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 ?
6751	(2^397696+1042)/2	119719	Stefano Morozzi	09/2020
6752	(19*10^119716+101)/3	119717	Robert Price	09/2019
6753	29563^11208+11208^29563	119717	Hans Havermann	02/2021
6754	458^44991-44991^458	119715	Norman Luhn	09/2024
6755	2^397655-933075	119707	Paul Bourdelais	06/2021
6756	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
6757	28243^17308+17308^28243	119701	Hans Havermann	02/2021
6758	77*10^119688+3	119690	Robert Price	06/2020
6759	586*25^85601+3717	119668	Eric Chen	10/2023
6760	(2^397504+1698)/2	119661	Stefano Morozzi	09/2020
6761	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
6762	2^397426+73849	119638	Enzo Doria	04/2016
6763	8*10^119509+29	119510	Robert Price	11/2021
6764	2^396933-112723	119489	Enzo Doria	06/2014
6765	11^114738-150	119488	Enzo Doria	10/2012
6766	(4*10^119474+149)/9	119474	Robert Price	04/2018
6767	26964^26964-13^13	119472	Henri Lifchitz	08/2024
6768	11^114702+10	119450	Alfred Reich	04/2026
6769	2^396790-21	119446	Lelio R Paula	04/2013
6770	8^132246+45045	119431	Enzo Doria	08/2026
6771	32061^5300+5300^32061	119405	Hans Havermann	01/2021
6772	(2^396633-7)/5	119398	Lelio R Paula	04/2014
6773	27382^22913+22913^27382	119388	Hans Havermann	03/2021
6774	(2^396577+2522)/2	119382	Stefano Morozzi	09/2020
6775	(2^396492+2230)/2	119356	Stefano Morozzi	01/2021
6776	(47*10^119354+259)/9	119355	Robert Price	03/2022
6778	105^59050+104	119352	Norbert Schneider	11/2016
6777	126^56824-125	119352	Norbert Schneider	12/2018
6779	2^396469+111546435	119350	Paul Bourdelais	10/2021
6780	139^55690-138	119345	Norbert Schneider	04/2019
6781	Phi(66220,p(66220))	119337	Henri Lifchitz	12/2025
6782	Phi(132889,-9)	119334	Henri Lifchitz	12/2025
6783	790^41179+41179^790	119322	Norbert Schneider	04/2019
6784	2^396374+73729	119321	Enzo Doria	04/2016
6786	88*10^119295+3	119297	Robert Price	05/2020
6785	21*29^81575+129664	119297	Eric Chen	06/2025
6787	2^396258-459491	119286	Enzo Doria	05/2015
6788	(2^396248+3126)/2	119283	Stefano Morozzi	09/2020
6789	2^396128-396128-1	119247	Karsten Bonath	06/2018
6790	(893*10^119228+7)/9	119230	Robert Price	06/2021
6791	(31*10^119229+257)/9	119230	Robert Price	12/2021
6792	(28*10^119206-67)/3	119207	Robert Price	10/2020
6793	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
6794	11^114458+6	119196	Paul Bourdelais	02/2021
6795	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
6796	(2^395902+202)/2	119179	Stefano Morozzi	09/2020
6797	(2^395825+582)/2	119155	Stefano Morozzi	09/2020
6798	(2^395733+1130)/2	119128	Stefano Morozzi	09/2020
6799	(23^119099)%(10^119099)	119099	Henri Lifchitz	05/2025
6800	29548^10725+10725^29548	119091	Hans Havermann	02/2021
6801	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
6802	(30^80599+1)/31	119054	Robert Price	07/2013
6803	Phi(80599,-5#)	119054	Henri Lifchitz	12/2025
6804	(232*10^119047+17)/3	119049	Robert Price	04/2021
6805	(43*10^119024-403)/9	119025	Robert Price	01/2019
6806	(4*10^119021+47)/3	119022	Robert Price	01/2022
6807	fibonacci(569433)+3	119005	Jon Grantham	08/2023
6808	26603^26888-26888^26603	118978	Norbert Schneider	07/2021
6809	912^40193-40193^912	118972	Norman Luhn	09/2024
6810	681^41992-41992^681	118970	Norman Luhn	09/2024
6811	6*10^118964+43	118965	Robert Price	07/2020
6812	(8*10^118960+49)/3	118961	Robert Price	05/2020
6813	31253^6402+6402^31253	118959	Hans Havermann	02/2021
6814	(194*10^118925-17)/3	118927	Robert Price	09/2020
6815	2^395062-109121	118926	Enzo Doria	04/2014
6816	2^395055-4627	118924	Yves Minet	05/2019
6817	(2^395054+702)/2	118923	Stefano Morozzi	09/2020
6818	2^395018-224141	118913	Harrison Mesh	06/2022
6819	(2^395011+2526)/2	118910	Stefano Morozzi	09/2020
6820	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
6821	25771^26948-26948^25771	118872	Frank Doornink	02/2024
6822	374^46201-46201^374	118870	Norman Luhn	09/2024
6823	(2^394858+1018)/2	118864	Stefano Morozzi	09/2020
6824	(77*10^118862-149)/9	118863	Robert Price	03/2022
6825	(16*10^118852+77)/3	118853	Robert Price	03/2019
6826	fibonacci(568658)-2	118843	Jon Grantham	08/2023
6827	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
6828	10^118772+163599	118773	Patrick De Geest	02/2021
6829	10^118772-40000000001	118772	Robert Price	09/2020
6830	10^118772-207603	118772	Patrick De Geest	02/2021
6831	26842^26577+26577^26842	118763	Hans Havermann	02/2021
6832	(2^394513+2034)/2	118760	Stefano Morozzi	09/2020
6833	(2^394473+2774)/2	118748	Stefano Morozzi	02/2021
6834	27949^17710+17710^27949	118734	Hans Havermann	02/2021
6835	2^394266+71389	118686	Enzo Doria	04/2016
6836	(10^118681-3^118681)/7	118681	Jon Grantham	08/2023
6837	2^394215-51261	118671	Tony Prest / Never Odd Or Even	04/2018
6838	(2^394215-48793)/5/5	118670	Tony Prest / Never Odd Or Even	04/2018
6839	(2^394215-17063)/3/3/5	118669	Tony Prest / Never Odd Or Even	04/2018
6840	(2^394215-24393)/5/5/5/5/5	118668	Tony Prest / Never Odd Or Even	04/2018
6841	(2^394215-35885)/3/71/173	118666	Tony Prest / Never Odd Or Even	04/2018
6842	(2^394215-47925)/353/2269	118665	Tony Prest / Never Odd Or Even	04/2018
6843	29201^11568+11568^29201	118652	Hans Havermann	02/2021
6844	(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673	118650	Tony Prest / Never Odd Or Even	04/2018
6845	(2^394131+2214)/2	118645	Stefano Morozzi	09/2020
6846	(17*10^118635+13)/3	118636	Robert Price	01/2019
6847	5^169727+2	118635	Lelio R Paula	08/2013
6848	2^394034-3	118617	M. Frind & P. Underwood	09/2002
6849	(7*10^118607+179)/3	118608	Robert Price	09/2018
6850	3^248572-6242	118599	Enzo Doria	05/2014
6851	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
6852	(49*10^118576-319)/9	118577	Robert Price	10/2021
6853	7^140303-6	118570	Robert Price	11/2014
6854	(2^393864+2686)/2	118565	Stefano Morozzi	09/2020
6855	(2^393862+3150)/2	118564	Stefano Morozzi	09/2020
6856	(2^393849+3762)/2	118561	Stefano Morozzi	01/2021
6857	(529*10^118554-7)/9	118556	Robert Price	08/2021
6858	26712^26777-26777^26712	118534	Norbert Schneider	07/2021
6859	(2^393661+2666)/2	118504	Stefano Morozzi	09/2020
6860	(2^393650+1614)/2	118501	Stefano Morozzi	09/2020
6861	27655^19264+19264^27655	118495	Hans Havermann	02/2021
6862	10^118485+469413	118486	Patrick De Geest	05/2021
6863	10^118485-50001	118485	Robert Price	08/2020
6864	(2^393528+1030)/2	118464	Stefano Morozzi	09/2020
6865	2^393427+75683	118434	Enzo Doria	04/2016
6867	2^393376-114749	118418	Enzo Doria	04/2015
6866	(65*10^118417+493)/9	118418	Robert Price	08/2021
6868	30960^6671+6671^30960	118397	Hans Havermann	02/2021
6869	(2^393234+2010)/2	118375	Stefano Morozzi	09/2020
6870	(2^393205+3030)/2	118367	Stefano Morozzi	09/2020
6871	(2^393191+2174)/2	118362	Stefano Morozzi	09/2020
6872	2^393180+73	118359	Lelio R Paula	04/2013
6873	3*2^393125+5	118343	Jon Grantham	07/2023
6874	27546^19771+19771^27546	118339	Hans Havermann	02/2021
6875	822^40595-40595^822	118330	Norman Luhn	09/2024
6876	p(23881)#/2+256	118328	Robert Price	05/2017
6877	(10^118324+359)/9	118324	Serge Batalov	12/2014
6878	(2^393048+570)/2	118319	Stefano Morozzi	09/2020
6879	p(23879)#/2+64	118317	Robert Price	03/2017
6880	2^393033+20147	118315	Enzo Doria	08/2023
6881	8*10^118308+59	118309	Robert Price	11/2021
6882	Phi(186197,5)	118308	Henri Lifchitz	12/2025
6883	9*10^118282+29	118283	Robert Price	03/2022
6884	(9*35^76602+12877)/34	118279	Eric Chen	05/2025
6885	(238*10^118265-1)/3	118267	Robert Price	04/2020
6887	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
6886	(2^392707+1710)/2	118217	Stefano Morozzi	09/2020
6888	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
6889	Phi(89679,-100)	118192	Henri Lifchitz	12/2025
6890	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
6891	(2^392567+2750)/2	118175	Stefano Morozzi	01/2021
6892	55*10^118172+3	118174	Robert Price	07/2022
6893	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
6894	27185^22222+22222^27185	118168	Hans Havermann	01/2021
6895	2^392516-29219	118160	Enzo Doria	07/2015
6896	66*10^118155+7	118157	Robert Price	07/2020
6897	Phi(177231,10)	118152	Maksym Voznyy	09/2015
6898	2^392413-112123	118129	Enzo Doria	06/2014
6899	27491^19798+19798^27491	118119	Hans Havermann	02/2021
6900	(49*10^118109-319)/9	118110	Robert Price	10/2021
6901	(2^392342+5)/27	118106	Lelio R Paula	04/2014
6902	(2^392333+1782)/2	118104	Stefano Morozzi	01/2021
6903	2^392300-1841429	118095	Enzo Doria	06/2015
6904	3*2^392260-5	118083	Jon Grantham	07/2023
6905	2^392220+75241	118070	Enzo Doria	04/2016
6906	27836^17409+17409^27836	118047	Hans Havermann	02/2021
6907	(13^118026)%(10^118026)	118026	Henri Lifchitz	05/2025
6908	10^118009+664447	118010	Patrick De Geest	07/2018
6909	10^118009-20001	118009	Robert Price	01/2018
6910	(14*10^117991+61)/3	117992	Robert Price	12/2018
6911	2^391933+5897	117984	Yves Minet	02/2011
6912	2^391912-1849259	117978	Enzo Doria	08/2015
6913	(2*34^77029+1043)/11	117968	Eric Chen	08/2023
6914	5*2^391836-3	117956	Jon Grantham	07/2023
6915	28357^14440+14440^28357	117953	Hans Havermann	02/2021
6916	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
6917	85^61124-61124^85	117934	Norman Luhn	09/2024
6918	(7*10^117930-79)/9	117930	Robert Price	01/2021
6919	27531^19168+19168^27531	117904	Hans Havermann	02/2021
6920	(46*10^117902+683)/9	117903	Robert Price	03/2019
6921	26349^26668-26668^26349	117893	Frank Doornink	03/2024
6922	27670^18189+18189^27670	117869	Hans Havermann	02/2021
6923	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
6924	(56*10^117856+583)/9	117857	Robert Price	08/2021
6925	32169^4606+4606^32169	117846	Hans Havermann	02/2021
6926	(71*10^117803-143)/9	117804	Robert Price	10/2021
6927	2^391324+90901	117801	Yves Minet	02/2011
6928	2^391301-1859923	117794	Enzo Doria	03/2016
6929	2^391261-4131	117782	Yves Minet	02/2018
6930	(2^391211+554)/2	117766	Stefano Morozzi	09/2020
6931	816^40445-40445^816	117764	Norman Luhn	09/2024
6932	38434^1157+1157^38434	117737	Hans Havermann	01/2021
6933	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
6934	(85*10^117719+473)/9	117720	Robert Price	01/2020
6935	(2^391049+582)/2	117718	Stefano Morozzi	09/2020
6936	(21*23^86445-197)/22	117715	Eric Chen	08/2023
6937	31083^6122+6122^31083	117709	Hans Havermann	02/2021
6938	2^390960+1880881	117691	Enzo Doria	11/2016
6939	(71*10^117685+91)/9	117686	Robert Price	04/2022
6941	2^390897-1860553	117672	Enzo Doria	11/2015
6940	(61*10^117671+47)/9	117672	Robert Price	07/2022
6942	2^390889-115003	117670	Enzo Doria	06/2015
6943	12^109010+35	117642	Riley Fisher	08/2023
6944	2^390779-30337	117637	Paul Bourdelais	02/2012
6945	(2^390735+378)/2	117623	Stefano Morozzi	02/2021
6946	11^112916-780	117590	Enzo Doria	12/2012
6947	27641^17916+17916^27641	117564	Hans Havermann	02/2021
6948	27906^16321+16321^27906	117561	Hans Havermann	02/2021
6949	27294^20275+20275^27294	117555	Hans Havermann	02/2021
6950	(2^390473+1002)/2	117544	Stefano Morozzi	09/2020
6951	35912^1875+1875^35912	117541	Hans Havermann	02/2021
6952	(16^97613-5^97613)/11	117537	Robert Price	07/2013
6953	(2^390438+1774)/2	117534	Stefano Morozzi	01/2021
6954	(2^390418+1722)/2	117528	Stefano Morozzi	09/2020
6955	(2^390403+654)/2	117523	Stefano Morozzi	09/2020
6956	(2^390343+2246)/2	117505	Stefano Morozzi	01/2021
6957	28043^15478+15478^28043	117493	Hans Havermann	02/2021
6958	Phi(247237,3)	117487	Henri Lifchitz	12/2025
6959	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
6960	37077^1474+1474^37077	117479	Hans Havermann	01/2021
6961	31^78759-30	117459	Theodore Burton	02/2007
6962	(2^390176+1222)/2	117455	Stefano Morozzi	09/2020
6963	(2^390133+1242)/2	117442	Stefano Morozzi	09/2020
6964	(2^390013+2634)/2	117406	Stefano Morozzi	09/2020
6965	3*10^117402+61	117403	Robert Price	09/2020
6966	2^389998+37	117402	Lelio R Paula	03/2013
6967	(2^389977+314)/2	117395	Stefano Morozzi	09/2020
6968	(2^389921+342)/2	117378	Stefano Morozzi	01/2021
6969	71830^43+43^71830	117333	Hans Havermann	01/2021
6970	(2^389768+1582)/2	117332	Stefano Morozzi	09/2020
6971	33802^2951+2951^33802	117292	Hans Havermann	02/2021
6972	(2^561185)%L(561185)	117281	Henri Lifchitz	05/2025
6973	26789^23866+23866^26789	117277	Hans Havermann	02/2021
6974	29^80192-1*80192^29	117273	Dylan Delgado	12/2019
6975	(101*10^117260+7)/9	117262	Robert Price	02/2022
6976	(13*10^117249+161)/3	117250	Robert Price	11/2018
6977	2^389478+43	117245	Lelio R Paula	03/2013
6978	(298*10^117229-7)/3	117231	Robert Price	06/2020
6979	(2^389416+342)/2	117226	Stefano Morozzi	01/2021
6980	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
6981	5*10^117205+23	117206	Robert Price	03/2019
6982	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
6983	27272^19827+19827^27272	117195	Hans Havermann	01/2021
6984	(2^389276+2650)/2	117184	Stefano Morozzi	09/2020
6985	(844*10^117175-7)/9	117177	Robert Price	05/2021
6986	10^117142+209223	117143	Patrick De Geest	04/2018
6987	10^117142-1000000001	117142	Robert Price	03/2018
6988	10^117142-966057	117142	Patrick De Geest	04/2018
6989	10^117135+360577	117136	Patrick De Geest	07/2018
6990	10^117135-401	117135	Robert Price	01/2018
6991	26415^26488-26488^26415	117126	Norbert Schneider	05/2021
6992	4*10^117123+79	117124	Robert Price	08/2018
6993	2^389033-12797413	117111	Enzo Doria	04/2016
6994	(2^388987+2634)/2	117097	Stefano Morozzi	09/2020
6995	2^388960-109505	117089	Enzo Doria	04/2014
6996	7*10^117082-57	117083	Robert Price	06/2020
6997	791^40398-40398^791	117081	Norman Luhn	09/2024
6998	(2^388928-5)/569	117077	Lelio R Paula	03/2014
6999	2^388888-1529	117067	Yves Minet	01/2013
7000	10^117059+28879	117060	Patrick De Geest	05/2016

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Probable Primes Top 10000

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