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 ?
8751	(148*10^103718-1)/3	103720	Robert Price	03/2020
8752	2^344541-19561	103718	Enzo Doria	05/2013
8753	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
8754	(8896^26263-1)/8895	103714	Serge Batalov	06/2022
8755	(2^344503+1758)/2	103706	Stefano Morozzi	09/2020
8756	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
8757	2^344444-455	103688	Yves Minet	03/2012
8758	(4*10^103678-43)/3	103679	Robert Price	01/2022
8759	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
8760	(2^344367+2738)/2	103665	Stefano Morozzi	01/2021
8762	2^344317-109933	103650	Enzo Doria	04/2014
8761	26055^9508+9508^26055	103650	Hans Havermann	09/2020
8763	2^344309-1852033	103648	Enzo Doria	08/2015
8764	25729^10672+10672^25729	103643	Hans Havermann	09/2020
8765	(2^344289+1166)/2	103642	Stefano Morozzi	09/2020
8766	3*10^103637+61	103638	Robert Price	09/2020
8767	(2^344246+1614)/2	103629	Stefano Morozzi	09/2020
8768	2^344213-21253	103619	Enzo Doria	06/2013
8769	2^344196-465	103614	Lelio R Paula	11/2016
8770	2^344187-20001	103611	Enzo Doria	06/2013
8771	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
8772	(237^43627-1)/236	103601	Serge Batalov	06/2022
8773	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
8774	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
8775	(9^108553-2^108553)/7	103586	Jon Grantham	07/2023
8776	2^344085-20365	103580	Enzo Doria	06/2013
8777	5^148169+54	103566	Lelio R Paula	11/2016
8778	2^344017-108795	103560	Enzo Doria	03/2014
8779	(2^343974+2670)/2	103547	Stefano Morozzi	09/2020
8780	2^343971-5077	103546	Lelio R Paula	09/2011
8781	(7*10^103531+71)/3	103532	Robert Price	05/2018
8782	2^343899+141	103524	Lelio R Paula	08/2011
8783	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
8784	6^133029-67	103517	Lelio R Paula	11/2016
8785	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
8786	66*10^103507+7	103509	Robert Price	07/2020
8787	26297^8614+8614^26297	103485	Hans Havermann	09/2020
8788	(2^343764+2658)/2	103483	Stefano Morozzi	09/2020
8789	26499^8036+8036^26499	103480	Hans Havermann	09/2020
8790	(103^51413-1)/4478483706	103477	Paul Vanderveen	06/2025
8791	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
8792	5^148014-24	103458	Lelio R Paula	11/2016
8793	25^74007-24	103458	Anonymous	09/2024
8794	28316^4503+4503^28316	103453	Hans Havermann	09/2020
8795	(22*10^103450+53)/3	103451	Robert Price	07/2019
8796	2^343604+9931	103436	Yves Minet	01/2011
8797	2^343601-21189	103435	Enzo Doria	06/2013
8798	(10^103423+173)/3	103423	Robert Price	05/2021
8799	2^343508-115229	103407	Enzo Doria	06/2015
8800	(8766^26227-1)/8765	103404	Serge Batalov	06/2022
8801	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
8802	3^216685-113056	103386	Enzo Doria	07/2014
8803	24829^14580+14580^24829	103382	Hans Havermann	08/2020
8804	91355!4+1024	103381	Robert Price	09/2019
8805	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
8806	11^99262-20	103371	Lelio R Paula	12/2016
8807	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
8808	(2^343363+3570)/2	103363	Stefano Morozzi	09/2020
8809	2^343356-2791889	103361	Enzo Doria	03/2016
8810	(25*10^103360-241)/9	103361	Robert Price	05/2018
8811	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
8812	(371*33^68040-19)/32	103321	Eric Chen	05/2023
8813	24826^14511+14511^24826	103319	Hans Havermann	09/2020
8814	2^343182-171	103309	Lelio R Paula	08/2011
8815	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
8816	(16487^24649-1)/(16487^157-1)	103287	Ryan Propper	11/2023
8817	(10680^25639-1)/10679	103285	Serge Batalov	06/2022
8818	(7427^26683-1)/7426	103282	Serge Batalov	06/2022
8819	2^343079-1835611	103278	Enzo Doria	05/2015
8820	2^343063-1147	103273	Yves Minet	06/2013
8821	24741^14930+14930^24741	103271	Hans Havermann	09/2020
8822	(16*10^103255-73)/3	103256	Robert Price	07/2020
8823	(219^44119-1)/218	103256	Serge Batalov	06/2022
8824	9*6^132689+7	103254	Lelio R Paula	11/2014
8825	2^342979-18085	103247	Enzo Doria	05/2013
8826	(16*10^103244-31)/3	103245	Robert Price	03/2019
8827	2^342966-16995	103244	Lelio R Paula	11/2016
8828	23797^21774+21774^23797	103230	Hans Havermann	09/2020
8829	25388^11637+11637^25388	103224	Hans Havermann	09/2020
8830	(2^342876+2086)/2	103216	Stefano Morozzi	09/2020
8831	(16*10^103214-31)/3	103215	Robert Price	03/2019
8833	(37*10^103211+611)/9	103212	Robert Price	11/2018
8832	(238*10^103210-1)/3	103212	Robert Price	04/2020
8834	5^147650+16	103203	Lelio R Paula	11/2016
8835	gcd(Phi(852060,10),(10^42603+1)^3(10^42603+1-10^21302)+(10^85206+10^42603)(10^21302+1)+10^127809)	103201	Serge Batalov	04/2015
8836	Phi(852060L,10)	103201	Anonymous	03/2025
8837	2^342817+2707067	103199	Enzo Doria	03/2016
8838	43^63177-42	103198	Theodore Burton	02/2007
8839	2^342805-21025	103195	Enzo Doria	06/2013
8840	24129^18890+18890^24129	103182	Hans Havermann	09/2020
8841	(622*10^103171-1)/9	103173	Robert Price	11/2021
8842	2^342714+12285	103168	Lelio R Paula	11/2016
8843	(2*10^103161-17)/3	103161	Serge Batalov	11/2022
8844	18^82178-4481	103156	Enzo Doria	03/2013
8845	2^342665-17349	103153	Enzo Doria	05/2013
8846	30408^2467+2467^30408	103150	Hans Havermann	09/2020
8847	(5^147571-3^147571)/2	103148	Kellen Shenton	05/2022
8848	(2^342615+3090)/2	103138	Stefano Morozzi	09/2020
8849	2^342612+175	103137	Lelio R Paula	08/2011
8850	5*2^342585-3	103130	Lelio R Paula	09/2014
8851	(16*10^103127+77)/3	103128	Robert Price	03/2019
8852	(2^342527+3774)/2	103111	Stefano Morozzi	02/2021
8853	2^342503-19209	103104	Enzo Doria	05/2013
8854	(2^342484+2586)/2	103098	Stefano Morozzi	09/2020
8855	2^342476+51	103096	Lelio R Paula	08/2011
8856	2^342460-18885	103091	Enzo Doria	05/2013
8857	(2^342442+862)/2	103086	Stefano Morozzi	02/2021
8858	(194*10^103074-17)/3	103076	Robert Price	09/2020
8859	7^121968+82	103075	Lelio R Paula	10/2016
8860	2^342392-108863	103071	Enzo Doria	03/2014
8861	(2^342389+806)/2	103070	Stefano Morozzi	01/2021
8862	3^216014+28	103065	Lelio R Paula	11/2016
8863	2^342353-108879	103059	Enzo Doria	03/2014
8864	10^103055+276081	103056	Patrick De Geest	12/2016
8865	10^103055-53	103055	Lelio R Paula	11/2016
8866	(58*10^103046+419)/9	103047	Robert Price	05/2019
8867	7^121933+4	103046	Lelio R Paula	11/2014
8868	(71*10^103028-143)/9	103029	Robert Price	10/2021
8869	(2^342235+3618)/2	103023	Stefano Morozzi	09/2020
8870	19^80560-68	103017	Lelio R Paula	10/2016
8871	2^342209+76607	103016	Enzo Doria	05/2016
8873	328^40945+40945^328	103013	Norbert Schneider	12/2014
8872	12^95454-91	103013	Lelio R Paula	10/2016
8874	25833^9716+9716^25833	103009	Hans Havermann	01/2019
8875	(893*10^103004+7)/9	103006	Robert Price	06/2021
8876	(1475^32503-1)/1474	102993	Serge Batalov	06/2022
8877	65^56809-64^56809	102990	Robert Price	08/2013
8878	5^147338-6	102985	Lelio R Paula	11/2014
8879	2^342084-112739	102978	Enzo Doria	06/2014
8880	9*6^132330+7	102974	Lelio R Paula	11/2014
8881	2^342034-16737	102963	Enzo Doria	05/2013
8882	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
8883	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
8884	2^341991-17421	102950	Enzo Doria	05/2013
8885	2^341969-112225	102943	Enzo Doria	06/2014
8886	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
8887	2^341859+1869413	102910	Enzo Doria	05/2016
8888	10^102909+61	102910	Lelio R Paula	11/2016
8889	10^102909-67049	102909	Patrick De Geest	12/2016
8890	23814^20935+20935^23814	102898	Hans Havermann	02/2019
8891	28345^4264+4264^28345	102888	Hans Havermann	02/2019
8892	25665^10204+10204^25665	102886	Hans Havermann	02/2019
8893	26288^8181+8181^26288	102860	Hans Havermann	02/2019
8894	2^341659+1836773	102850	Enzo Doria	03/2016
8895	2^341608-110639	102835	Enzo Doria	05/2014
8896	10^102824+49	102825	Lelio R Paula	11/2016
8897	10^102824-168011	102824	Patrick De Geest	12/2016
8898	(156^46877-1)/155	102805	Anonymous	06/2024
8899	11^98708-8	102794	Lelio R Paula	10/2016
8900	2^341466+4429	102792	Lelio R Paula	09/2011
8901	2^341460-107	102790	Lelio R Paula	08/2011
8902	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
8903	2^341355+21	102759	Lelio R Paula	08/2011
8904	2^341319+224885	102748	Enzo Doria	07/2024
8905	(419^39181-1)/418	102739	Tom Wu	07/2024
8906	(6496^26947-1)/6495	102736	Serge Batalov	06/2022
8907	2^341246+40755	102726	Lelio R Paula	11/2016
8908	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
8909	7^121547+78	102720	Lelio R Paula	10/2016
8910	2^341223-461197	102719	Enzo Doria	06/2015
8911	27838^4893+4893^27838	102711	Hans Havermann	03/2019
8913	2^341190-20577	102709	Enzo Doria	06/2013
8912	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
8914	(25*10^102698+77)/3	102699	Robert Price	09/2022
8915	6^131976-65	102698	Lelio R Paula	10/2016
8916	2^341134+2533	102692	Henri Lifchitz	09/2005
8917	13^92184-54	102688	Lelio R Paula	10/2016
8918	2^341116-20873	102687	Enzo Doria	06/2013
8919	2^341094-19953	102680	Enzo Doria	06/2013
8920	23761^20950+20950^23761	102676	Hans Havermann	03/2019
8922	2^341053+129	102668	Lelio R Paula	08/2011
8921	(4724^27943-1)/4723	102668	Serge Batalov	06/2022
8924	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
8923	7^121471+94	102655	Lelio R Paula	10/2016
8926	2^341004-173	102653	Lelio R Paula	08/2011
8925	20^78901+3	102653	Lelio R Paula	10/2016
8927	(2^341001+1674)/2	102652	Stefano Morozzi	09/2020
8928	5^146853-52	102646	Lelio R Paula	10/2016
8929	2^340969-216931	102642	Enzo Doria	05/2014
8930	122^49196+121	102641	Norbert Schneider	10/2018
8931	2^340952+1870021	102637	Enzo Doria	05/2016
8932	5*2^340940-3	102634	Lelio R Paula	08/2014
8933	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
8934	(11*10^102629-23)/3	102630	Robert Price	09/2021
8935	3^215094+5*2^215094	102626	Jon Grantham	08/2023
8936	25876^9239+9239^25876	102615	Hans Havermann	02/2019
8937	(4*10^102612+83)/3	102613	Robert Price	02/2018
8938	(234^43313-1)/20184091	102611	Aurel Gibier	03/2025
8940	75^54717+74	102598	Norbert Schneider	01/2015
8939	(17*10^102597+13)/3	102598	Robert Price	01/2019
8941	2^340806-20393	102593	Enzo Doria	06/2013
8942	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
8943	6^131821+77	102577	Lelio R Paula	10/2016
8944	(203*10^102561-11)/3	102563	Robert Price	12/2020
8945	(67^56171-1)/2053280351166	102561	Paul Vanderveen	05/2025
8946	2^340688-29	102558	Henri Lifchitz	05/2005
8947	2^340685-109101	102557	Enzo Doria	04/2014
8948	65^56567-64	102552	Norbert Schneider	11/2014
8949	26230^8121+8121^26230	102550	Hans Havermann	03/2019
8950	(64*10^102547+161)/9	102548	Robert Price	08/2022
8951	(8*10^102541+49)/3	102542	Robert Price	05/2020
8952	(536*10^102533-23)/9	102535	Robert Price	02/2020
8953	2^340547-108897	102515	Enzo Doria	03/2014
8954	(2^340536+778)/2	102512	Stefano Morozzi	09/2020
8955	25592^10119+10119^25592	102500	Hans Havermann	02/2019
8956	(5*10^102492-23)/9	102492	Serge Batalov	11/2022
8957	7^121268+82	102484	Lelio R Paula	10/2016
8958	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
8959	2^340434-5955	102481	Lelio R Paula	11/2016
8960	(7*10^102480-19)/3	102481	Robert Price	10/2020
8961	(2^340381+47)/7	102465	Lelio R Paula	12/2013
8962	111^50095+110	102461	Norbert Schneider	04/2017
8963	180^45427-45427^180	102451	Norman Luhn	09/2024
8964	2^340291-20301	102438	Enzo Doria	06/2013
8965	12^94915+89	102431	Lelio R Paula	10/2016
8966	(106*10^102422+17)/3	102424	Robert Price	04/2021
8967	24466^15349+15349^24466	102417	Hans Havermann	03/2019
8968	2^340212+111546435	102415	Paul Bourdelais	10/2021
8969	2^340208-20373	102413	Enzo Doria	06/2013
8970	6^131598-17273	102404	Enzo Doria	02/2013
8971	(2^340132+1182)/2	102390	Stefano Morozzi	09/2020
8972	(2^340133+1166)/2	102390	Stefano Morozzi	09/2020
8973	2^340115-21181	102385	Enzo Doria	06/2013
8974	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
8975	(2^340064+3630)/2	102370	Stefano Morozzi	09/2020
8976	9348*31^68638+13	102369	Eric Chen	04/2024
8977	89^52511-88^52511	102365	Robert Price	06/2015
8978	3^214539-112756	102362	Enzo Doria	07/2014
8979	Phi(562221,2)/53723397926257372614541581386770268796893300042857	102361	Anonymous	06/2025
8980	23159^23450-23450^23159	102353	Norbert Schneider	12/2019
8981	2^340000-19877	102351	Enzo Doria	06/2013
8983	2^339990-114845	102348	Enzo Doria	05/2015
8982	311^41058-41058^311	102348	Norman Luhn	09/2024
8984	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
8985	20^78661-99	102341	Lelio R Paula	09/2016
8986	2^339951-19585	102336	Enzo Doria	05/2013
8987	(17*10^102335-167)/3	102336	Robert Price	05/2022
8988	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
8989	(236282#+121441)/(121441*25499429)	102332	Makoto Morimoto	08/2020
8990	5*10^102323-91	102324	Robert Price	03/2021
8992	2^339889+29327	102317	Yves Minet	06/2010
8991	(167*10^102315-17)/3	102317	Robert Price	03/2020
8993	26348^7641+7641^26348	102314	Hans Havermann	03/2019
8994	Phi(239414,10)/6333218543	102303	Makoto Kamada	08/2019
8995	2^339834-109493	102301	Enzo Doria	04/2014
8996	(16*10^102299-19)/3	102300	Robert Price	02/2019
8997	(11^98221-5^98221)/6	102286	Robert Price	01/2013
8998	3^214365+1820	102279	Lelio R Paula	10/2016
8999	31978^1579+1579^31978	102278	Hans Havermann	03/2019
9000	(89*10^102262-467)/9	102263	Robert Price	04/2022

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Probable Primes Top 10000

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