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 ?
9251	2^338912+179821	102023	Stefano Morozzi	01/2022
9252	2^338909+100769	102022	Stefano Morozzi	11/2021
9253	2^338908-100839	102022	Stefano Morozzi	12/2021
9254	2^338909-25951	102022	Stefano Morozzi	12/2021
9255	2^338909+66845	102022	Stefano Morozzi	09/2022
9256	2^338907+73509	102022	Stefano Morozzi	11/2022
9257	2^338906-25823	102021	Stefano Morozzi	12/2021
9258	2^338904+75951	102021	Stefano Morozzi	12/2021
9259	2^338906+6685	102021	Stefano Morozzi	01/2022
9260	2^338905+160365	102021	Stefano Morozzi	03/2022
9261	2^338906+92617	102021	Stefano Morozzi	09/2022
9262	2^338904+47065	102021	Stefano Morozzi	11/2022
9263	2^338905+70427	102021	Stefano Morozzi	11/2022
9264	2^338905-163975	102021	Stefano Morozzi	12/2022
9265	2^338903+4155	102020	Stefano Morozzi	01/2022
9266	2^338901+55571	102020	Stefano Morozzi	01/2022
9267	2^338901-55479	102020	Stefano Morozzi	02/2022
9268	2^338903+33555	102020	Stefano Morozzi	03/2022
9269	2^338901+39777	102020	Stefano Morozzi	05/2022
9270	2^338903+165981	102020	Stefano Morozzi	06/2022
9271	2^338901-34863	102020	Stefano Morozzi	06/2022
9272	2^338899-150051	102019	Stefano Morozzi	12/2021
9273	2^338899+125951	102019	Stefano Morozzi	12/2021
9274	2^338898+179623	102019	Stefano Morozzi	01/2022
9275	2^338899-154467	102019	Stefano Morozzi	02/2022
9276	2^338898-60753	102019	Stefano Morozzi	06/2022
9277	2^338898+68635	102019	Stefano Morozzi	09/2022
9278	2^338897-85963	102019	Stefano Morozzi	12/2022
9279	2^338898+174129	102019	Stefano Morozzi	02/2023
9280	2^338894-133295	102018	Stefano Morozzi	04/2022
9281	2^338894+165573	102018	Stefano Morozzi	06/2022
9282	2^338894-60957	102018	Stefano Morozzi	06/2022
9283	2^338894-89463	102018	Stefano Morozzi	01/2023
9293	2^338891-18885	102017	Enzo Doria	05/2013
9284	2^338891+26499	102017	Stefano Morozzi	12/2021
9285	2^338891-2625	102017	Stefano Morozzi	12/2021
9286	2^338893+128727	102017	Stefano Morozzi	01/2022
9287	2^338890-52965	102017	Stefano Morozzi	01/2022
9288	2^338892-55467	102017	Stefano Morozzi	02/2022
9289	2^338892-83393	102017	Stefano Morozzi	04/2022
9290	2^338893+13649	102017	Stefano Morozzi	05/2022
9291	2^338892+117957	102017	Stefano Morozzi	09/2022
9292	2^338892-14643	102017	Stefano Morozzi	01/2023
9294	2^338887+154029	102016	Stefano Morozzi	01/2022
9295	2^338889-104293	102016	Stefano Morozzi	02/2022
9296	2^338887+147741	102016	Stefano Morozzi	11/2022
9297	2^338889+195975	102016	Stefano Morozzi	11/2022
9298	2^338889-117873	102016	Stefano Morozzi	02/2023
9299	2^338886+177159	102015	Stefano Morozzi	12/2021
9300	2^338885+40425	102015	Stefano Morozzi	06/2022
9301	2^338884-13053	102015	Stefano Morozzi	12/2022
9302	2^338885-112569	102015	Stefano Morozzi	12/2022
9303	2^338880+11341	102014	Stefano Morozzi	03/2022
9304	2^338880-160383	102014	Stefano Morozzi	06/2022
9305	2^338880-161627	102014	Stefano Morozzi	12/2022
9306	2^338879-1059	102013	Stefano Morozzi	12/2021
9307	2^338879-54525	102013	Stefano Morozzi	02/2022
9308	2^338877-82813	102013	Stefano Morozzi	03/2022
9309	2^338878-185883	102013	Stefano Morozzi	06/2022
9310	2^338879-60355	102013	Stefano Morozzi	06/2022
9311	2^338878+43719	102013	Stefano Morozzi	09/2022
9312	2^338879+122049	102013	Stefano Morozzi	11/2022
9313	2^338874-15063	102012	Stefano Morozzi	01/2023
9314	2^338874+148993	102012	Stefano Morozzi	02/2023
9315	2^338871+7679	102011	Stefano Morozzi	02/2022
9316	2^338872+61141	102011	Stefano Morozzi	03/2022
9317	2^338872-183923	102011	Stefano Morozzi	04/2022
9318	2^338873+19527	102011	Stefano Morozzi	09/2022
9319	2^338870+70719	102011	Stefano Morozzi	11/2022
9320	(19*10^102011+287)/9/3	102011	Alfred Reich	11/2022
9321	2^338870-37571	102011	Stefano Morozzi	12/2022
9322	2^338872-138573	102011	Stefano Morozzi	12/2022
9323	2^338873-63843	102011	Stefano Morozzi	12/2022
9324	2^338868-5985	102010	Stefano Morozzi	02/2022
9325	2^338867+38079	102010	Stefano Morozzi	05/2022
9326	2^338868+140437	102010	Stefano Morozzi	06/2022
9327	2^338868-110175	102010	Stefano Morozzi	06/2022
9328	2^338868+123337	102010	Stefano Morozzi	11/2022
9329	2^338867-13327	102010	Stefano Morozzi	12/2022
9330	2^338868-11279	102010	Stefano Morozzi	12/2022
9331	2^338868-115685	102010	Stefano Morozzi	01/2023
9332	2^338864+158191	102009	Stefano Morozzi	02/2022
9333	2^338865-39699	102009	Stefano Morozzi	01/2023
9334	2^338865-40789	102009	Stefano Morozzi	01/2023
9335	2^338862+60433	102008	Stefano Morozzi	03/2022
9336	2^338861-9453	102008	Stefano Morozzi	04/2022
9337	2^338861+98067	102008	Stefano Morozzi	11/2022
9338	2^338862+146545	102008	Stefano Morozzi	11/2022
9339	2^338863-186207	102008	Stefano Morozzi	12/2022
9340	2^338860-41429	102008	Stefano Morozzi	01/2023
9341	2^338862-115833	102008	Stefano Morozzi	01/2023
9342	2^338863+74259	102008	Stefano Morozzi	02/2023
9343	2^338863-193017	102008	Stefano Morozzi	02/2023
9344	2^338858-190185	102007	Stefano Morozzi	01/2023
9345	2^338855+102141	102006	Stefano Morozzi	12/2021
9346	2^338856-27173	102006	Stefano Morozzi	12/2021
9347	2^338856-102839	102006	Stefano Morozzi	01/2022
9348	2^338855+79629	102006	Stefano Morozzi	01/2022
9349	2^338856+47755	102006	Stefano Morozzi	11/2022
9350	2^338850+27987	102005	Stefano Morozzi	01/2022
9351	2^338853+111791	102005	Stefano Morozzi	04/2022
9352	2^338852+145797	102005	Stefano Morozzi	11/2022
9353	2^338852-88497	102005	Stefano Morozzi	12/2022
9354	2^338850+124843	102005	Stefano Morozzi	02/2023
9355	2^338853-167695	102005	Stefano Morozzi	02/2023
9356	2^338847+176013	102004	Stefano Morozzi	12/2021
9357	2^338847-2365	102004	Stefano Morozzi	12/2021
9358	2^338848+158941	102004	Stefano Morozzi	03/2022
9359	2^338848+16671	102004	Stefano Morozzi	06/2022
9360	2^338847-35061	102004	Stefano Morozzi	06/2022
9361	2^338848+145063	102004	Stefano Morozzi	11/2022
9362	2^338847-61885	102004	Stefano Morozzi	12/2022
9363	2^338845+135831	102003	Stefano Morozzi	03/2022
9364	2^338846+85695	102003	Stefano Morozzi	03/2022
9365	2^338845+186525	102003	Stefano Morozzi	04/2022
9366	2^338846-163473	102003	Stefano Morozzi	12/2022
9367	2^338844-16077	102003	Stefano Morozzi	01/2023
9368	2^338844-165143	102003	Stefano Morozzi	01/2023
9369	2^338843-127261	102002	Stefano Morozzi	12/2021
9370	2^338843+107205	102002	Stefano Morozzi	02/2022
9371	2^338842-33185	102002	Stefano Morozzi	04/2022
9372	2^338842+14227	102002	Stefano Morozzi	05/2022
9373	2^338842+147973	102002	Stefano Morozzi	11/2022
9381	8*10^102000+51	102001	Robert Price	08/2019
9374	2^338838+150837	102001	Stefano Morozzi	11/2021
9375	2^338838+141397	102001	Stefano Morozzi	06/2022
9376	2^338839+194363	102001	Stefano Morozzi	09/2022
9377	2^338838+95637	102001	Stefano Morozzi	11/2022
9378	2^338839+171545	102001	Stefano Morozzi	11/2022
9379	2^338837-40071	102001	Stefano Morozzi	01/2023
9380	2^338838-90251	102001	Stefano Morozzi	01/2023
9382	2^338835-150625	102000	Stefano Morozzi	12/2021
9383	2^338834-32877	102000	Stefano Morozzi	04/2022
9387	(2^338832+642)/2	101999	Stefano Morozzi	09/2020
9384	2^338833-100905	101999	Stefano Morozzi	12/2021
9385	2^338831+54419	101999	Stefano Morozzi	01/2022
9386	2^338831-63687	101999	Stefano Morozzi	12/2022
9395	2^338829-113239	101998	Enzo Doria	07/2014
9396	2^338828-113297	101998	Enzo Doria	07/2014
9388	2^338830+25017	101998	Stefano Morozzi	11/2021
9389	2^338831+321	101998	Stefano Morozzi	11/2021
9390	2^338827-26197	101998	Stefano Morozzi	12/2021
9391	2^338829+52727	101998	Stefano Morozzi	01/2022
9392	2^338827-55461	101998	Stefano Morozzi	02/2022
9393	2^338828-65859	101998	Stefano Morozzi	01/2023
9394	2^338829+99365	101998	Stefano Morozzi	02/2023
9397	2^338825-27453	101997	Stefano Morozzi	12/2021
9398	2^338824+89355	101997	Stefano Morozzi	05/2022
9399	2^338825-10995	101997	Stefano Morozzi	06/2022
9400	2^338824+149865	101997	Stefano Morozzi	02/2023
9401	2^338822+111175	101996	Stefano Morozzi	03/2022
9402	2^338822+187819	101996	Stefano Morozzi	04/2022
9403	2^338823+139545	101996	Stefano Morozzi	05/2022
9404	2^338823-184905	101996	Stefano Morozzi	06/2022
9405	2^338821-38919	101996	Stefano Morozzi	12/2022
9406	2^338820+41317	101995	Stefano Morozzi	06/2022
9407	2^338817+46019	101995	Stefano Morozzi	11/2022
9408	2^338820+148083	101995	Stefano Morozzi	11/2022
9409	2^338817-163251	101995	Stefano Morozzi	12/2022
9410	2^338819-63705	101995	Stefano Morozzi	12/2022
9411	2^338817-92509	101995	Stefano Morozzi	02/2023
9412	2^338815+151175	101994	Stefano Morozzi	12/2021
9413	2^338814-30011	101994	Stefano Morozzi	02/2022
9414	2^338814+12309	101994	Stefano Morozzi	04/2022
9415	2^338816-60647	101994	Stefano Morozzi	06/2022
9416	2^338816+171043	101994	Stefano Morozzi	11/2022
9417	2^338814-11513	101994	Stefano Morozzi	12/2022
9418	2^338811-126999	101993	Stefano Morozzi	12/2021
9419	2^338811+131621	101993	Stefano Morozzi	02/2022
9420	2^338812-107637	101993	Stefano Morozzi	03/2022
9421	2^338813+192725	101993	Stefano Morozzi	09/2022
9422	2^338812+94731	101993	Stefano Morozzi	11/2022
9423	2^338813+49205	101993	Stefano Morozzi	02/2023
9424	2^338809-152755	101992	Stefano Morozzi	01/2022
9425	2^338808+156531	101992	Stefano Morozzi	01/2022
9426	2^338808+7885	101992	Stefano Morozzi	02/2022
9427	2^338808-105797	101992	Stefano Morozzi	02/2022
9428	2^338807-35899	101992	Stefano Morozzi	06/2022
9429	2^338808-89175	101992	Stefano Morozzi	01/2023
9430	2^338808-91475	101992	Stefano Morozzi	01/2023
9431	2^338805+29879	101991	Stefano Morozzi	01/2022
9432	2^338805+157925	101991	Stefano Morozzi	02/2022
9433	2^338804-6809	101991	Stefano Morozzi	03/2022
9434	2^338806-157095	101991	Stefano Morozzi	03/2022
9435	2^338804-133173	101991	Stefano Morozzi	04/2022
9436	2^338805-115189	101991	Stefano Morozzi	01/2023
9437	2^338802+150403	101990	Stefano Morozzi	11/2021
9438	2^338801+154587	101990	Stefano Morozzi	01/2022
9439	2^338802-180603	101990	Stefano Morozzi	02/2022
9440	2^338803-31921	101990	Stefano Morozzi	03/2022
9441	2^338803-81735	101990	Stefano Morozzi	03/2022
9442	2^338803+195141	101990	Stefano Morozzi	11/2022
9443	2^338800+160141	101989	Stefano Morozzi	03/2022
9444	2^338797-82489	101989	Stefano Morozzi	03/2022
9449	2^338796+93	101988	Donovan Johnson	06/2008
9445	2^338795+455	101988	Stefano Morozzi	11/2021
9446	2^338795-102075	101988	Stefano Morozzi	12/2021
9447	2^338794-3483	101988	Stefano Morozzi	01/2022
9448	2^338796+179641	101988	Stefano Morozzi	01/2022
9450	2^338793-5155	101987	Stefano Morozzi	02/2022
9451	2^338793+111107	101987	Stefano Morozzi	03/2022
9452	2^338791+112083	101987	Stefano Morozzi	04/2022
9453	2^338792-85097	101987	Stefano Morozzi	06/2022
9454	(61*10^101986+47)/9	101987	Robert Price	07/2022
9455	2^338787+53309	101986	Stefano Morozzi	01/2022
9456	2^338787-153817	101986	Stefano Morozzi	01/2022
9457	2^338789+56229	101986	Stefano Morozzi	01/2022
9458	2^338790+6429	101986	Stefano Morozzi	01/2022
9459	2^338788+131701	101986	Stefano Morozzi	02/2022
9460	2^338785+104639	101985	Stefano Morozzi	01/2022
9461	2^338784+37591	101985	Stefano Morozzi	04/2022
9462	2^338786-9831	101985	Stefano Morozzi	04/2022
9463	2^338783+109065	101984	Stefano Morozzi	03/2022
9464	2^338779+86711	101983	Stefano Morozzi	04/2022
9465	2^338778+113589	101983	Stefano Morozzi	05/2022
9466	2^338775-30369	101982	Stefano Morozzi	02/2022
9467	2^338774+159135	101982	Stefano Morozzi	03/2022
9468	2^338776+113001	101982	Stefano Morozzi	04/2022
9469	2^338774+117039	101982	Stefano Morozzi	09/2022
9470	2^338775+167109	101982	Stefano Morozzi	09/2022
9471	2^338774+147595	101982	Stefano Morozzi	11/2022
9472	2^338772+42733	101981	Stefano Morozzi	09/2022
9473	2^338771-138805	101981	Stefano Morozzi	12/2022
9474	2^338768-181007	101980	Stefano Morozzi	02/2022
9475	2^338768+108807	101980	Stefano Morozzi	03/2022
9476	2^338767+169155	101980	Stefano Morozzi	09/2022
9477	2^338769+95369	101980	Stefano Morozzi	11/2022
9478	2^338769+195965	101980	Stefano Morozzi	11/2022
9479	2^338770-12725	101980	Stefano Morozzi	12/2022
9480	2^338768-140843	101980	Stefano Morozzi	01/2023
9481	2^338764+138013	101979	Stefano Morozzi	04/2022
9482	2^338765-160323	101979	Stefano Morozzi	06/2022
9483	2^338765+124545	101979	Stefano Morozzi	02/2023
9489	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
9484	2^338761+103671	101978	Stefano Morozzi	01/2022
9485	2^338763-7651	101978	Stefano Morozzi	03/2022
9486	2^338763+65591	101978	Stefano Morozzi	06/2022
9487	2^338762-111875	101978	Stefano Morozzi	12/2022
9488	2^338762-192237	101978	Stefano Morozzi	02/2023
9490	2^338757-5151	101977	Stefano Morozzi	02/2022
9491	2^338760-79037	101977	Stefano Morozzi	02/2022
9492	2^338757-82143	101977	Stefano Morozzi	03/2022
9493	2^338757+137007	101977	Stefano Morozzi	04/2022
9494	2^338755+158531	101976	Stefano Morozzi	03/2022
9495	2^338755+74081	101976	Stefano Morozzi	02/2023
9496	2^338752-153353	101975	Stefano Morozzi	01/2022
9497	2^338751+8001	101975	Stefano Morozzi	02/2022
9498	2^338752+32977	101975	Stefano Morozzi	02/2022
9499	2^338753-79233	101975	Stefano Morozzi	02/2022
9500	2^338752-88157	101975	Stefano Morozzi	12/2022

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301815 PRPs in the top)