(2^1200912+274110)/2361511Stefano Morozzi01/2021
323(2^1200887+344126)/2361503Stefano Morozzi10/2020
3242^1200861+198521361495Stefano Morozzi11/2021
325(2^1200856+305790)/2361494Stefano Morozzi10/2020
326(2^1200853+372822)/2361493Stefano Morozzi06/2021
3272^1200812+324178)/2361481Stefano Morozzi06/2021
328(2^1200768+380458)/2361467Stefano Morozzi01/2021
329(2^1200741+293402)/2361459Stefano Morozzi07/2021
3302^1200672+1880881361439Enzo Doria10/2016
3312^1200660+198555361435Stefano Morozzi12/2021
332(2^1200603+356030)/2361418Stefano Morozzi10/2020
333(2^1200590+275854)/2361414Stefano Morozzi03/2021
3342^1200550+139297361402Stefano Morozzi10/2021
335(2^1200456+320526)/2361373Stefano Morozzi10/2020
3362^1200416+164065361362Stefano Morozzi01/2022
3372^1200331+155429361336Stefano Morozzi10/2021
338(2^1200289+348366)/2361323Stefano Morozzi10/2020
339(2^1200284+273162)/2361322Stefano Morozzi10/2020
3402^1200252+194535361312Stefano Morozzi11/2021
341(2^1200250+364230)/2361311Stefano Morozzi10/2020
342(2^1200209+305990)/2361299Stefano Morozzi10/2020
343(2^1200210+376278)/2361299Stefano Morozzi10/2020
344(2^1200182+274462)/2361291Stefano Morozzi01/2021
345(2^1200162+275910)/2361285Stefano Morozzi03/2021
346(2^1200131+360150)/2361276Stefano Morozzi10/2020
347(2^1200118+290718)/2361272Stefano Morozzi01/2021
348(64*10^360173-1)/243360173Serge Batalov09/2014
349(59^203309+1)/60360029Paul Bourdelais09/2021
3502^1195093+1882577359759Enzo Doria12/2016
351(6^461108-11)/5358812Paul Bourdelais04/2019
3522^1191375+8543358640Phil Moore06/2008
3532^1190972+1880191358519Enzo Doria11/2016
354(45^216551-1)/44358004Paul Bourdelais08/2020
355(50^210319-1)/49357324Paul Bourdelais08/2020
356(531^131072+25^131072)/2357184Kellen Shenton03/2021
3572^1179836+1885021355167Enzo Doria02/2017
35820^271951+3353817Paul Bourdelais01/2021
359(63^195893-1)/62352477Paul Bourdelais08/2020
360numbpart(100000135540)352269Serge Batalov04/2017
361(10^352237-1)/9/10567111/950335427352221Maksym Voznyy01/2015
3622^1168554+783529351770Enzo Doria01/2017
363(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
3642^1166152+1882411351047Enzo Doria12/2016
36510^350071+7350072Alfred Reich05/2021
3662^1162154+1890207349844Enzo Doria08/2017
367(7*10^348724-61)/9348724Erik Branger09/2016
368(127^165601-1)/126348390Alexander Zhirkov09/2015
3692^1153083+1883693347113Enzo Doria04/2017
370(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
3712^1145882+80779344945Enzo Doria09/2016
3722^1136462+1887289342110Enzo Doria05/2017
373F(1636007)341905Henri Lifchitz03/2009
3742^1133678+782569341272Enzo Doria11/2016
375(11^327001+1)/12340536Paul Bourdelais09/2013
376(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
377Tau(907^20848)339132Nik Lygeros / Olivier Rozier01/2016
3782^1126380-3339075Paul Bourdelais06/2019
3792^1125446+1885099338794Enzo Doria08/2017
380(63^188147+1)/64338539Paul Bourdelais12/2020
3812^1124549+143807338523Enzo Doria10/2016
3822^1121187+1886783337511Enzo Doria04/2017
383(48^200443-1)/47336992Paul Bourdelais08/2020
384(94^170371-1)/93336162Paul Bourdelais09/2020
3852^1116184+1883521336005Enzo Doria02/2017
3862^1114517+1880087335504Enzo Doria10/2016
387(101^166849+1)/102334418Paul Bourdelais12/2020
388(3^700897+1)/4334413Paul Bourdelais04/2010
3892^1104408-114539332460Enzo Doria03/2015
3902^1101921+82085331712Enzo Doria10/2016
3912^1100655+683513331331Enzo Doria01/2017
392(10^330906+71)/9330906Serge Batalov07/2015
3932^1098346+482899330636Enzo Doria11/2016
3942^1095679+1878713329833Enzo Doria09/2016
3952^1094740-1851539329550Enzo Doria08/2015
3962^1091469-379369328565Enzo Doria03/2014
397(69^178093-1)/68327485Paul Bourdelais08/2020
398(10^326884+7)/421326882Alfred Reich12/2021
3992^1085750+582349326844Enzo Doria11/2016
4002^1083596+483061326195Enzo Doria12/2016
401(2^541456-1)*10^162995+2^541455-1325990paolo galliani01/2019
4022^1082908+583561325988Enzo Doria05/2017
40330^220411-29^220411325574Jean-Louis Charton10/2018
4042^1078242+1881649324584Enzo Doria11/2016
4052^1077737+1880117324432Enzo Doria10/2016
4062^1075425+1880117323736Enzo Doria10/2016
407(28^223381+1)/29323267Paul Bourdelais12/2020
40810^322999+187071323000Stefano Morozzi03/2019
40910^322999-143151322999Patrick De Geest05/2020
4102^1072146+1886869322749Enzo Doria04/2017
4112^1072118-7321953322740Enzo Doria02/2015
4122^1071026+1886869322411Enzo Doria04/2017
4132^1070539+1880633322265Enzo Doria10/2016
4142^1069293-1147195321890Enzo Doria05/2015
4152^1065968+1880941320889Enzo Doria10/2016
4162^1065897-1147195320867Enzo Doria05/2015
4172^1063427+1882103320124Enzo Doria12/2016
4182^1061095-1061095319422Henri Lifchitz10/2013
4192^1060950+653119319378Enzo Doria12/2016
4202^1060363+782753319202Enzo Doria11/2016
421(71^172259-1)/70318895Paul Bourdelais08/2020
4222^1054736+483061317508Enzo Doria12/2016
4232^1053965+1879667317276Enzo Doria10/2016
424(43^194119-1)/42317086Paul Bourdelais08/2020
4252^1052186-458165316740Enzo Doria03/2015
4262^1046613-114685315062Enzo Doria04/2015
4272^1045625-459373314765Enzo Doria06/2015
428(7*10^314564-61)/9314564Erik Branger09/2016
429(7^371669-1)/6314096Paul Bourdelais02/2010
430(53^181981-1)/52313784Paul Bourdelais08/2020
4312^1041944+283051313657Enzo Doria12/2016
4322^1041153-114391313419Enzo Doria02/2015
433(74^167311+1)/75312742Paul Bourdelais12/2020
4342^1038871+1866983312732Enzo Doria04/2016
435(55^179573-1)/54312521Paul Bourdelais08/2020
4362^1037647+1881263312363Enzo Doria11/2016
4372^1037226+1879699312237Enzo Doria10/2016
4382^1036867+1865843312129Enzo Doria02/2016
439(76^165947+1)/77312114Paul Bourdelais01/2021
4402^1036020-114539311874Enzo Doria02/2015
441(90^159463-1)/89311628Paul Bourdelais08/2020
4422^1032240+1883431310736Enzo Doria01/2017
4432^1030352+1870021310167Enzo Doria06/2016
4442^1030046+1882843310075Enzo Doria11/2016
4453^648872+16309591Robert Price04/2020
4465^442281+2309142Paul Bourdelais01/2021
447(11^293831-1)/10305993Paul Bourdelais03/2010
448(67^167449-1)/66305773Paul Bourdelais08/2020
449(62^170539+1)/63305671Paul Bourdelais12/2020
4502^1015321-1015321305643Henri Lifchitz08/2013
4512^1014224-2791229305312Enzo Doria01/2016
452(10^304986+7)/673304984Alfred Reich11/2021
4532^1010751-107709304267Enzo Doria03/2014
454(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
45577842^8039+8039^77842303989Hans Havermann01/2022
4562^1009577+1869587303913Enzo Doria06/2016
4578^336419-7^336419303817Jean-Louis Charton01/2008
45880766^5771+5771^80766303782Hans Havermann01/2022
45978390^7459+7459^78390303580Hans Havermann01/2022
4602^1008301+1869377303529Enzo Doria06/2016
461(2^1007838+5)/3303389Serge Batalov08/2015
4626^389756+5303290Paul Bourdelais02/2021
46371016^18649+18649^71016303285Hans Havermann01/2022
46480160^6047+6047^80160303129Hans Havermann01/2022
46571790^16553+16553^71790302874Hans Havermann11/2021
46665208^44129+44129^65208302874Hans Havermann11/2021
46784181^3960+3960^84181302858Hans Havermann11/2021
46871956^16087+16087^71956302682Hans Havermann11/2021
4692^1005326+383059302634Enzo Doria12/2016
4702^1004929+1877567302514Enzo Doria08/2016
47169341^22978+22978^69341302418Hans Havermann12/2021
472111443^516+516^111443302306Hans Havermann12/2021
47367638^29387+29387^67638302218Hans Havermann11/2021
4742^1003494+1874899302082Enzo Doria06/2016
47575189^10400+10400^75189302037Hans Havermann12/2021
47667237^31042+31042^67237302026Hans Havermann12/2021
47764540^47791+47791^64540302005Hans Havermann11/2021
4782^1003046+60529301947Enzo Doria04/2016
47983278^4209+4209^83278301815Hans Havermann09/2021
48064431^48250+48250^64431301763Hans Havermann09/2021
48167237^30714+30714^67237301716Hans Havermann09/2021
48264641^46288+46288^64641301581Hans Havermann09/2021
48371513^16482+16482^71513301572Hans Havermann10/2021
48472017^15396+15396^72017301565Hans Havermann09/2021
48565534^39927+39927^65534301540Hans Havermann10/2021
486(23^221411-1)/22301501Paul Bourdelais08/2020
48763169^59152+59152^63169301441Hans Havermann09/2021
48875055^10348+10348^75055301336Hans Havermann09/2021
4892^1000647+1881353301225Enzo Doria11/2016
49083686^3961+3961^83686301086Hans Havermann10/2021
49168529^24742+24742^68529301078Hans Havermann09/2021
49265207^41416+41416^65207301072Hans Havermann10/2021
4932^1000000+821751301030Tony Prest / Never Odd Or Even10/2015
49490762^2071+2071^90762300984Hans Havermann06/2021
49563909^51142+51142^63909300934Hans Havermann08/2021
4962^999646+1874029300924Enzo Doria06/2016
49766280^34607+34607^66280300856Hans Havermann06/2021
49865534^38925+38925^65534300817Hans Havermann07/2021
49963296^56517+56517^63296300794Hans Havermann06/2021
500110610^523+523^110610300694Hans Havermann06/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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