Henri & Renaud Lifchitz's PRP Top records

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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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 ?
8502	2^199872+93	60168	Donovan Johnson	06/2008
8501	6^77321+77	60168	Lelio R Paula	04/2013
8503	(86*10^60165-77)/9	60166	Robert Price	05/2016
8504	(2^199868+78557)/23373	60162	Lelio R Paula	05/2012
8505	7^71180+82	60155	Lelio R Paula	04/2013
8507	2^199814-112295	60151	Enzo Doria	06/2014
8506	(51^35227-1)/50	60151	Paul Bourdelais	08/2017
8508	42964!3-81	60135	Robert Price	09/2014
8509	2^199709-51	60119	Lelio R Paula	05/2011
8510	2^199700-111623	60116	Enzo Doria	05/2014
8511	(15185*2^199681-1)/159	60112	Lelio R Paula	04/2015
8512	2^199672+2533	60108	Henri Lifchitz	09/2004
8513	20^46198-11	60105	Lelio R Paula	04/2013
8514	2^199657+93257	60103	Yves Minet	03/2010
8515	3^125967-110	60102	Lelio R Paula	10/2012
8516	2^199654-18813	60102	Enzo Doria	05/2013
8517	(29*10^60100+19)/3	60101	Robert Price	01/2017
8518	2^199615-2*199615+1	60091	Robert Price	04/2018
8519	129^28468+28468^129	60085	Serge Batalov	05/2014
8520	2^199572-15873	60078	Enzo Doria	04/2013
8521	9*2^199559+7	60075	Lelio R Paula	03/2014
8522	2^199527-111919	60064	Enzo Doria	05/2014
8523	2^199522+82875	60063	Lelio R Paula	10/2012
8524	5^85928-72	60062	Lelio R Paula	10/2012
8525	39^37749+38	60062	Norbert Schneider	05/2014
8526	6^77182-143	60060	Lelio R Paula	10/2012
8527	2^199502-2145	60057	Lelio R Paula	06/2011
8528	2^199493+4257	60054	Lelio R Paula	06/2011
8529	2^199488+40755	60052	Lelio R Paula	06/2011
8530	(2^199451+9)/25619	60037	Lelio R Paula	02/2012
8531	2^199425-61	60033	Lelio R Paula	05/2011
8532	(85*10^60026+23)/9	60027	Robert Price	11/2015
8533	65^33107+62	60021	Lelio R Paula	01/2016
8535	2^199362-1215	60014	Lelio R Paula	06/2011
8534	2^199362-111633	60014	Enzo Doria	05/2014
8536	1537^18832+18832^1537	60012	Serge Batalov	05/2014
8537	2^199324-17433	60003	Enzo Doria	05/2013
8538	10^60000+204331	60001	Milton L. Brown	04/2006
8539	10^60000+87129	60001	Milton L. Brown	04/2006
8540	143^27838-2	60001	Lelio R Paula	10/2017
8559	10^59999+65197	60000	Patrick De Geest	04/2005
8558	10^60000-32529	60000	Patrick De Geest	08/2009
8554	(10^60000+2249)/9	60000	Makoto Morimoto	09/2016
8555	((2^43112609)/10^24296)%10^60000	60000	Michael Vang	10/2016
8556	(2^57885161/10^105090)%10^60000	60000	Michael Vang	10/2016
8557	(2^42643801/10^58945)%10^60000	60000	Michael Vang	10/2016
8541	(2^37156667/10^243655)%10^60000	60000	Michael Vang	10/2016
8542	(2^30402457/10^69028)%10^60000	60000	Michael Vang	11/2016
8543	(2^32582657/10^248088)%10^60000	60000	Michael Vang	11/2016
8544	(2^32582657/10^238942)%10^60000	60000	Michael Vang	11/2016
8545	(2^24036583/10^13547)%10^60000	60000	Michael Vang	11/2016
8546	(2^20996011/10^131008)%10^60000	60000	Michael Vang	11/2016
8547	(2^13466917/10^79774)%10^60000	60000	Michael Vang	11/2016
8548	(2^13466917/10^102581)%10^60000	60000	Michael Vang	11/2016
8549	(2^6972593/10^339640)%10^60000	60000	Michael Vang	11/2016
8550	(2^2976221/10^65464)%10^60000	60000	Michael Vang	12/2016
8551	(2^1398269/10^61138)%10^60000	60000	Michael Vang	12/2016
8552	(2^3021377/10^418881)%10^60000	60000	Michael Vang	12/2016
8553	(2^1257787/10^164080)%10^60000	60000	Michael Vang	12/2016
8562	10^59999-516267	59999	Patrick De Geest	06/2009
8561	20^46116-41	59999	Lelio R Paula	03/2013
8560	(2^74207281/10^184638)%10^60000	59999	Michael Vang	10/2016
8563	(2^25964951/10^135429)%10^60000	59999	Michael Vang	11/2016
8564	6^77100-55	59996	Lelio R Paula	10/2012
8566	(19*2^199274+1)/161	59987	Lelio R Paula	07/2012
8565	(23^44053+1)/24	59987	Robert Price	06/2013
8567	9^62848+6^62848-2^62848	59973	Mike Oakes	08/2010
8568	15852^6061+6061^15852	59961	Hans Havermann	08/2016
8569	19^46880-20	59948	Lelio R Paula	03/2013
8570	2^199107-17737	59938	Enzo Doria	05/2013
8571	(13*10^59928+83)/3	59929	Robert Price	09/2016
8572	10^59913+108931431	59914	Marisa Kirisame	02/2015
8573	10^59913+48619	59914	Patrick De Geest	04/2016
8574	10^59913-74123	59913	Patrick De Geest	03/2016
8575	t(199528)	59890	Robert Price	01/2015
8576	2^198903-17901	59876	Enzo Doria	05/2013
8577	9*10^59862-19	59863	Robert Price	10/2017
8578	gcd(V(776555),5F(155311)(F(155311)+1)+1)	59858	Serge Batalov	04/2015
8579	(3^125447+7)/2	59854	Lelio R Paula	04/2012
8580	5^85630+4^(85630-1)	59853	Robert Price	03/2016
8581	2^198824-2135	59852	Yves Minet	06/2013
8582	(124^28591-1)/123	59851	Richard Fischer	10/2017
8583	2^198799-16117	59845	Enzo Doria	04/2013
8584	7^70811+6^(70811+1)	59843	Robert Price	07/2016
8585	2^198774-15945	59837	Enzo Doria	04/2013
8586	2^198753-15873	59831	Enzo Doria	04/2013
8587	(31*2^198748-1)/45	59829	Lelio R Paula	01/2014
8588	2^198725+69	59823	Lelio R Paula	04/2011
8589	(68*10^59821+31)/9	59822	Robert Price	10/2015
8590	(37*25^42785+1867)/8	59812	Curtis Bright	05/2015
8591	3^125354+2660	59810	Lelio R Paula	10/2012
8592	105^29591-104	59810	Norbert Schneider	08/2013
8593	4*5^85565-3	59808	Lelio R Paula	09/2014
8594	13963842222*Bern(19550)/55727275	59803	Thomas Ritschel	03/2014
8596	125330^3+3^125330	59798	Anatoly F. Selevich	06/2010
8595	2^198643-3189	59798	Yves Minet	10/2014
8597	(13*10^59797+191)/3	59798	Robert Price	08/2017
8598	(7*10^59796-1)/3	59797	Erik Branger	03/2014
8599	2^198595+153	59784	Lelio R Paula	04/2011
8600	(19*10^59766+161)/9	59767	Robert Price	07/2016
8601	2^198510-1965	59758	Lelio R Paula	06/2011
8602	2^198506-19077	59757	Enzo Doria	05/2013
8603	2^198484-16005	59750	Enzo Doria	04/2013
8604	2^198473-16821	59747	Enzo Doria	05/2013
8605	(2^198481-5)/28311	59745	Lelio R Paula	02/2012
8606	2^198400-189	59725	Lelio R Paula	04/2011
8607	2^198384-12837	59720	Enzo Doria	10/2012
8608	42694!3-729	59719	Robert Price	09/2014
8609	2^198320-18717	59701	Enzo Doria	05/2013
8610	20^45881-1183	59693	Enzo Doria	03/2013
8611	2^198224-6855	59672	Lelio R Paula	05/2011
8612	2^198181-19101	59659	Enzo Doria	05/2013
8613	5*10^59650+41	59651	Robert Price	08/2017
8614	2^198149-112213	59649	Enzo Doria	06/2014
8615	2^198138+73699	59646	Enzo Doria	04/2016
8616	2^198129-55	59643	Lelio R Paula	04/2011
8617	5^85318-14636	59635	Enzo Doria	02/2013
8618	(2^198119+47)/1560935	59634	Lelio R Paula	02/2012
8619	2^198090-16097	59632	Enzo Doria	04/2013
8620	9*10^59617+89	59618	Robert Price	11/2016
8621	42625!3+81	59612	Robert Price	09/2014
8622	5^85277-84	59607	Lelio R Paula	10/2012
8623	(871*10^59599-7)/9	59601	Robert Price	11/2017
8624	2^197984-18245	59600	Enzo Doria	05/2013
8625	12202^14583-14583^12202	59593	Norbert Schneider	01/2019
8626	2^197951-2137	59590	Yves Minet	06/2013
8627	(38*10^59589+187)/9	59590	Robert Price	11/2017
8628	66^32749-65^32749	59589	Robert Price	09/2013
8629	5*10^59586-3	59587	Dmitry Domanov	11/2010
8630	(35*10^59584-197)/9	59585	Robert Kinser	10/2017
8631	2^197932-3959	59584	Yves Minet	04/2017
8632	2^197909-18961	59577	Enzo Doria	05/2013
8633	(3^124871+2)/45031	59574	Lelio R Paula	04/2012
8634	2^197872+81	59566	Henri Lifchitz	10/2005
8635	2^197873-18469	59566	Enzo Doria	05/2013
8636	(22*10^59558-31)/9	59559	Robert Price	04/2015
8638	2^197840-465	59556	Lelio R Paula	05/2011
8637	(31*2^197856-1)/3889605	59556	Lelio R Paula	01/2014
8639	2^197808-17805	59547	Enzo Doria	05/2013
8640	2^197781-17905	59539	Enzo Doria	05/2013
8641	2^197777-17473	59537	Enzo Doria	05/2013
8642	6^76507-149	59535	Lelio R Paula	10/2012
8644	Phi(61456,109)	59526	Enzo Doria	05/2012
8643	18^47420+23	59526	Lelio R Paula	03/2013
8645	(59^33613+1)/60	59522	Paul Bourdelais	08/2017
8646	3^124747+94	59520	Lelio R Paula	10/2012
8647	17^48370+18	59517	Lelio R Paula	03/2013
8648	20^45740-1523	59510	Enzo Doria	03/2013
8649	(47*10^59509+493)/9	59510	Robert Price	11/2017
8650	(7*2^197642-1)/3051	59494	Lelio R Paula	01/2014
8651	18^47390-1853	59488	Enzo Doria	03/2013
8652	(2^197581-7)/1915	59475	Lelio R Paula	02/2012
8653	(24737*2^197559+1)/77	59474	Lelio R Paula	06/2014
8654	2^197540-2459	59466	Yves Minet	07/2014
8655	(44*10^59454+1)/9	59455	Serge Batalov	11/2010
8656	2^197494-17805	59452	Enzo Doria	05/2013
8657	2^197482-16821	59449	Enzo Doria	05/2013
8658	2^197485+75767	59449	Enzo Doria	04/2016
8659	(3*2^197483+1)/25	59448	Lelio R Paula	07/2012
8660	2^197466-1868351	59444	Enzo Doria	04/2016
8661	2^197411-17781	59427	Enzo Doria	05/2013
8662	(F(142164)^3-F(142163)^3)/F(142162)	59421	Wayne Halsdorf	03/2012
8663	2^197392-114629	59421	Enzo Doria	05/2015
8664	2^197355-157	59410	Lelio R Paula	04/2011
8665	5^84992-84	59407	Lelio R Paula	10/2012
8666	2*3^124504-5	59404	Lelio R Paula	04/2014
8667	2^197307-19165	59396	Enzo Doria	05/2013
8669	2^197303+32769	59395	Lelio R Paula	05/2011
8668	2*10^59394-69	59395	Robert Price	07/2017
8670	(53*10^59389+1)/9	59390	Serge Batalov	11/2010
8671	6^76316-35	59386	Lelio R Paula	10/2012
8672	2^197259-2929	59381	Yves Minet	09/2014
8673	lucasU(46,1,35715)-lucasU(46,1,35714)	59377	Mike Oakes	04/2009
8674	17^48253-6	59373	Lelio R Paula	03/2013
8675	2^197156-15837	59350	Enzo Doria	04/2013
8676	2^197152-4295	59349	Yves Minet	08/2018
8677	2^197149-18481	59348	Enzo Doria	05/2013
8678	2^197142-17157	59346	Enzo Doria	05/2013
8680	(F(6)^65707-F(5)^65707)/F(4)	59339	Wayne Halsdorf	04/2010
8679	(8^65707-5^65707)/3	59339	Robert Price	12/2012
8681	(2*14283^14283+1)/7925497975	59334	David Broadhurst	09/2010
8682	2^197012-111719	59307	Enzo Doria	05/2014
8683	2^196975+513	59296	Lelio R Paula	05/2011
8684	(61*10^59294+119)/9	59295	Robert Price	09/2017
8685	4*10^59292+39	59293	Robert Price	11/2017
8686	2^196960+97	59291	Lelio R Paula	04/2011
8687	9^62116+8^(62116-1)	59274	Robert Price	03/2016
8688	2^196900-97305	59273	Lelio R Paula	09/2011
8689	5*6^76155+7	59261	Lelio R Paula	09/2014
8690	15^50385-14	59258	Wojciech Florek	06/2006
8691	(136777#-1)/8823581477	59254	Donovan Johnson	05/2006
8692	(2^196744-3)*6-7	59227	Gilbert Mozzo	05/2016
8693	(67607*2^196696+1)/3	59216	Lelio R Paula	05/2014
8694	2^196696-112967	59212	Enzo Doria	06/2014
8695	20^45508-4223	59208	Enzo Doria	03/2013
8696	gcd(Phi(325820,10),(10^16291+1)^3(10^16291+1-10^8146)+(10^32582+10^16291)(10^8146+1)+10^48873)	59201	Serge Batalov	04/2015
8697	14^51651-81	59199	Lelio R Paula	03/2013
8698	2^196650-1451	59198	Yves Minet	08/2012
8699	2^196636-2797799	59194	Enzo Doria	04/2016
8700	1111*2^196610-555	59189	Henri Lifchitz	04/2005
8701	3^124041+658	59183	Lelio R Paula	10/2012
8702	2^196590-111797	59180	Enzo Doria	05/2014
8703	(10^59174-13)/3	59174	Robert Price	02/2017
8704	(2*10^59174-113)/3	59174	Robert Price	09/2017
8705	(9179*2^196533-1)/783	59164	Lelio R Paula	04/2015
8706	379*10^59152+9	59155	Arkadiusz Wesolowski	10/2011
8707	(404*10^59149-53)/9	59151	Robert Price	11/2017
8708	13^53095+40	59145	Lelio R Paula	03/2013
8710	2*F(282999)-1	59144	Henri Lifchitz	12/2009
8709	4*7^69984+3	59144	Lelio R Paula	09/2014
8711	(5*10^59142+1)/3	59143	Erik Branger	12/2013
8712	2^196463+5711	59142	Lelio R Paula	10/2011
8713	2^196453-97305	59139	Lelio R Paula	09/2011
8714	(28*10^59135+53)/9	59136	Serge Batalov	11/2008
8715	(28*10^59133+113)/3	59134	Robert Price	03/2016
8716	2^196434+7	59133	Lelio R Paula	04/2011
8717	(8*10^59127-29)/3	59128	Robert Price	05/2016
8718	2^196414+255	59127	Lelio R Paula	05/2011
8719	5^84586-92	59124	Lelio R Paula	10/2012
8720	2^196388-17177	59119	Enzo Doria	05/2013
8721	79427!6-6	59119	Robert Price	08/2018
8722	3^123890+20	59111	Lelio R Paula	10/2012
8723	2^196355-1021777	59109	Paul Bourdelais	11/2012
8724	11^56754-1410	59104	Enzo Doria	11/2012
8725	(7*2^196297-1)/1200407	59087	Lelio R Paula	01/2014
8726	(16*10^59062-19)/3	59063	Robert Price	03/2016
8727	35^38249-1228	59060	Enzo Doria	03/2013
8728	5^84475-18	59046	Lelio R Paula	10/2012
8729	2^196123-17701	59039	Enzo Doria	05/2013
8730	12^54702-31	59034	Lelio R Paula	03/2013
8731	2^196101-175	59033	Lelio R Paula	04/2011
8732	2^196085+5775	59028	Lelio R Paula	05/2011
8733	2^196034+11715	59013	Lelio R Paula	05/2011
8734	2^196018-18485	59008	Enzo Doria	05/2013
8735	2^195984-2163	58998	Yves Minet	08/2013
8736	3^123645-16	58994	Lelio R Paula	10/2012
8737	39^37078-38	58994	Norbert Schneider	05/2014
8738	2^195958-16853	58990	Enzo Doria	05/2013
8739	2^195930-3071	58981	Yves Minet	10/2014
8740	2^195924+513	58980	Lelio R Paula	05/2011
8741	2^195863+155	58961	Lelio R Paula	04/2011
8742	(28*10^58956+113)/3	58957	Robert Price	03/2016
8743	11^56612-9300	58956	Enzo Doria	02/2013
8744	2^195833-17173	58952	Enzo Doria	05/2013
8745	(27*2^195833-1)/53	58952	Lelio R Paula	01/2014
8746	(13*2^195821-1)/122425	58945	Lelio R Paula	01/2014
8747	139^27504-138	58942	Norbert Schneider	10/2015
8748	(418*10^58923+23)/9	58925	Robert Price	08/2017
8749	3^123495+44	58923	Lelio R Paula	10/2012
8750	2^195737-18565	58923	Enzo Doria	05/2013

Find by discoverer :

PRP Records

Probable Primes Top 10000

(252538 PRPs in the top)