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	(25*2^281577-1)/23	84764	Lelio R Paula	02/2014
9002	2^281574-111546435	84763	Paul Bourdelais	10/2021
9003	20320^14819+14819^20320	84752	Hans Havermann	07/2020
9004	2^281500-455	84740	Yves Minet	03/2012
9005	10^84725+1145141919	84726	Marisa Kirisame	03/2015
9006	10^84725+142041	84726	Patrick De Geest	10/2015
9007	10^84725-138677	84725	Patrick De Geest	02/2016
9008	76^45044+75	84720	Norbert Schneider	02/2015
9009	54^48897-53	84709	Norbert Schneider	08/2014
9010	(9913*2^281377-1)/65	84706	Lelio R Paula	04/2015
9011	Phi(171124,10)/29946701/7761329021/58560344041	84700	Maksym Voznyy	11/2015
9012	2^281337-111223	84691	Enzo Doria	05/2014
9013	2^281308+54615	84683	Lelio R Paula	09/2013
9014	7*5^121144-6	84677	Lelio R Paula	10/2014
9015	(2^281270+3858)/2	84671	Stefano Morozzi	01/2020
9016	(2^281252+47)/3	84665	Lelio R Paula	01/2013
9017	11^81297-3150	84663	Enzo Doria	12/2012
9018	2^281208-303	84653	Yves Minet	02/2012
9019	197^36892-2	84648	Lelio R Paula	10/2017
9020	(21*2^281187+1)/2483	84644	Lelio R Paula	01/2013
9021	(4*10^84632-61)/3	84633	Robert Price	12/2021
9022	11^81247-84	84611	Lelio R Paula	10/2015
9023	(10876^20959-1)/10875	84597	Serge Batalov	08/2020
9024	2067^25516+25516^2067	84595	Norbert Schneider	11/2019
9026	17^68747-64	84590	Lelio R Paula	11/2015
9025	(2^281002+3718)/2	84590	Stefano Morozzi	01/2020
9027	5^121018-15596	84588	Enzo Doria	02/2013
9028	6^108702+7	84587	Lelio R Paula	11/2014
9029	10^84582+100677	84583	Patrick De Geest	05/2016
9030	10^84582-8001	84582	Robert Price	03/2016
9031	1828^25929+25929^1828	84580	Norbert Schneider	12/2019
9032	(2^280968+1446)/2	84580	Stefano Morozzi	01/2020
9033	3*5^121004-8	84579	Lelio R Paula	10/2014
9034	5^120996-84	84573	Lelio R Paula	10/2015
9035	(2^280896+1522)/2	84558	Stefano Morozzi	01/2020
9036	(10223*2^280881+1)/68419	84553	Lelio R Paula	06/2014
9037	2^280852+97681	84545	Yves Minet	08/2004
9038	2^280848-1203	84544	Lelio R Paula	09/2013
9039	5^120946-24	84538	Lelio R Paula	10/2015
9040	2^280810-2111	84533	Yves Minet	08/2013
9041	11^81161-5160	84521	Enzo Doria	01/2013
9042	2^280737-93	84511	Lelio R Paula	08/2012
9043	(2^280737+494)/2	84510	Stefano Morozzi	01/2020
9044	(2^280717+1166)/2	84504	Stefano Morozzi	01/2020
9045	2^280698+315	84499	Lelio R Paula	09/2013
9046	3^177099-340	84498	Lelio R Paula	12/2015
9047	(8201^21589-1)/8200	84493	Serge Batalov	08/2020
9048	(5*10^84469-107)/3	84470	Robert Price	01/2017
9049	(3^177002+7)/6696022272161744	84436	Lelio R Paula	12/2012
9050	(2^280500-1017)/823	84436	Lelio R Paula	01/2013
9051	24677^2640+2640^24677	84435	Hans Havermann	07/2020
9052	14^73660-5	84424	Lelio R Paula	11/2015
9053	(83*10^84413-101)/9	84414	Robert Price	08/2021
9054	(2^280405+746)/2	84411	Stefano Morozzi	01/2020
9056	(19*10^84409-61)/3	84410	Robert Price	04/2017
9055	20862^11119+11119^20862	84410	Hans Havermann	07/2020
9057	2^280388+117	84406	Lelio R Paula	08/2012
9058	2^280389-566533	84406	Paul Bourdelais	03/2013
9059	23423^4008+4008^23423	84392	Hans Havermann	07/2020
9060	(2^280340+3322)/2	84391	Stefano Morozzi	01/2020
9061	(141584^16384+1)/65537	84390	Syoichiro Yamada	06/2008
9062	(1897^25741-1)/1896	84378	Serge Batalov	08/2020
9064	119^40652+118	84376	Norbert Schneider	09/2018
9063	(2^280291+2274)/2	84376	Stefano Morozzi	01/2020
9065	2^280240-173	84361	Lelio R Paula	08/2012
9066	(184*10^84348-1)/3	84350	Robert Price	02/2017
9067	21068^10083+10083^21068	84348	Hans Havermann	07/2020
9068	4*10^84346+93	84347	Robert Price	01/2017
9069	7*2^280156-5	84337	Lelio R Paula	08/2014
9070	(8760^21391-1)/8759	84331	Serge Batalov	08/2020
9071	8*7^99782-3	84327	Lelio R Paula	10/2014
9072	(38*10^84325+169)/9	84326	Robert Price	11/2021
9073	2^280116+133	84324	Lelio R Paula	08/2012
9074	2^280118+54615	84324	Lelio R Paula	09/2013
9075	(509203*2^280090-1)/3	84321	Lelio R Paula	04/2015
9076	6^108354+47	84316	Lelio R Paula	12/2015
9077	(2^280069+462)/2	84309	Stefano Morozzi	01/2020
9078	20657^12058+12058^20657	84307	Hans Havermann	07/2020
9079	10^84305+141963	84306	Patrick De Geest	07/2013
9080	10^84305-57	84305	Robert Price	05/2011
9081	9^88339+38^88339-24^88339-3*2^88339	84297	Mike Oakes	01/2011
9082	75843!4-32	84295	Robert Price	11/2019
9083	3^176648-112804	84283	Enzo Doria	06/2014
9084	6^108310+115	84282	Lelio R Paula	12/2015
9085	(11*2^279968-1)/5	84280	Lelio R Paula	02/2014
9086	6^108288-16643	84265	Enzo Doria	02/2013
9087	2^279917-58695	84264	Lelio R Paula	08/2013
9088	65^46477+36	84259	Lelio R Paula	01/2016
9089	(2^279883+3230)/2	84253	Stefano Morozzi	01/2020
9090	(2^279876+1422)/2	84251	Stefano Morozzi	01/2020
9091	2^279866-1907	84249	Yves Minet	05/2013
9092	23140^4373+4373^23140	84248	Hans Havermann	07/2020
9093	19736^18567+18567^19736	84248	Hans Havermann	07/2020
9094	(3^176580-5)/28076	84246	Lelio R Paula	12/2012
9095	(p(17530)#+4)/2	84246	Robert Price	09/2017
9096	(2*10^84239+1)/3	84239	Serge Batalov	07/2009
9097	(7*10^84236-493)/9	84236	Robert Price	04/2021
9098	18^67103-41	84233	Lelio R Paula	11/2015
9099	20^64743-43	84233	Lelio R Paula	01/2016
9100	(2^279807+2454)/2	84230	Stefano Morozzi	01/2020
9101	19717^18672+18672^19717	84216	Hans Havermann	07/2020
9102	(2^279754+3574)/2	84215	Stefano Morozzi	01/2020
9103	143^39070+39070^143	84209	Serge Batalov	05/2014
9104	11^80857-5400	84204	Enzo Doria	01/2013
9105	23*10^84185-9	84187	Robert Price	10/2021
9106	(2^279642+3130)/2	84181	Stefano Morozzi	01/2020
9107	(13*10^84179+161)/3	84180	Robert Price	04/2017
9108	2^279634-110405	84179	Enzo Doria	05/2014
9109	(74*10^84170+313)/9	84171	Robert Price	11/2017
9110	2^279582-1017	84163	Lelio R Paula	08/2013
9111	(22*10^84159-19)/3	84160	Robert Price	02/2017
9112	p(17513)#/2+512	84156	Robert Price	05/2017
9113	(19*10^84144-43)/3	84145	Robert Price	10/2017
9114	(9*2^279507-1)/137	84139	Lelio R Paula	02/2014
9115	11^80792-810	84137	Enzo Doria	11/2012
9116	(97*10^84134-1)/3	84136	Serge Batalov	12/2014
9117	p(17507)#/2+32	84125	Robert Price	12/2016
9118	(1750^25939-1)/1749	84118	Serge Batalov	08/2020
9119	21485^8224+8224^21485	84116	Hans Havermann	04/2017
9120	3^176294-340	84114	Lelio R Paula	12/2015
9121	(3^176287+4)/2191	84107	Lelio R Paula	12/2012
9122	2^279388-719	84105	Yves Minet	05/2012
9123	(22699*2^279378+1)/221	84104	Lelio R Paula	06/2014
9124	(28*10^84095-67)/3	84096	Robert Price	10/2020
9125	(2^279343+578)/2	84091	Stefano Morozzi	01/2020
9126	2^279332-110447	84088	Enzo Doria	05/2014
9127	2^279320+7	84084	Lelio R Paula	06/2012
9128	127^39966-2	84081	Lelio R Paula	10/2017
9129	(2^279299+2490)/2	84078	Stefano Morozzi	01/2020
9130	(2^279301+1694)/2	84078	Stefano Morozzi	01/2020
9131	(2^279285+962)/2	84073	Stefano Morozzi	01/2020
9132	(2^279269+1122)/2	84069	Stefano Morozzi	01/2020
9133	(11*2^279240-1)/95	84059	Lelio R Paula	02/2014
9134	2^279218-111347	84053	Enzo Doria	05/2014
9135	35^54435+2	84052	Lelio R Paula	05/2013
9136	(2^279176+2998)/2	84041	Stefano Morozzi	01/2020
9137	(31*2^279191-1)/12511523	84040	Lelio R Paula	02/2014
9138	20996^10059+10059^20996	84038	Hans Havermann	05/2017
9139	97*10^84033-3	84035	Robert Price	01/2017
9140	(2^279153+1326)/2	84034	Stefano Morozzi	01/2020
9141	(2^279155+3534)/2	84034	Stefano Morozzi	01/2020
9142	21234^9067+9067^21234	84033	Hans Havermann	05/2017
9143	(134569^16384+1)/2	84033	Richard Fischer	06/2018
9144	(5858^22303-1)/5857	84029	Serge Batalov	08/2020
9145	(29*10^84024-119)/9	84025	Robert Price	12/2021
9146	2^279095-109717	84016	Enzo Doria	04/2014
9147	(2^279054+1438)/2	84004	Stefano Morozzi	01/2020
9148	10^83997+555597	83998	Patrick De Geest	02/2021
9149	10^83997-40001	83997	Robert Price	01/2021
9150	14^73282-99	83991	Lelio R Paula	11/2015
9151	21457^8200+8200^21457	83979	Hans Havermann	06/2017
9152	89*10^83976-7	83978	Robert Price	03/2017
9153	2^278955+173	83974	Lelio R Paula	06/2012
9154	(7*2^278851+1)/39	83942	Lelio R Paula	12/2012
9155	(9913*2^278844-1)/40803	83940	Lelio R Paula	04/2015
9156	5^120076-14846	83930	Enzo Doria	02/2013
9157	(85*10^83921-1)/3	83923	Robert Price	07/2017
9158	(2^278770-3)/23	83917	Lelio R Paula	12/2012
9159	(10^83916+449)/9	83916	Serge Batalov	12/2014
9161	2^278715+99	83902	Lelio R Paula	06/2012
9160	(132109^16384+1)/2	83902	Richard Fischer	05/2018
9162	40235!2-2^40235	83899	Robert Price	09/2015
9163	2^278698-171	83897	Lelio R Paula	06/2012
9164	(19*10^83894-43)/3	83895	Robert Price	10/2017
9165	6^107802+25	83887	Lelio R Paula	12/2015
9166	8*10^83880+39	83881	Robert Price	01/2017
9167	(58*10^83878+23)/9	83879	Robert Price	09/2015
9168	7^99244-90	83871	Lelio R Paula	10/2015
9169	(2^278601+1674)/2	83867	Stefano Morozzi	01/2020
9170	2^278554+4257	83854	Lelio R Paula	08/2013
9171	2^278504-109619	83839	Enzo Doria	04/2014
9172	2^278499+1870433	83837	Enzo Doria	05/2016
9173	(2^278487+570)/2	83833	Stefano Morozzi	01/2020
9174	105^41475+104	83829	Norbert Schneider	11/2016
9175	15^71276-68	83828	Lelio R Paula	11/2015
9176	2^278464-216413	83827	Enzo Doria	04/2013
9177	(2^278440+1602)/2	83819	Stefano Morozzi	01/2020
9178	(76*10^83816-211)/9	83817	Robert Price	10/2017
9179	(2^278429+1950)/2	83816	Stefano Morozzi	01/2020
9180	(2^278428+1750)/2	83815	Stefano Morozzi	01/2020
9181	(8*10^83811-101)/3	83812	Robert Price	10/2017
9182	2^278400+40755	83807	Lelio R Paula	08/2013
9183	(2^278394+3718)/2	83805	Stefano Morozzi	01/2020
9184	(2^278388+3586)/2	83803	Stefano Morozzi	01/2020
9185	(9*2^278381-1)/7	83802	Lelio R Paula	02/2014
9186	39^87813+6^87813+24^87813	83796	Mike Oakes	12/2010
9187	19551^19268+19268^19551	83773	Hans Havermann	05/2017
9188	20625^11522+11522^20625	83770	Hans Havermann	05/2017
9189	(44*10^83768-791)/9	83769	Robert Price	10/2017
9190	(87^43189+1)/88	83764	Paul Bourdelais	08/2017
9191	2^278235-49	83758	Lelio R Paula	06/2012
9192	23543^3610+3610^23543	83755	Hans Havermann	05/2017
9194	18^66711-91	83741	Lelio R Paula	11/2015
9193	4*10^83740-89	83741	Robert Price	08/2017
9195	(3*2^278172-1)/11	83738	Lelio R Paula	02/2014
9196	(15*29^57251+2561)/28	83724	Curtis Bright	05/2015
9197	4*7^99059-9	83716	Lelio R Paula	10/2014
9198	(2^278128-3)/126844724149	83714	Lelio R Paula	12/2012
9199	2^278077+1867211	83710	Enzo Doria	03/2016
9200	(85*10^83708+203)/9	83709	Robert Price	09/2020
9201	2^278059-27	83705	Lelio R Paula	06/2012
9202	214^35917+35917^214	83702	Norbert Schneider	12/2014
9203	(23*10^83693+7)/3	83694	Robert Price	10/2015
9204	85^43375-2	83689	Lelio R Paula	09/2013
9205	5*3^175360+4	83669	Lelio R Paula	07/2014
9206	(23^61441-1)/22	83665	Robert Price	01/2012
9207	20091^14596+14596^20091	83664	Hans Havermann	03/2017
9208	2^277907-110629	83659	Enzo Doria	05/2014
9209	19522^19283+19283^19522	83656	Hans Havermann	04/2017
9210	(2^277881+2570)/2	83651	Stefano Morozzi	01/2020
9211	8*5^119664-3	83643	Lelio R Paula	10/2014
9212	8*3^175299-7	83640	Lelio R Paula	07/2014
9213	(26*10^83638-413)/9	83639	Robert Price	10/2017
9214	(197*10^83636+7)/3	83638	Robert Price	12/2020
9215	3^175250+22	83616	Robert Price	12/2013
9217	11^80285+30	83609	Lelio R Paula	10/2015
9216	26870^1293+1293^26870	83609	Hans Havermann	03/2017
9218	(6730^21841-1)/6729	83604	Serge Batalov	08/2020
9219	(2828^24223-1)/2827	83602	Serge Batalov	08/2020
9220	2^277691+1874423	83594	Enzo Doria	06/2016
9221	13^75022-60	83571	Lelio R Paula	11/2015
9222	(2^277593+2622)/2	83564	Stefano Morozzi	01/2020
9223	14^72905-51	83559	Lelio R Paula	11/2015
9224	(17*2^277565-1)/543	83554	Lelio R Paula	02/2014
9225	5^119532-12	83550	Lelio R Paula	10/2015
9226	6^107358-16253	83541	Enzo Doria	02/2013
9227	10^83534+3593037	83535	Paul Bourdelais	10/2021
9228	2^277478-460211	83530	Enzo Doria	06/2015
9229	(2^277474+814)/2	83528	Stefano Morozzi	01/2020
9230	(22*10^83525-7)/3	83526	Erik Branger	09/2014
9231	(30^56543+1)/31	83520	Robert Price	07/2013
9232	2^277417-460783	83511	Paul Bourdelais	04/2013
9233	(2^277404+3582)/2	83507	Stefano Morozzi	01/2020
9234	(22699*2^277387+1)/219	83504	Lelio R Paula	06/2014
9235	(31*2^277383-1)/247	83500	Lelio R Paula	02/2014
9236	21368^8085+8085^21368	83500	Hans Havermann	04/2017
9237	(2^277353+3750)/2	83492	Stefano Morozzi	01/2020
9238	(2^277348+3538)/2	83490	Stefano Morozzi	01/2020
9239	(9*2^277342+1)/13	83489	Lelio R Paula	12/2012
9240	5^119439-66	83485	Lelio R Paula	10/2015
9241	(14*10^83471-101)/3	83472	Robert Price	04/2017
9242	5*6^107263+7	83468	Lelio R Paula	10/2014
9243	(64*10^83461-1)/9	83462	Serge Batalov	11/2010
9244	2^277244-175709	83459	Hans Havermann	10/2018
9245	(2^277230+1450)/2	83455	Stefano Morozzi	01/2020
9246	(2^277232+3658)/2	83455	Stefano Morozzi	01/2020
9247	17^67796-92	83420	Lelio R Paula	11/2015
9248	2^277106-110057	83418	Enzo Doria	04/2014
9249	6^107200-19	83418	Lelio R Paula	12/2015
9250	2*10^83416+47	83417	Robert Price	12/2021

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Probable Primes Top 10000

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