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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	2^338807-35899	101992	Stefano Morozzi	06/2022
9002	2^338808-89175	101992	Stefano Morozzi	01/2023
9003	2^338808-91475	101992	Stefano Morozzi	01/2023
9004	2^338805+29879	101991	Stefano Morozzi	01/2022
9005	2^338805+157925	101991	Stefano Morozzi	02/2022
9006	2^338804-6809	101991	Stefano Morozzi	03/2022
9007	2^338806-157095	101991	Stefano Morozzi	03/2022
9008	2^338804-133173	101991	Stefano Morozzi	04/2022
9009	2^338805-115189	101991	Stefano Morozzi	01/2023
9010	2^338802+150403	101990	Stefano Morozzi	11/2021
9011	2^338801+154587	101990	Stefano Morozzi	01/2022
9012	2^338802-180603	101990	Stefano Morozzi	02/2022
9013	2^338803-31921	101990	Stefano Morozzi	03/2022
9014	2^338803-81735	101990	Stefano Morozzi	03/2022
9015	2^338803+195141	101990	Stefano Morozzi	11/2022
9016	2^338800+160141	101989	Stefano Morozzi	03/2022
9017	2^338797-82489	101989	Stefano Morozzi	03/2022
9022	2^338796+93	101988	Donovan Johnson	06/2008
9018	2^338795+455	101988	Stefano Morozzi	11/2021
9019	2^338795-102075	101988	Stefano Morozzi	12/2021
9020	2^338794-3483	101988	Stefano Morozzi	01/2022
9021	2^338796+179641	101988	Stefano Morozzi	01/2022
9023	2^338793-5155	101987	Stefano Morozzi	02/2022
9024	2^338793+111107	101987	Stefano Morozzi	03/2022
9025	2^338791+112083	101987	Stefano Morozzi	04/2022
9026	2^338792-85097	101987	Stefano Morozzi	06/2022
9027	(61*10^101986+47)/9	101987	Robert Price	07/2022
9028	2^338787+53309	101986	Stefano Morozzi	01/2022
9029	2^338787-153817	101986	Stefano Morozzi	01/2022
9030	2^338789+56229	101986	Stefano Morozzi	01/2022
9031	2^338790+6429	101986	Stefano Morozzi	01/2022
9032	2^338788+131701	101986	Stefano Morozzi	02/2022
9033	2^338785+104639	101985	Stefano Morozzi	01/2022
9034	2^338784+37591	101985	Stefano Morozzi	04/2022
9035	2^338786-9831	101985	Stefano Morozzi	04/2022
9036	2^338783+109065	101984	Stefano Morozzi	03/2022
9037	2^338779+86711	101983	Stefano Morozzi	04/2022
9038	2^338778+113589	101983	Stefano Morozzi	05/2022
9039	2^338775-30369	101982	Stefano Morozzi	02/2022
9040	2^338774+159135	101982	Stefano Morozzi	03/2022
9041	2^338776+113001	101982	Stefano Morozzi	04/2022
9042	2^338774+117039	101982	Stefano Morozzi	09/2022
9043	2^338775+167109	101982	Stefano Morozzi	09/2022
9044	2^338774+147595	101982	Stefano Morozzi	11/2022
9045	2^338772+42733	101981	Stefano Morozzi	09/2022
9046	2^338771-138805	101981	Stefano Morozzi	12/2022
9047	2^338768-181007	101980	Stefano Morozzi	02/2022
9048	2^338768+108807	101980	Stefano Morozzi	03/2022
9049	2^338767+169155	101980	Stefano Morozzi	09/2022
9050	2^338769+95369	101980	Stefano Morozzi	11/2022
9051	2^338769+195965	101980	Stefano Morozzi	11/2022
9052	2^338770-12725	101980	Stefano Morozzi	12/2022
9053	2^338768-140843	101980	Stefano Morozzi	01/2023
9054	2^338764+138013	101979	Stefano Morozzi	04/2022
9055	2^338765-160323	101979	Stefano Morozzi	06/2022
9056	2^338765+124545	101979	Stefano Morozzi	02/2023
9062	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
9057	2^338761+103671	101978	Stefano Morozzi	01/2022
9058	2^338763-7651	101978	Stefano Morozzi	03/2022
9059	2^338763+65591	101978	Stefano Morozzi	06/2022
9060	2^338762-111875	101978	Stefano Morozzi	12/2022
9061	2^338762-192237	101978	Stefano Morozzi	02/2023
9063	2^338757-5151	101977	Stefano Morozzi	02/2022
9064	2^338760-79037	101977	Stefano Morozzi	02/2022
9065	2^338757-82143	101977	Stefano Morozzi	03/2022
9066	2^338757+137007	101977	Stefano Morozzi	04/2022
9067	2^338755+158531	101976	Stefano Morozzi	03/2022
9068	2^338755+74081	101976	Stefano Morozzi	02/2023
9069	2^338752-153353	101975	Stefano Morozzi	01/2022
9070	2^338751+8001	101975	Stefano Morozzi	02/2022
9071	2^338752+32977	101975	Stefano Morozzi	02/2022
9072	2^338753-79233	101975	Stefano Morozzi	02/2022
9073	2^338752-88157	101975	Stefano Morozzi	12/2022
9074	2^338750-175625	101974	Stefano Morozzi	12/2021
9075	2^338747-2731	101974	Stefano Morozzi	12/2021
9076	2^338750-29597	101974	Stefano Morozzi	02/2022
9077	2^338748+35095	101974	Stefano Morozzi	03/2022
9078	2^338747+137475	101974	Stefano Morozzi	04/2022
9079	2^338747+162005	101974	Stefano Morozzi	04/2022
9080	2^338750+162237	101974	Stefano Morozzi	04/2022
9081	2^338747-184365	101974	Stefano Morozzi	04/2022
9082	2^338748+64341	101974	Stefano Morozzi	05/2022
9083	2^338750+24445	101974	Stefano Morozzi	02/2023
9084	2^338746+59577	101973	Stefano Morozzi	03/2022
9085	2^338746+62055	101973	Stefano Morozzi	04/2022
9086	2^338744+194065	101973	Stefano Morozzi	09/2022
9087	2^338741+25359	101972	Stefano Morozzi	12/2021
9088	2^338743+176981	101972	Stefano Morozzi	12/2021
9089	2^338741+183029	101972	Stefano Morozzi	02/2022
9090	2^338743-130309	101972	Stefano Morozzi	02/2022
9091	2^338741+86349	101972	Stefano Morozzi	04/2022
9092	2^338741+111561	101972	Stefano Morozzi	04/2022
9093	2^338743+172301	101972	Stefano Morozzi	11/2022
9094	2^338741-189969	101972	Stefano Morozzi	01/2023
9095	2^338739+76959	101971	Stefano Morozzi	12/2021
9096	2^338739-105957	101971	Stefano Morozzi	02/2022
9097	2^338739+190149	101971	Stefano Morozzi	05/2022
9098	2^338738+64947	101971	Stefano Morozzi	05/2022
9099	2^338740+119947	101971	Stefano Morozzi	11/2022
9100	2^338740-186837	101971	Stefano Morozzi	12/2022
9101	2^338737+127547	101970	Stefano Morozzi	12/2021
9102	2^338737+128591	101970	Stefano Morozzi	01/2022
9103	2^338735-153165	101970	Stefano Morozzi	01/2022
9104	2^338734+13719	101970	Stefano Morozzi	05/2022
9105	2^338734-138225	101970	Stefano Morozzi	12/2022
9106	2^338735-186129	101970	Stefano Morozzi	12/2022
9112	25295^10744+10744^25295	101969	Hans Havermann	01/2019
9113	25712^9243+9243^25712	101969	Hans Havermann	01/2019
9107	2^338731-150895	101969	Stefano Morozzi	12/2021
9108	2^338731+54911	101969	Stefano Morozzi	01/2022
9109	2^338731+85863	101969	Stefano Morozzi	03/2022
9110	2^338732+185047	101969	Stefano Morozzi	03/2022
9111	2^338733+193791	101969	Stefano Morozzi	09/2022
9114	2^338729+69221	101968	Stefano Morozzi	09/2022
9115	2^338728+123355	101968	Stefano Morozzi	11/2022
9116	2^338730-87063	101968	Stefano Morozzi	12/2022
9117	2^338726+128199	101967	Stefano Morozzi	01/2022
9118	2^338727+127745	101967	Stefano Morozzi	01/2022
9119	2^338724+32971	101967	Stefano Morozzi	02/2022
9120	2^338727+189683	101967	Stefano Morozzi	05/2022
9121	2^338727+118293	101967	Stefano Morozzi	09/2022
9122	2^338723-76651	101966	Stefano Morozzi	12/2021
9123	2^338721+79037	101966	Stefano Morozzi	01/2022
9124	2^338723-132621	101966	Stefano Morozzi	03/2022
9125	2^338722+137313	101966	Stefano Morozzi	04/2022
9126	2^338722+162915	101966	Stefano Morozzi	04/2022
9127	2^338723+199161	101966	Stefano Morozzi	02/2023
9128	2^338718-126861	101965	Stefano Morozzi	12/2021
9129	2^338718-109127	101965	Stefano Morozzi	04/2022
9134	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
9130	2^338714+30835	101964	Stefano Morozzi	01/2022
9131	2^338714+156715	101964	Stefano Morozzi	02/2022
9132	2^338715+19923	101964	Stefano Morozzi	09/2022
9133	2^338716+173253	101964	Stefano Morozzi	11/2022
9135	2^338711+125399	101963	Stefano Morozzi	12/2021
9136	2^338713-30895	101963	Stefano Morozzi	02/2022
9137	2^338712-132545	101963	Stefano Morozzi	03/2022
9138	2^338713+87825	101963	Stefano Morozzi	04/2022
9139	2^338712+190333	101963	Stefano Morozzi	06/2022
9140	2^338709-154429	101962	Stefano Morozzi	02/2022
9141	2^338710+140545	101962	Stefano Morozzi	06/2022
9142	2^338706-102917	101961	Stefano Morozzi	01/2022
9143	2^338705+34727	101961	Stefano Morozzi	03/2022
9144	2^338706-165633	101961	Stefano Morozzi	01/2023
9145	2^338707-116115	101961	Stefano Morozzi	01/2023
9146	2^338698+104083	101959	Stefano Morozzi	01/2022
9147	2^338700-184565	101959	Stefano Morozzi	04/2022
9148	2^338700+189777	101959	Stefano Morozzi	05/2022
9149	2^338698+41779	101959	Stefano Morozzi	09/2022
9150	2^338699+148533	101959	Stefano Morozzi	11/2022
9151	2^338700+97381	101959	Stefano Morozzi	11/2022
9152	2^338698-142181	101959	Stefano Morozzi	02/2023
9153	2^338696+181671	101958	Stefano Morozzi	02/2022
9154	2^338697+146651	101958	Stefano Morozzi	11/2022
9155	2^338695-116977	101958	Stefano Morozzi	02/2023
9156	2^338692+106297	101957	Stefano Morozzi	01/2022
9157	2^338692+33195	101957	Stefano Morozzi	02/2022
9158	2^338692+110505	101957	Stefano Morozzi	03/2022
9159	2^338692+190093	101957	Stefano Morozzi	05/2022
9160	2^338692+173343	101957	Stefano Morozzi	11/2022
9161	2^338693+144975	101957	Stefano Morozzi	11/2022
9162	2^338692+149281	101957	Stefano Morozzi	02/2023
9163	2^338688+82203	101956	Stefano Morozzi	02/2022
9164	2^338689+82365	101956	Stefano Morozzi	02/2022
9165	2^338688-92159	101956	Stefano Morozzi	02/2023
9166	2^338686-81303	101955	Stefano Morozzi	03/2022
9167	2^338687+40461	101955	Stefano Morozzi	06/2022
9168	2^338687+65283	101955	Stefano Morozzi	06/2022
9174	2^338682-19865	101954	Enzo Doria	06/2013
9175	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
9169	(8*10^101954-269)/9	101954	Robert Price	09/2021
9170	2^338683+50303	101954	Stefano Morozzi	11/2021
9171	2^338682-107205	101954	Stefano Morozzi	03/2022
9172	2^338682+13839	101954	Stefano Morozzi	05/2022
9173	2^338683-42837	101954	Stefano Morozzi	02/2023
9176	2^338678-180005	101953	Stefano Morozzi	02/2022
9177	2^338680+15855	101953	Stefano Morozzi	06/2022
9178	2^338678+93175	101953	Stefano Morozzi	09/2022
9179	2^338680+99217	101953	Stefano Morozzi	02/2023
9180	2^338674-175967	101952	Stefano Morozzi	12/2021
9181	2^338677-177373	101952	Stefano Morozzi	12/2021
9182	2^338677+102999	101952	Stefano Morozzi	01/2022
9183	2^338676+33381	101952	Stefano Morozzi	03/2022
9184	2^338677-82699	101952	Stefano Morozzi	03/2022
9185	2^338676-34299	101952	Stefano Morozzi	04/2022
9186	2^338675+188445	101952	Stefano Morozzi	05/2022
9187	2^338676+165271	101952	Stefano Morozzi	06/2022
9188	2^338674-187551	101952	Stefano Morozzi	12/2022
9189	2^338676-42243	101952	Stefano Morozzi	02/2023
9190	2^338671-55041	101951	Stefano Morozzi	02/2022
9191	2^338673-80203	101951	Stefano Morozzi	02/2022
9192	2^338672-182063	101951	Stefano Morozzi	03/2022
9193	2^338672+36667	101951	Stefano Morozzi	04/2022
9194	2^338668+2583	101950	Stefano Morozzi	12/2021
9195	2^338670-157001	101950	Stefano Morozzi	03/2022
9196	2^338669-8353	101950	Stefano Morozzi	04/2022
9197	2^338670+40635	101950	Stefano Morozzi	06/2022
9205	(2^338666+3154)/2	101949	Stefano Morozzi	09/2020
9198	2^338665+1577	101949	Stefano Morozzi	12/2021
9199	2^338665-51133	101949	Stefano Morozzi	12/2021
9200	2^338664+4345	101949	Stefano Morozzi	01/2022
9201	2^338666-128943	101949	Stefano Morozzi	01/2022
9202	2^338664+131535	101949	Stefano Morozzi	01/2022
9203	2^338667+14943	101949	Stefano Morozzi	05/2022
9204	2^338665+166637	101949	Stefano Morozzi	09/2022
9206	2^338662+31587	101948	Stefano Morozzi	02/2022
9207	2^338663-58375	101948	Stefano Morozzi	04/2022
9208	2^338663-107869	101948	Stefano Morozzi	04/2022
9209	2^338663+90435	101948	Stefano Morozzi	06/2022
9210	2^338661+70457	101948	Stefano Morozzi	11/2022
9211	2^338662+70519	101948	Stefano Morozzi	11/2022
9212	2^338663-39447	101948	Stefano Morozzi	01/2023
9213	2^338658-159191	101947	Stefano Morozzi	04/2022
9214	2^338659-159687	101947	Stefano Morozzi	04/2022
9215	2^338659+15543	101947	Stefano Morozzi	05/2022
9216	2^338658+44395	101947	Stefano Morozzi	09/2022
9217	2^338658+192537	101947	Stefano Morozzi	09/2022
9218	2^338659-90531	101947	Stefano Morozzi	01/2023
9219	2^338659-114759	101947	Stefano Morozzi	01/2023
9220	2^338659+124079	101947	Stefano Morozzi	02/2023
9221	2^338654+51027	101946	Stefano Morozzi	12/2021
9222	2^338656-152115	101946	Stefano Morozzi	12/2021
9223	2^338654+32415	101946	Stefano Morozzi	02/2022
9224	2^338654+39799	101946	Stefano Morozzi	05/2022
9225	2^338655+144579	101946	Stefano Morozzi	09/2022
9226	2^338657+97509	101946	Stefano Morozzi	11/2022
9227	2^338653+126629	101945	Stefano Morozzi	12/2021
9228	2^338653+33279	101945	Stefano Morozzi	02/2022
9229	2^338652-107097	101945	Stefano Morozzi	03/2022
9230	2^338653+94475	101945	Stefano Morozzi	09/2022
9231	2^338651+194073	101945	Stefano Morozzi	09/2022
9232	2^338652-89157	101945	Stefano Morozzi	01/2023
9233	2^338649-154663	101944	Stefano Morozzi	02/2022
9234	2^338650+61399	101944	Stefano Morozzi	04/2022
9235	2^338650-35655	101944	Stefano Morozzi	06/2022
9236	2^338650+169623	101944	Stefano Morozzi	09/2022
9237	2^338649-40743	101944	Stefano Morozzi	01/2023
9238	2^338645+150311	101943	Stefano Morozzi	11/2021
9239	2^338645+28481	101943	Stefano Morozzi	01/2022
9240	2^338647-77895	101943	Stefano Morozzi	01/2022
9241	2^338647-84607	101943	Stefano Morozzi	04/2022
9242	2^338647+164523	101943	Stefano Morozzi	05/2022
9243	2^338645+64845	101943	Stefano Morozzi	05/2022
9244	2^338644-35969	101943	Stefano Morozzi	12/2022
9245	2^338645-15715	101943	Stefano Morozzi	01/2023
9246	2^338641-152541	101942	Stefano Morozzi	12/2021
9247	2^338643-56487	101942	Stefano Morozzi	03/2022
9248	2^338642-186525	101942	Stefano Morozzi	12/2022
9249	2^338643-41715	101942	Stefano Morozzi	02/2023
9250	2^338638+100575	101941	Stefano Morozzi	12/2021

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301157 PRPs in the top)