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) !!!

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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 ?
9001	10^98288+3	98289	Robert Price	03/2011
9002	10^98288-117017	98288	Patrick De Geest	11/2011
9003	(44*10^98284-719)/9	98285	Robert Price	12/2017
9004	(5985^26021-1)/5984	98280	Serge Batalov	06/2022
9005	23466^15419+15419^23466	98277	Hans Havermann	02/2020
9006	2^326421-2797573	98263	Enzo Doria	04/2016
9007	2^326401+16095	98257	Lelio R Paula	07/2016
9008	(6494^25771-1)/6493	98249	Serge Batalov	06/2022
9009	7^116240-116240^7	98235	Norbert Schneider	05/2017
9010	17^79826-78	98222	Lelio R Paula	08/2016
9011	2^326268-809	98217	Yves Minet	04/2011
9012	22659^21590+21590^22659	98210	Hans Havermann	10/2019
9013	22268^22587-22587^22268	98202	Norbert Schneider	08/2020
9014	(418*10^98199+23)/9	98201	Robert Price	08/2017
9015	12*10^98198-7	98200	Robert Price	11/2017
9016	15^83496-76	98199	Lelio R Paula	08/2016
9017	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
9018	9*5^140471-4	98186	Lelio R Paula	11/2014
9019	(35103^21601-1)/35102	98180	Serge Batalov	06/2022
9021	22774^20455+20455^22774	98175	Hans Havermann	07/2020
9020	(4516^26863-1)/4515	98175	Serge Batalov	06/2022
9022	2^326069-2383	98157	Yves Minet	10/2013
9023	(9661^24631-1)/9660	98152	Serge Batalov	06/2022
9024	(4175^27109-1)/4174	98149	Serge Batalov	06/2022
9025	(57801^20611-1)/57800	98144	Serge Batalov	06/2022
9026	2^325973+1185	98128	Lelio R Paula	07/2016
9027	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
9028	2^325945-1847269	98120	Enzo Doria	07/2015
9029	8*10^98111-67	98112	Robert Price	10/2017
9030	(2^325902+1138)/2	98106	Stefano Morozzi	09/2020
9031	(215^42061-1)/214	98103	Serge Batalov	06/2022
9032	(6775^25609-1)/6774	98102	Serge Batalov	06/2022
9033	(6718^25633-1)/6717	98100	Serge Batalov	06/2022
9034	2^325866+15	98096	Lelio R Paula	12/2012
9035	22591^21952+21952^22591	98079	Hans Havermann	02/2020
9036	2^325765+1974305	98066	Enzo Doria	06/2016
9037	2^325733-58695	98056	Lelio R Paula	07/2016
9038	(7*10^98055-529)/9	98055	Robert Price	08/2021
9039	2^325717-3645	98051	Lelio R Paula	07/2016
9040	(2^325704+718)/2	98047	Stefano Morozzi	09/2020
9041	(15679^23371-1)/15678	98045	Serge Batalov	06/2022
9042	(23342^22441-1)/23341	98022	Serge Batalov	06/2022
9043	23968^12293+12293^23968	98021	Hans Havermann	11/2019
9044	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
9045	(7*10^98007-13)/3	98008	Robert Price	06/2016
9046	(2^325544+1110)/2	97999	Stefano Morozzi	09/2020
9047	2^325512-459959	97989	Enzo Doria	05/2015
9048	(2^325492+682)/2	97983	Stefano Morozzi	09/2020
9049	(3^205354-8)/17	97978	Lelio R Paula	09/2013
9050	2^325433+76817	97966	Enzo Doria	05/2016
9051	5*10^97963+81	97964	Robert Price	08/2017
9052	(13208^23773-1)/13207	97961	Serge Batalov	06/2022
9053	2^325390-109061	97953	Enzo Doria	04/2014
9054	(55*10^97940+323)/9	97941	Robert Price	10/2021
9055	13^87921+24	97940	Lelio R Paula	08/2016
9056	10^97930+188277	97931	Patrick De Geest	09/2022
9058	10^97930-7000001	97930	Robert Price	06/2021
9057	10^97930-66951	97930	Patrick De Geest	09/2022
9059	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
9060	(17968^23017-1)/17967	97922	Serge Batalov	06/2022
9061	(3337^27793-1)/3336	97922	Serge Batalov	06/2022
9063	22600^21499+21499^22600	97913	Hans Havermann	05/2020
9062	(18703^22921-1)/18702	97913	Serge Batalov	06/2022
9064	2^325215+12909	97900	Lelio R Paula	07/2016
9065	22619^21286+21286^22619	97898	Hans Havermann	04/2020
9066	(85*10^97876-49)/9	97877	Robert Price	12/2020
9067	7*10^97874-69	97875	Robert Price	01/2017
9068	5*10^97869-63	97870	Robert Price	04/2021
9069	(643*32^65022-23)/31	97870	Eric Chen	04/2023
9071	(17^79537+5^79537)/22	97865	Robert Price	06/2013
9070	15^83212+22	97865	Lelio R Paula	08/2016
9072	2^325087-109057	97861	Enzo Doria	04/2014
9073	2^325074+1870657	97858	Enzo Doria	05/2016
9075	2^325066-2111	97855	Yves Minet	08/2013
9074	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
9076	(8694^24841-1)/8693	97851	Serge Batalov	06/2022
9077	(21159^22621-1)/21158	97843	Serge Batalov	06/2022
9078	26660^4677+4677^26660	97842	Hans Havermann	12/2019
9079	18^77944-89	97841	Lelio R Paula	07/2016
9080	119^47136+118	97833	Norbert Schneider	09/2018
9081	6^125720-17663	97830	Enzo Doria	02/2013
9082	(73640^20101-1)/73639	97829	Serge Batalov	06/2022
9083	2^324972-2069	97827	Yves Minet	05/2013
9084	2^324958-4691	97823	Yves Minet	05/2019
9085	(8087^25033-1)/8086	97820	Serge Batalov	06/2022
9086	2^324944-2788319	97818	Enzo Doria	03/2016
9087	22845^19112+19112^22845	97807	Hans Havermann	10/2019
9088	(2^324898+1270)/2	97804	Stefano Morozzi	09/2020
9090	4*10^97799-9	97800	Erik Branger	11/2013
9089	2^324882+577294575	97800	Lelio R Paula	09/2016
9091	2^324863-1867921	97794	Enzo Doria	04/2016
9092	6^125662-18473	97785	Enzo Doria	03/2013
9093	12^90604+11	97779	Lelio R Paula	07/2016
9094	(29*10^97751+49)/3	97752	Robert Price	09/2021
9095	(37108^21391-1)/37107	97741	Serge Batalov	06/2022
9096	5^139830+24	97737	Lelio R Paula	04/2016
9097	(2^324672+1198)/2	97736	Stefano Morozzi	09/2020
9098	(101*10^97724+7)/9	97726	Robert Price	02/2022
9099	2^324612+1155	97718	Lelio R Paula	07/2016
9100	(2^324597+3542)/2	97714	Stefano Morozzi	09/2020
9101	19^76404-44	97702	Lelio R Paula	07/2016
9102	(5939^25889-1)/5938	97694	Serge Batalov	06/2022
9104	2^324505-2983	97686	Yves Minet	04/2011
9103	(7740^25121-1)/7739	97686	Serge Batalov	06/2022
9105	(144^45259+1)/145	97684	Paul Bourdelais	08/2019
9106	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
9107	(11234^24109-1)/11233	97651	Serge Batalov	06/2022
9108	6^125488-17843	97649	Enzo Doria	02/2013
9109	(2^324350+3198)/2	97639	Stefano Morozzi	09/2020
9110	(75638^20011-1)/75637	97624	Serge Batalov	06/2022
9111	7^115515-2	97622	Lelio R Paula	09/2013
9112	(15672^23269-1)/15671	97613	Serge Batalov	06/2022
9113	(89^50069-1)/88	97603	Paul Bourdelais	08/2017
9114	6^125418-5	97595	Lelio R Paula	11/2014
9115	(2^324193+3522)/2	97592	Stefano Morozzi	09/2020
9116	(2422^28837-1)/2421	97587	Serge Batalov	06/2022
9117	(2^324172+666)/2	97586	Stefano Morozzi	09/2020
9118	2^324091+111546435	97562	Paul Bourdelais	10/2021
9119	2^324076+1155	97557	Lelio R Paula	07/2016
9120	(2^324074+9)/13	97555	Lelio R Paula	10/2013
9121	(11*10^97539-71)/3	97540	Robert Price	04/2022
9122	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
9123	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
9124	2^323946+73939	97518	Enzo Doria	04/2016
9125	2^323937+1866947	97515	Enzo Doria	03/2016
9126	(98339^19531-1)/98338	97508	Serge Batalov	06/2022
9128	6^125290-18533	97495	Enzo Doria	03/2013
9127	(2^323870+1650)/2	97495	Stefano Morozzi	09/2020
9129	2^323845+101	97488	Lelio R Paula	12/2012
9130	18^77662+65	97487	Lelio R Paula	07/2016
9131	22634^20265+20265^22634	97479	Hans Havermann	04/2020
9132	(5533^26041-1)/5532	97467	Serge Batalov	06/2022
9133	2^323772+76771	97466	Enzo Doria	05/2016
9134	2^323765-112213	97463	Enzo Doria	06/2014
9135	22730^19389+19389^22730	97457	Hans Havermann	02/2020
9136	2^323720-6555	97450	Lelio R Paula	07/2016
9137	2^323694-1860401	97442	Enzo Doria	03/2016
9138	20^74886+3	97429	Lelio R Paula	06/2016
9139	24476^9561+9561^24476	97427	Hans Havermann	01/2020
9140	(2^323623+1766)/2	97420	Stefano Morozzi	09/2020
9141	(3250^27739-1)/3249	97413	Serge Batalov	06/2022
9143	3*10^97399+73	97400	Robert Price	04/2016
9142	7^115252-50	97400	Lelio R Paula	07/2016
9144	(4715^26513-1)/4714	97392	Serge Batalov	06/2022
9145	2^323521+213317	97390	Enzo Doria	09/2023
9146	224737#+393581	97389	Nicolas PALAU	12/2016
9147	(2^323468+3186)/2	97374	Stefano Morozzi	09/2020
9148	(2^323456+538)/2	97370	Stefano Morozzi	09/2020
9149	23277^15236+15236^23277	97365	Hans Havermann	07/2020
9151	(26*10^97353+31)/3	97354	Robert Price	07/2016
9150	(2^323403+3510)/2	97354	Stefano Morozzi	09/2020
9152	23756^12519+12519^23756	97342	Hans Havermann	07/2020
9153	10^97335+271641	97336	Patrick De Geest	09/2022
9155	10^97335-4000001	97335	Robert Price	07/2021
9154	10^97335-98193	97335	Patrick De Geest	09/2022
9156	(637*10^97331+11)/9	97333	Robert Price	10/2021
9157	23991^11402+11402^23991	97332	Hans Havermann	07/2020
9158	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
9159	(38*10^97329+187)/9	97330	Robert Price	11/2017
9160	(31147^21661-1)/31146	97328	Serge Batalov	06/2022
9161	86455!4+8	97319	Robert Price	09/2019
9162	22591^20310+20310^22591	97316	Hans Havermann	06/2020
9163	2^323261-431173	97312	Harrison Mesh	06/2022
9164	(3996^27017-1)/3995	97302	Serge Batalov	06/2022
9165	25101^7520+7520^25101	97297	Hans Havermann	05/2020
9166	(233*10^97294+7)/3	97296	Robert Price	03/2022
9167	p(19982)#/2-1024	97293	Robert Price	09/2017
9168	(65*10^97288+277)/9	97289	Robert Price	08/2021
9169	6^125021-85	97286	Lelio R Paula	08/2016
9170	2^323164-47355	97283	Lelio R Paula	07/2016
9171	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
9172	2^323054-6555	97249	Lelio R Paula	07/2016
9173	22822^18247+18247^22822	97249	Hans Havermann	02/2020
9174	9*10^97247-29	97248	Robert Price	05/2017
9175	24382^9735+9735^24382	97244	Hans Havermann	02/2020
9176	(31*10^97242+41)/9	97243	Robert Price	04/2015
9177	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
9178	12^90098-41	97233	Lelio R Paula	07/2016
9179	2^322928-216929	97212	Enzo Doria	05/2014
9180	(16731^23017-1)/16730	97209	Serge Batalov	06/2022
9181	3*10^97205-61	97206	Robert Price	04/2021
9182	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
9183	(35*10^97194-341)/9	97195	Robert Price	08/2021
9184	(4872^26357-1)/4871	97194	Serge Batalov	06/2022
9185	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
9186	(796*10^97183-31)/9	97185	Robert Price	07/2022
9187	(2^322789+2214)/2	97169	Stefano Morozzi	09/2020
9188	2^322725+75761	97150	Enzo Doria	04/2016
9189	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
9190	(2175^29101-1)/2174	97121	Serge Batalov	06/2022
9191	22402^21639+21639^22402	97118	Hans Havermann	07/2020
9192	23399^14128+14128^23399	97108	Hans Havermann	06/2020
9193	(2892^28057-1)/2891	97108	Serge Batalov	06/2022
9194	(9578^24391-1)/9577	97104	Serge Batalov	06/2022
9195	(2^322525+2606)/2	97090	Stefano Morozzi	09/2020
9196	(9563^24391-1)/9562	97087	Serge Batalov	06/2022
9197	(41*10^97085+373)/9	97086	Robert Price	04/2017
9198	(2^322473+854)/2	97074	Stefano Morozzi	02/2021
9199	2^322413+77	97056	Lelio R Paula	12/2012
9200	2^322406+177	97054	Lelio R Paula	12/2012
9201	(349^38167-1)/348	97050	Serge Batalov	06/2022
9202	(14*10^97044+31)/9	97045	Robert Price	02/2015
9203	2^322302+255255	97023	Lelio R Paula	07/2016
9204	2^322286+212659	97018	Enzo Doria	09/2023
9205	(1302^31147-1)/1301	97008	Serge Batalov	06/2022
9206	2^322196-113093	96991	Enzo Doria	07/2014
9207	(2^322169+2690)/2	96983	Stefano Morozzi	09/2020
9208	(49*10^96980+221)/9	96981	Robert Price	02/2022
9209	9*10^96968-47	96969	Robert Price	11/2021
9210	(5895^25717-1)/5894	96962	Serge Batalov	06/2022
9211	(27473^21841-1)/27472	96946	Serge Batalov	06/2022
9212	23109^15668+15668^23109	96943	Hans Havermann	07/2020
9213	2^322000-1861469	96932	Enzo Doria	03/2016
9214	2^321971-112747	96923	Enzo Doria	06/2014
9215	23754^12023+12023^23754	96917	Hans Havermann	07/2020
9216	11^93062-92	96915	Lelio R Paula	06/2016
9217	(37871^21169-1)/37870	96914	Serge Batalov	06/2022
9218	(2^321922+2214)/2	96908	Stefano Morozzi	09/2020
9219	(2^321900+2086)/2	96902	Stefano Morozzi	09/2020
9220	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
9221	3^203051+34	96880	Lelio R Paula	05/2016
9222	2*10^96867-51	96868	Robert Price	11/2017
9223	(2^321779+2618)/2	96865	Stefano Morozzi	09/2020
9224	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
9225	2^321716-2786939	96847	Enzo Doria	03/2016
9226	22496^20181+20181^22496	96844	Hans Havermann	03/2020
9227	2^321701-113053	96842	Enzo Doria	07/2014
9228	2^321700-28635	96842	Lelio R Paula	06/2016
9229	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
9230	6*10^96835+13	96836	Robert Price	10/2021
9231	6^124433-124433	96828	Robert Price	01/2014
9232	2^321631+69	96821	Lelio R Paula	12/2012
9233	(27109^21841-1)/27108	96820	Serge Batalov	06/2022
9234	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
9235	(5052^26141-1)/5051	96809	Serge Batalov	06/2022
9236	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
9237	(59*10^96798+31)/9	96799	Robert Price	09/2015
9238	(2^321536+2062)/2	96792	Stefano Morozzi	09/2020
9239	223319#+231223	96790	Makoto Morimoto	02/2016
9240	2^321519-28635	96787	Lelio R Paula	06/2016
9241	2^321487-1867237	96778	Enzo Doria	03/2016
9242	2^321461-63	96770	Lelio R Paula	12/2012
9243	(16053^23011-1)/16052	96770	Serge Batalov	06/2022
9244	2^321439+123	96763	Lelio R Paula	12/2012
9245	2^321434+709	96762	Lelio R Paula	02/2013
9246	2^321419+22703	96757	Enzo Doria	09/2023
9247	(2^321415+554)/2	96756	Stefano Morozzi	09/2020
9248	14^84413+89	96749	Lelio R Paula	07/2016
9249	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
9250	13^86847+96	96743	Lelio R Paula	06/2016

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Probable Primes Top 10000

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