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	2^338813+192725	101993	Stefano Morozzi	09/2022
8752	2^338812+94731	101993	Stefano Morozzi	11/2022
8753	2^338813+49205	101993	Stefano Morozzi	02/2023
8754	2^338809-152755	101992	Stefano Morozzi	01/2022
8755	2^338808+156531	101992	Stefano Morozzi	01/2022
8756	2^338808+7885	101992	Stefano Morozzi	02/2022
8757	2^338808-105797	101992	Stefano Morozzi	02/2022
8758	2^338807-35899	101992	Stefano Morozzi	06/2022
8759	2^338808-89175	101992	Stefano Morozzi	01/2023
8760	2^338808-91475	101992	Stefano Morozzi	01/2023
8761	2^338805+29879	101991	Stefano Morozzi	01/2022
8762	2^338805+157925	101991	Stefano Morozzi	02/2022
8763	2^338804-6809	101991	Stefano Morozzi	03/2022
8764	2^338806-157095	101991	Stefano Morozzi	03/2022
8765	2^338804-133173	101991	Stefano Morozzi	04/2022
8766	2^338805-115189	101991	Stefano Morozzi	01/2023
8767	2^338802+150403	101990	Stefano Morozzi	11/2021
8768	2^338801+154587	101990	Stefano Morozzi	01/2022
8769	2^338802-180603	101990	Stefano Morozzi	02/2022
8770	2^338803-31921	101990	Stefano Morozzi	03/2022
8771	2^338803-81735	101990	Stefano Morozzi	03/2022
8772	2^338803+195141	101990	Stefano Morozzi	11/2022
8773	2^338800+160141	101989	Stefano Morozzi	03/2022
8774	2^338797-82489	101989	Stefano Morozzi	03/2022
8779	2^338796+93	101988	Donovan Johnson	06/2008
8775	2^338795+455	101988	Stefano Morozzi	11/2021
8776	2^338795-102075	101988	Stefano Morozzi	12/2021
8777	2^338794-3483	101988	Stefano Morozzi	01/2022
8778	2^338796+179641	101988	Stefano Morozzi	01/2022
8780	2^338793-5155	101987	Stefano Morozzi	02/2022
8781	2^338793+111107	101987	Stefano Morozzi	03/2022
8782	2^338791+112083	101987	Stefano Morozzi	04/2022
8783	2^338792-85097	101987	Stefano Morozzi	06/2022
8784	(61*10^101986+47)/9	101987	Robert Price	07/2022
8785	2^338787+53309	101986	Stefano Morozzi	01/2022
8786	2^338787-153817	101986	Stefano Morozzi	01/2022
8787	2^338789+56229	101986	Stefano Morozzi	01/2022
8788	2^338790+6429	101986	Stefano Morozzi	01/2022
8789	2^338788+131701	101986	Stefano Morozzi	02/2022
8790	2^338785+104639	101985	Stefano Morozzi	01/2022
8791	2^338784+37591	101985	Stefano Morozzi	04/2022
8792	2^338786-9831	101985	Stefano Morozzi	04/2022
8793	2^338783+109065	101984	Stefano Morozzi	03/2022
8794	2^338779+86711	101983	Stefano Morozzi	04/2022
8795	2^338778+113589	101983	Stefano Morozzi	05/2022
8796	2^338775-30369	101982	Stefano Morozzi	02/2022
8797	2^338774+159135	101982	Stefano Morozzi	03/2022
8798	2^338776+113001	101982	Stefano Morozzi	04/2022
8799	2^338774+117039	101982	Stefano Morozzi	09/2022
8800	2^338775+167109	101982	Stefano Morozzi	09/2022
8801	2^338774+147595	101982	Stefano Morozzi	11/2022
8802	2^338772+42733	101981	Stefano Morozzi	09/2022
8803	2^338771-138805	101981	Stefano Morozzi	12/2022
8804	2^338768-181007	101980	Stefano Morozzi	02/2022
8805	2^338768+108807	101980	Stefano Morozzi	03/2022
8806	2^338767+169155	101980	Stefano Morozzi	09/2022
8807	2^338769+95369	101980	Stefano Morozzi	11/2022
8808	2^338769+195965	101980	Stefano Morozzi	11/2022
8809	2^338770-12725	101980	Stefano Morozzi	12/2022
8810	2^338768-140843	101980	Stefano Morozzi	01/2023
8811	2^338764+138013	101979	Stefano Morozzi	04/2022
8812	2^338765-160323	101979	Stefano Morozzi	06/2022
8813	2^338765+124545	101979	Stefano Morozzi	02/2023
8819	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
8814	2^338761+103671	101978	Stefano Morozzi	01/2022
8815	2^338763-7651	101978	Stefano Morozzi	03/2022
8816	2^338763+65591	101978	Stefano Morozzi	06/2022
8817	2^338762-111875	101978	Stefano Morozzi	12/2022
8818	2^338762-192237	101978	Stefano Morozzi	02/2023
8820	2^338757-5151	101977	Stefano Morozzi	02/2022
8821	2^338760-79037	101977	Stefano Morozzi	02/2022
8822	2^338757-82143	101977	Stefano Morozzi	03/2022
8823	2^338757+137007	101977	Stefano Morozzi	04/2022
8824	2^338755+158531	101976	Stefano Morozzi	03/2022
8825	2^338755+74081	101976	Stefano Morozzi	02/2023
8826	2^338752-153353	101975	Stefano Morozzi	01/2022
8827	2^338751+8001	101975	Stefano Morozzi	02/2022
8828	2^338752+32977	101975	Stefano Morozzi	02/2022
8829	2^338753-79233	101975	Stefano Morozzi	02/2022
8830	2^338752-88157	101975	Stefano Morozzi	12/2022
8831	2^338750-175625	101974	Stefano Morozzi	12/2021
8832	2^338747-2731	101974	Stefano Morozzi	12/2021
8833	2^338750-29597	101974	Stefano Morozzi	02/2022
8834	2^338748+35095	101974	Stefano Morozzi	03/2022
8835	2^338747+137475	101974	Stefano Morozzi	04/2022
8836	2^338747+162005	101974	Stefano Morozzi	04/2022
8837	2^338750+162237	101974	Stefano Morozzi	04/2022
8838	2^338747-184365	101974	Stefano Morozzi	04/2022
8839	2^338748+64341	101974	Stefano Morozzi	05/2022
8840	2^338750+24445	101974	Stefano Morozzi	02/2023
8841	2^338746+59577	101973	Stefano Morozzi	03/2022
8842	2^338746+62055	101973	Stefano Morozzi	04/2022
8843	2^338744+194065	101973	Stefano Morozzi	09/2022
8844	2^338741+25359	101972	Stefano Morozzi	12/2021
8845	2^338743+176981	101972	Stefano Morozzi	12/2021
8846	2^338741+183029	101972	Stefano Morozzi	02/2022
8847	2^338743-130309	101972	Stefano Morozzi	02/2022
8848	2^338741+86349	101972	Stefano Morozzi	04/2022
8849	2^338741+111561	101972	Stefano Morozzi	04/2022
8850	2^338743+172301	101972	Stefano Morozzi	11/2022
8851	2^338741-189969	101972	Stefano Morozzi	01/2023
8852	2^338739+76959	101971	Stefano Morozzi	12/2021
8853	2^338739-105957	101971	Stefano Morozzi	02/2022
8854	2^338739+190149	101971	Stefano Morozzi	05/2022
8855	2^338738+64947	101971	Stefano Morozzi	05/2022
8856	2^338740+119947	101971	Stefano Morozzi	11/2022
8857	2^338740-186837	101971	Stefano Morozzi	12/2022
8858	2^338737+127547	101970	Stefano Morozzi	12/2021
8859	2^338737+128591	101970	Stefano Morozzi	01/2022
8860	2^338735-153165	101970	Stefano Morozzi	01/2022
8861	2^338734+13719	101970	Stefano Morozzi	05/2022
8862	2^338734-138225	101970	Stefano Morozzi	12/2022
8863	2^338735-186129	101970	Stefano Morozzi	12/2022
8869	25295^10744+10744^25295	101969	Hans Havermann	01/2019
8870	25712^9243+9243^25712	101969	Hans Havermann	01/2019
8864	2^338731-150895	101969	Stefano Morozzi	12/2021
8865	2^338731+54911	101969	Stefano Morozzi	01/2022
8866	2^338731+85863	101969	Stefano Morozzi	03/2022
8867	2^338732+185047	101969	Stefano Morozzi	03/2022
8868	2^338733+193791	101969	Stefano Morozzi	09/2022
8871	2^338729+69221	101968	Stefano Morozzi	09/2022
8872	2^338728+123355	101968	Stefano Morozzi	11/2022
8873	2^338730-87063	101968	Stefano Morozzi	12/2022
8874	2^338726+128199	101967	Stefano Morozzi	01/2022
8875	2^338727+127745	101967	Stefano Morozzi	01/2022
8876	2^338724+32971	101967	Stefano Morozzi	02/2022
8877	2^338727+189683	101967	Stefano Morozzi	05/2022
8878	2^338727+118293	101967	Stefano Morozzi	09/2022
8879	2^338723-76651	101966	Stefano Morozzi	12/2021
8880	2^338721+79037	101966	Stefano Morozzi	01/2022
8881	2^338723-132621	101966	Stefano Morozzi	03/2022
8882	2^338722+137313	101966	Stefano Morozzi	04/2022
8883	2^338722+162915	101966	Stefano Morozzi	04/2022
8884	2^338723+199161	101966	Stefano Morozzi	02/2023
8885	2^338718-126861	101965	Stefano Morozzi	12/2021
8886	2^338718-109127	101965	Stefano Morozzi	04/2022
8891	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
8887	2^338714+30835	101964	Stefano Morozzi	01/2022
8888	2^338714+156715	101964	Stefano Morozzi	02/2022
8889	2^338715+19923	101964	Stefano Morozzi	09/2022
8890	2^338716+173253	101964	Stefano Morozzi	11/2022
8892	2^338711+125399	101963	Stefano Morozzi	12/2021
8893	2^338713-30895	101963	Stefano Morozzi	02/2022
8894	2^338712-132545	101963	Stefano Morozzi	03/2022
8895	2^338713+87825	101963	Stefano Morozzi	04/2022
8896	2^338712+190333	101963	Stefano Morozzi	06/2022
8897	2^338709-154429	101962	Stefano Morozzi	02/2022
8898	2^338710+140545	101962	Stefano Morozzi	06/2022
8899	2^338706-102917	101961	Stefano Morozzi	01/2022
8900	2^338705+34727	101961	Stefano Morozzi	03/2022
8901	2^338706-165633	101961	Stefano Morozzi	01/2023
8902	2^338707-116115	101961	Stefano Morozzi	01/2023
8903	2^338698+104083	101959	Stefano Morozzi	01/2022
8904	2^338700-184565	101959	Stefano Morozzi	04/2022
8905	2^338700+189777	101959	Stefano Morozzi	05/2022
8906	2^338698+41779	101959	Stefano Morozzi	09/2022
8907	2^338699+148533	101959	Stefano Morozzi	11/2022
8908	2^338700+97381	101959	Stefano Morozzi	11/2022
8909	2^338698-142181	101959	Stefano Morozzi	02/2023
8910	2^338696+181671	101958	Stefano Morozzi	02/2022
8911	2^338697+146651	101958	Stefano Morozzi	11/2022
8912	2^338695-116977	101958	Stefano Morozzi	02/2023
8913	2^338692+106297	101957	Stefano Morozzi	01/2022
8914	2^338692+33195	101957	Stefano Morozzi	02/2022
8915	2^338692+110505	101957	Stefano Morozzi	03/2022
8916	2^338692+190093	101957	Stefano Morozzi	05/2022
8917	2^338692+173343	101957	Stefano Morozzi	11/2022
8918	2^338693+144975	101957	Stefano Morozzi	11/2022
8919	2^338692+149281	101957	Stefano Morozzi	02/2023
8920	2^338688+82203	101956	Stefano Morozzi	02/2022
8921	2^338689+82365	101956	Stefano Morozzi	02/2022
8922	2^338688-92159	101956	Stefano Morozzi	02/2023
8923	2^338686-81303	101955	Stefano Morozzi	03/2022
8924	2^338687+40461	101955	Stefano Morozzi	06/2022
8925	2^338687+65283	101955	Stefano Morozzi	06/2022
8931	2^338682-19865	101954	Enzo Doria	06/2013
8932	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
8926	(8*10^101954-269)/9	101954	Robert Price	09/2021
8927	2^338683+50303	101954	Stefano Morozzi	11/2021
8928	2^338682-107205	101954	Stefano Morozzi	03/2022
8929	2^338682+13839	101954	Stefano Morozzi	05/2022
8930	2^338683-42837	101954	Stefano Morozzi	02/2023
8933	2^338678-180005	101953	Stefano Morozzi	02/2022
8934	2^338680+15855	101953	Stefano Morozzi	06/2022
8935	2^338678+93175	101953	Stefano Morozzi	09/2022
8936	2^338680+99217	101953	Stefano Morozzi	02/2023
8937	2^338674-175967	101952	Stefano Morozzi	12/2021
8938	2^338677-177373	101952	Stefano Morozzi	12/2021
8939	2^338677+102999	101952	Stefano Morozzi	01/2022
8940	2^338676+33381	101952	Stefano Morozzi	03/2022
8941	2^338677-82699	101952	Stefano Morozzi	03/2022
8942	2^338676-34299	101952	Stefano Morozzi	04/2022
8943	2^338675+188445	101952	Stefano Morozzi	05/2022
8944	2^338676+165271	101952	Stefano Morozzi	06/2022
8945	2^338674-187551	101952	Stefano Morozzi	12/2022
8946	2^338676-42243	101952	Stefano Morozzi	02/2023
8947	2^338671-55041	101951	Stefano Morozzi	02/2022
8948	2^338673-80203	101951	Stefano Morozzi	02/2022
8949	2^338672-182063	101951	Stefano Morozzi	03/2022
8950	2^338672+36667	101951	Stefano Morozzi	04/2022
8951	2^338668+2583	101950	Stefano Morozzi	12/2021
8952	2^338670-157001	101950	Stefano Morozzi	03/2022
8953	2^338669-8353	101950	Stefano Morozzi	04/2022
8954	2^338670+40635	101950	Stefano Morozzi	06/2022
8962	(2^338666+3154)/2	101949	Stefano Morozzi	09/2020
8955	2^338665+1577	101949	Stefano Morozzi	12/2021
8956	2^338665-51133	101949	Stefano Morozzi	12/2021
8957	2^338664+4345	101949	Stefano Morozzi	01/2022
8958	2^338666-128943	101949	Stefano Morozzi	01/2022
8959	2^338664+131535	101949	Stefano Morozzi	01/2022
8960	2^338667+14943	101949	Stefano Morozzi	05/2022
8961	2^338665+166637	101949	Stefano Morozzi	09/2022
8963	2^338662+31587	101948	Stefano Morozzi	02/2022
8964	2^338663-58375	101948	Stefano Morozzi	04/2022
8965	2^338663-107869	101948	Stefano Morozzi	04/2022
8966	2^338663+90435	101948	Stefano Morozzi	06/2022
8967	2^338661+70457	101948	Stefano Morozzi	11/2022
8968	2^338662+70519	101948	Stefano Morozzi	11/2022
8969	2^338663-39447	101948	Stefano Morozzi	01/2023
8970	2^338658-159191	101947	Stefano Morozzi	04/2022
8971	2^338659-159687	101947	Stefano Morozzi	04/2022
8972	2^338659+15543	101947	Stefano Morozzi	05/2022
8973	2^338658+44395	101947	Stefano Morozzi	09/2022
8974	2^338658+192537	101947	Stefano Morozzi	09/2022
8975	2^338659-90531	101947	Stefano Morozzi	01/2023
8976	2^338659-114759	101947	Stefano Morozzi	01/2023
8977	2^338659+124079	101947	Stefano Morozzi	02/2023
8978	2^338654+51027	101946	Stefano Morozzi	12/2021
8979	2^338656-152115	101946	Stefano Morozzi	12/2021
8980	2^338654+32415	101946	Stefano Morozzi	02/2022
8981	2^338654+39799	101946	Stefano Morozzi	05/2022
8982	2^338655+144579	101946	Stefano Morozzi	09/2022
8983	2^338657+97509	101946	Stefano Morozzi	11/2022
8984	2^338653+126629	101945	Stefano Morozzi	12/2021
8985	2^338653+33279	101945	Stefano Morozzi	02/2022
8986	2^338652-107097	101945	Stefano Morozzi	03/2022
8987	2^338653+94475	101945	Stefano Morozzi	09/2022
8988	2^338651+194073	101945	Stefano Morozzi	09/2022
8989	2^338652-89157	101945	Stefano Morozzi	01/2023
8990	2^338649-154663	101944	Stefano Morozzi	02/2022
8991	2^338650+61399	101944	Stefano Morozzi	04/2022
8992	2^338650-35655	101944	Stefano Morozzi	06/2022
8993	2^338650+169623	101944	Stefano Morozzi	09/2022
8994	2^338649-40743	101944	Stefano Morozzi	01/2023
8995	2^338645+150311	101943	Stefano Morozzi	11/2021
8996	2^338645+28481	101943	Stefano Morozzi	01/2022
8997	2^338647-77895	101943	Stefano Morozzi	01/2022
8998	2^338647-84607	101943	Stefano Morozzi	04/2022
8999	2^338647+164523	101943	Stefano Morozzi	05/2022
9000	2^338645+64845	101943	Stefano Morozzi	05/2022

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PRP Records

Probable Primes Top 10000

(300560 PRPs in the top)