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	2^342353-108879	103059	Enzo Doria	03/2014
9002	10^103055+276081	103056	Patrick De Geest	12/2016
9003	10^103055-53	103055	Lelio R Paula	11/2016
9004	(58*10^103046+419)/9	103047	Robert Price	05/2019
9005	7^121933+4	103046	Lelio R Paula	11/2014
9006	(71*10^103028-143)/9	103029	Robert Price	10/2021
9007	(2^342235+3618)/2	103023	Stefano Morozzi	09/2020
9008	19^80560-68	103017	Lelio R Paula	10/2016
9009	2^342209+76607	103016	Enzo Doria	05/2016
9011	328^40945+40945^328	103013	Norbert Schneider	12/2014
9010	12^95454-91	103013	Lelio R Paula	10/2016
9012	25833^9716+9716^25833	103009	Hans Havermann	01/2019
9013	(893*10^103004+7)/9	103006	Robert Price	06/2021
9014	(1475^32503-1)/1474	102993	Serge Batalov	06/2022
9015	65^56809-64^56809	102990	Robert Price	08/2013
9016	5^147338-6	102985	Lelio R Paula	11/2014
9017	2^342084-112739	102978	Enzo Doria	06/2014
9018	9*6^132330+7	102974	Lelio R Paula	11/2014
9019	2^342034-16737	102963	Enzo Doria	05/2013
9020	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
9021	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
9022	2^341991-17421	102950	Enzo Doria	05/2013
9023	2^341969-112225	102943	Enzo Doria	06/2014
9024	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
9025	2^341859+1869413	102910	Enzo Doria	05/2016
9026	10^102909+61	102910	Lelio R Paula	11/2016
9027	10^102909-67049	102909	Patrick De Geest	12/2016
9028	23814^20935+20935^23814	102898	Hans Havermann	02/2019
9029	28345^4264+4264^28345	102888	Hans Havermann	02/2019
9030	25665^10204+10204^25665	102886	Hans Havermann	02/2019
9031	26288^8181+8181^26288	102860	Hans Havermann	02/2019
9032	2^341659+1836773	102850	Enzo Doria	03/2016
9033	2^341608-110639	102835	Enzo Doria	05/2014
9034	10^102824+49	102825	Lelio R Paula	11/2016
9035	10^102824-168011	102824	Patrick De Geest	12/2016
9036	(156^46877-1)/155	102805	Anonymous	06/2024
9037	11^98708-8	102794	Lelio R Paula	10/2016
9038	2^341466+4429	102792	Lelio R Paula	09/2011
9039	2^341460-107	102790	Lelio R Paula	08/2011
9040	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
9041	2^341355+21	102759	Lelio R Paula	08/2011
9042	2^341319+224885	102748	Enzo Doria	07/2024
9043	(419^39181-1)/418	102739	Tom Wu	07/2024
9044	(6496^26947-1)/6495	102736	Serge Batalov	06/2022
9045	2^341246+40755	102726	Lelio R Paula	11/2016
9046	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
9047	7^121547+78	102720	Lelio R Paula	10/2016
9048	2^341223-461197	102719	Enzo Doria	06/2015
9049	27838^4893+4893^27838	102711	Hans Havermann	03/2019
9051	2^341190-20577	102709	Enzo Doria	06/2013
9050	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
9052	(25*10^102698+77)/3	102699	Robert Price	09/2022
9053	6^131976-65	102698	Lelio R Paula	10/2016
9054	2^341134+2533	102692	Henri Lifchitz	09/2005
9055	13^92184-54	102688	Lelio R Paula	10/2016
9056	2^341116-20873	102687	Enzo Doria	06/2013
9057	2^341094-19953	102680	Enzo Doria	06/2013
9058	23761^20950+20950^23761	102676	Hans Havermann	03/2019
9060	2^341053+129	102668	Lelio R Paula	08/2011
9059	(4724^27943-1)/4723	102668	Serge Batalov	06/2022
9062	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
9061	7^121471+94	102655	Lelio R Paula	10/2016
9064	2^341004-173	102653	Lelio R Paula	08/2011
9063	20^78901+3	102653	Lelio R Paula	10/2016
9065	(2^341001+1674)/2	102652	Stefano Morozzi	09/2020
9066	5^146853-52	102646	Lelio R Paula	10/2016
9067	2^340969-216931	102642	Enzo Doria	05/2014
9068	122^49196+121	102641	Norbert Schneider	10/2018
9069	2^340952+1870021	102637	Enzo Doria	05/2016
9070	5*2^340940-3	102634	Lelio R Paula	08/2014
9071	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
9072	(11*10^102629-23)/3	102630	Robert Price	09/2021
9073	3^215094+5*2^215094	102626	Jon Grantham	08/2023
9074	25876^9239+9239^25876	102615	Hans Havermann	02/2019
9075	(4*10^102612+83)/3	102613	Robert Price	02/2018
9076	(234^43313-1)/20184091	102611	Aurel Gibier	03/2025
9078	75^54717+74	102598	Norbert Schneider	01/2015
9077	(17*10^102597+13)/3	102598	Robert Price	01/2019
9079	2^340806-20393	102593	Enzo Doria	06/2013
9080	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
9081	6^131821+77	102577	Lelio R Paula	10/2016
9082	(203*10^102561-11)/3	102563	Robert Price	12/2020
9083	(67^56171-1)/2053280351166	102561	Paul Vanderveen	05/2025
9084	2^340688-29	102558	Henri Lifchitz	05/2005
9085	2^340685-109101	102557	Enzo Doria	04/2014
9086	65^56567-64	102552	Norbert Schneider	11/2014
9087	26230^8121+8121^26230	102550	Hans Havermann	03/2019
9088	(64*10^102547+161)/9	102548	Robert Price	08/2022
9089	(8*10^102541+49)/3	102542	Robert Price	05/2020
9090	(536*10^102533-23)/9	102535	Robert Price	02/2020
9091	2^340547-108897	102515	Enzo Doria	03/2014
9092	(2^340536+778)/2	102512	Stefano Morozzi	09/2020
9093	25592^10119+10119^25592	102500	Hans Havermann	02/2019
9094	(5*10^102492-23)/9	102492	Serge Batalov	11/2022
9095	7^121268+82	102484	Lelio R Paula	10/2016
9096	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
9097	2^340434-5955	102481	Lelio R Paula	11/2016
9098	(7*10^102480-19)/3	102481	Robert Price	10/2020
9099	(2^340381+47)/7	102465	Lelio R Paula	12/2013
9100	111^50095+110	102461	Norbert Schneider	04/2017
9101	180^45427-45427^180	102451	Norman Luhn	09/2024
9102	2^340291-20301	102438	Enzo Doria	06/2013
9103	12^94915+89	102431	Lelio R Paula	10/2016
9104	(106*10^102422+17)/3	102424	Robert Price	04/2021
9105	24466^15349+15349^24466	102417	Hans Havermann	03/2019
9106	2^340212+111546435	102415	Paul Bourdelais	10/2021
9107	2^340208-20373	102413	Enzo Doria	06/2013
9108	6^131598-17273	102404	Enzo Doria	02/2013
9109	(2^340132+1182)/2	102390	Stefano Morozzi	09/2020
9110	(2^340133+1166)/2	102390	Stefano Morozzi	09/2020
9111	2^340115-21181	102385	Enzo Doria	06/2013
9112	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
9113	(2^340064+3630)/2	102370	Stefano Morozzi	09/2020
9114	9348*31^68638+13	102369	Eric Chen	04/2024
9115	89^52511-88^52511	102365	Robert Price	06/2015
9116	3^214539-112756	102362	Enzo Doria	07/2014
9117	Phi(562221,2)/53723397926257372614541581386770268796893300042857	102361	Anonymous	06/2025
9118	23159^23450-23450^23159	102353	Norbert Schneider	12/2019
9119	2^340000-19877	102351	Enzo Doria	06/2013
9121	2^339990-114845	102348	Enzo Doria	05/2015
9120	311^41058-41058^311	102348	Norman Luhn	09/2024
9122	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
9123	20^78661-99	102341	Lelio R Paula	09/2016
9124	2^339951-19585	102336	Enzo Doria	05/2013
9125	(17*10^102335-167)/3	102336	Robert Price	05/2022
9126	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
9127	(236282#+121441)/(121441*25499429)	102332	Makoto Morimoto	08/2020
9128	5*10^102323-91	102324	Robert Price	03/2021
9130	2^339889+29327	102317	Yves Minet	06/2010
9129	(167*10^102315-17)/3	102317	Robert Price	03/2020
9131	26348^7641+7641^26348	102314	Hans Havermann	03/2019
9132	Phi(239414,10)/6333218543	102303	Makoto Kamada	08/2019
9133	2^339834-109493	102301	Enzo Doria	04/2014
9134	(16*10^102299-19)/3	102300	Robert Price	02/2019
9135	(11^98221-5^98221)/6	102286	Robert Price	01/2013
9136	3^214365+1820	102279	Lelio R Paula	10/2016
9137	31978^1579+1579^31978	102278	Hans Havermann	03/2019
9138	(89*10^102262-467)/9	102263	Robert Price	04/2022
9139	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
9140	2^339694-16995	102259	Lelio R Paula	09/2016
9141	(56*10^102255+691)/9	102256	Robert Price	05/2019
9142	122^49008+121	102249	Norbert Schneider	10/2018
9143	(2^339652+3178)/2	102246	Stefano Morozzi	09/2020
9144	7^120985-38	102245	Lelio R Paula	10/2016
9145	10^102244+122961	102245	Patrick De Geest	12/2016
9146	10^102244-27	102244	Lelio R Paula	09/2016
9147	7^120982-62	102242	Lelio R Paula	10/2016
9148	(2^339640+2670)/2	102242	Stefano Morozzi	09/2020
9149	4*6^131382-5	102236	Lelio R Paula	11/2014
9150	(2^339607+3290)/2	102232	Stefano Morozzi	02/2021
9151	2^339586-1091	102226	Yves Minet	11/2012
9152	11^98161-3072000	102225	Enzo Doria	12/2012
9153	9*7^120961-4	102225	Lelio R Paula	11/2014
9154	5*3^214250+2	102224	Serge Batalov	10/2010
9155	12^94713-59	102213	Lelio R Paula	10/2016
9156	12^94705+89	102204	Lelio R Paula	10/2016
9157	L(2*339475)%(2^339475)	102193	Henri Lifchitz	06/2025
9158	2^339407-177	102172	Lelio R Paula	08/2011
9159	4*10^102163-57	102164	Robert Price	10/2018
9160	2^339355+65	102157	Lelio R Paula	07/2011
9161	(28*10^102142-31)/3	102143	Robert Price	12/2019
9162	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
9163	(2^339268+1758)/2	102130	Stefano Morozzi	09/2020
9164	U(610865)	102130	Serge Batalov	07/2024
9165	s(178551)	102122	Robert Price	05/2020
9166	(797*10^102112-23)/9	102114	Robert Price	01/2022
9167	(5*10^102107+7)/3	102108	Tyler Busby	02/2023
9168	(2^339175+2790)/2	102102	Stefano Morozzi	02/2021
9171	2^339168+21	102100	Lelio R Paula	07/2011
9170	2^339167-108807	102100	Enzo Doria	03/2014
9169	(2^339169+42)/2	102100	Stefano Morozzi	09/2020
9172	2^339156+163	102097	Lelio R Paula	08/2011
9173	(2^339149+746)/2	102094	Stefano Morozzi	09/2020
9174	(25*10^102076-67)/3	102077	Robert Price	06/2019
9175	2^339081-4543	102074	Yves Minet	03/2019
9176	(3435^28867-1)/3434	102069	Serge Batalov	06/2022
9177	2*10^102062+77	102063	Robert Price	08/2020
9178	24327^15668+15668^24327	102053	Hans Havermann	02/2019
9179	10^102052+66793	102053	Patrick De Geest	09/2022
9181	10^102052-7000001	102052	Robert Price	06/2021
9180	10^102052-618623	102052	Patrick De Geest	09/2022
9182	2^339000-175635	102050	Stefano Morozzi	12/2021
9183	2^339000-151667	102050	Stefano Morozzi	12/2021
9184	2^338999+79289	102049	Stefano Morozzi	01/2022
9185	2^338998-63897	102049	Stefano Morozzi	12/2022
9186	2^338997+99659	102049	Stefano Morozzi	02/2023
9187	2^338994+188757	102048	Stefano Morozzi	05/2022
9188	2^338995+70785	102048	Stefano Morozzi	11/2022
9189	2^338994-12183	102048	Stefano Morozzi	12/2022
9190	2^338992+181591	102047	Stefano Morozzi	01/2022
9191	2^338992+136171	102047	Stefano Morozzi	03/2022
9192	2^338991-109435	102047	Stefano Morozzi	04/2022
9193	2^338991+193611	102047	Stefano Morozzi	09/2022
9194	2^338988-134619	102046	Stefano Morozzi	04/2022
9195	2^338987-62557	102046	Stefano Morozzi	12/2022
9196	2^338986-60141	102045	Stefano Morozzi	06/2022
9197	2^338986+98209	102045	Stefano Morozzi	11/2022
9198	2^338981+106391	102044	Stefano Morozzi	01/2022
9199	2^338982+34069	102044	Stefano Morozzi	03/2022
9200	2^338982-58781	102044	Stefano Morozzi	04/2022
9201	2^338980+70833	102044	Stefano Morozzi	11/2022
9202	2^338982-92111	102044	Stefano Morozzi	02/2023
9203	2^338977+83007	102043	Stefano Morozzi	02/2022
9204	2^338979-83601	102043	Stefano Morozzi	04/2022
9205	2^338975+28355	102042	Stefano Morozzi	01/2022
9206	2^338973+134619	102042	Stefano Morozzi	03/2022
9207	2^338974+183777	102042	Stefano Morozzi	03/2022
9208	2^338975+69293	102042	Stefano Morozzi	09/2022
9216	25080^11711+11711^25080	102041	Hans Havermann	02/2019
9209	2^338972+152343	102041	Stefano Morozzi	12/2021
9210	2^338972-180623	102041	Stefano Morozzi	02/2022
9211	2^338972+84441	102041	Stefano Morozzi	03/2022
9212	2^338971+64875	102041	Stefano Morozzi	05/2022
9213	2^338971+44985	102041	Stefano Morozzi	11/2022
9214	2^338971+145065	102041	Stefano Morozzi	11/2022
9215	2^338972-16635	102041	Stefano Morozzi	01/2023
9217	2^338968+53461	102040	Stefano Morozzi	01/2022
9218	2^338969+160175	102040	Stefano Morozzi	03/2022
9219	2^338967+13409	102040	Stefano Morozzi	04/2022
9220	2^338969+67635	102040	Stefano Morozzi	09/2022
9221	2^338969-15913	102040	Stefano Morozzi	01/2023
9222	2^338963-127455	102039	Stefano Morozzi	12/2021
9223	2^338963+132195	102039	Stefano Morozzi	02/2022
9224	2^338966+137919	102039	Stefano Morozzi	04/2022
9225	2^338963-87529	102039	Stefano Morozzi	12/2022
9226	2^338963-116859	102039	Stefano Morozzi	02/2023
9233	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
9227	2^338960+53935	102038	Stefano Morozzi	01/2022
9228	2^338962+83157	102038	Stefano Morozzi	02/2022
9229	2^338961+12341	102038	Stefano Morozzi	04/2022
9230	2^338960+63933	102038	Stefano Morozzi	05/2022
9231	2^338960+170791	102038	Stefano Morozzi	11/2022
9232	2^338962+21679	102038	Stefano Morozzi	11/2022
9234	2^338959-30919	102037	Stefano Morozzi	02/2022
9235	2^338959+164769	102037	Stefano Morozzi	05/2022
9236	2^338958-43161	102037	Stefano Morozzi	02/2023
9237	2^338954-177003	102036	Stefano Morozzi	12/2021
9238	2^338954+154207	102036	Stefano Morozzi	01/2022
9239	2^338956+182493	102036	Stefano Morozzi	02/2022
9240	2^338954+162715	102036	Stefano Morozzi	04/2022
9241	2^338955-158241	102036	Stefano Morozzi	04/2022
9242	2^338956-33395	102036	Stefano Morozzi	04/2022
9243	2^338954+190915	102036	Stefano Morozzi	06/2022
9244	2^338955+41643	102036	Stefano Morozzi	09/2022
9245	2^338954+194427	102036	Stefano Morozzi	09/2022
9246	2^338956+117967	102036	Stefano Morozzi	09/2022
9247	2^338956+195495	102036	Stefano Morozzi	11/2022
9248	2^338954-186371	102036	Stefano Morozzi	12/2022
9249	2^338950+175077	102035	Stefano Morozzi	12/2021
9250	2^338951-51687	102035	Stefano Morozzi	12/2021

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Probable Primes Top 10000

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