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 ?
9251	25592^10119+10119^25592	102500	Hans Havermann	02/2019
9252	(5*10^102492-23)/9	102492	Serge Batalov	11/2022
9253	7^121268+82	102484	Lelio R Paula	10/2016
9254	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
9255	2^340434-5955	102481	Lelio R Paula	11/2016
9256	(7*10^102480-19)/3	102481	Robert Price	10/2020
9257	(2^340381+47)/7	102465	Lelio R Paula	12/2013
9258	111^50095+110	102461	Norbert Schneider	04/2017
9259	180^45427-45427^180	102451	Norman Luhn	09/2024
9260	2^340291-20301	102438	Enzo Doria	06/2013
9261	12^94915+89	102431	Lelio R Paula	10/2016
9262	(106*10^102422+17)/3	102424	Robert Price	04/2021
9263	24466^15349+15349^24466	102417	Hans Havermann	03/2019
9264	2^340212+111546435	102415	Paul Bourdelais	10/2021
9265	2^340208-20373	102413	Enzo Doria	06/2013
9266	6^131598-17273	102404	Enzo Doria	02/2013
9267	(2^340132+1182)/2	102390	Stefano Morozzi	09/2020
9268	(2^340133+1166)/2	102390	Stefano Morozzi	09/2020
9269	2^340115-21181	102385	Enzo Doria	06/2013
9270	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
9271	(2^340064+3630)/2	102370	Stefano Morozzi	09/2020
9272	9348*31^68638+13	102369	Eric Chen	04/2024
9273	89^52511-88^52511	102365	Robert Price	06/2015
9274	3^214539-112756	102362	Enzo Doria	07/2014
9275	Phi(562221,2)/53723397926257372614541581386770268796893300042857	102361	Anonymous	06/2025
9276	23159^23450-23450^23159	102353	Norbert Schneider	12/2019
9277	2^340000-19877	102351	Enzo Doria	06/2013
9279	2^339990-114845	102348	Enzo Doria	05/2015
9278	311^41058-41058^311	102348	Norman Luhn	09/2024
9280	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
9281	20^78661-99	102341	Lelio R Paula	09/2016
9282	2^339951-19585	102336	Enzo Doria	05/2013
9283	(17*10^102335-167)/3	102336	Robert Price	05/2022
9284	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
9285	(236282#+121441)/(121441*25499429)	102332	Makoto Morimoto	08/2020
9286	5*10^102323-91	102324	Robert Price	03/2021
9288	2^339889+29327	102317	Yves Minet	06/2010
9287	(167*10^102315-17)/3	102317	Robert Price	03/2020
9289	26348^7641+7641^26348	102314	Hans Havermann	03/2019
9290	Phi(239414,10)/6333218543	102303	Makoto Kamada	08/2019
9291	2^339834-109493	102301	Enzo Doria	04/2014
9292	(16*10^102299-19)/3	102300	Robert Price	02/2019
9293	(11^98221-5^98221)/6	102286	Robert Price	01/2013
9294	3^214365+1820	102279	Lelio R Paula	10/2016
9295	31978^1579+1579^31978	102278	Hans Havermann	03/2019
9296	(89*10^102262-467)/9	102263	Robert Price	04/2022
9297	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
9298	2^339694-16995	102259	Lelio R Paula	09/2016
9299	(56*10^102255+691)/9	102256	Robert Price	05/2019
9300	122^49008+121	102249	Norbert Schneider	10/2018
9301	(2^339652+3178)/2	102246	Stefano Morozzi	09/2020
9302	7^120985-38	102245	Lelio R Paula	10/2016
9303	10^102244+122961	102245	Patrick De Geest	12/2016
9304	10^102244-27	102244	Lelio R Paula	09/2016
9305	7^120982-62	102242	Lelio R Paula	10/2016
9306	(2^339640+2670)/2	102242	Stefano Morozzi	09/2020
9307	4*6^131382-5	102236	Lelio R Paula	11/2014
9308	(2^339607+3290)/2	102232	Stefano Morozzi	02/2021
9309	2^339586-1091	102226	Yves Minet	11/2012
9310	11^98161-3072000	102225	Enzo Doria	12/2012
9311	9*7^120961-4	102225	Lelio R Paula	11/2014
9312	5*3^214250+2	102224	Serge Batalov	10/2010
9313	12^94713-59	102213	Lelio R Paula	10/2016
9314	12^94705+89	102204	Lelio R Paula	10/2016
9315	L(2*339475)%(2^339475)	102193	Henri Lifchitz	06/2025
9316	2^339407-177	102172	Lelio R Paula	08/2011
9317	4*10^102163-57	102164	Robert Price	10/2018
9318	2^339355+65	102157	Lelio R Paula	07/2011
9319	(28*10^102142-31)/3	102143	Robert Price	12/2019
9320	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
9321	(2^339268+1758)/2	102130	Stefano Morozzi	09/2020
9322	U(610865)	102130	Serge Batalov	07/2024
9323	s(178551)	102122	Robert Price	05/2020
9324	(797*10^102112-23)/9	102114	Robert Price	01/2022
9325	(5*10^102107+7)/3	102108	Tyler Busby	02/2023
9326	(2^339175+2790)/2	102102	Stefano Morozzi	02/2021
9329	2^339168+21	102100	Lelio R Paula	07/2011
9328	2^339167-108807	102100	Enzo Doria	03/2014
9327	(2^339169+42)/2	102100	Stefano Morozzi	09/2020
9330	2^339156+163	102097	Lelio R Paula	08/2011
9331	(2^339149+746)/2	102094	Stefano Morozzi	09/2020
9332	(25*10^102076-67)/3	102077	Robert Price	06/2019
9333	2^339081-4543	102074	Yves Minet	03/2019
9334	(3435^28867-1)/3434	102069	Serge Batalov	06/2022
9335	2*10^102062+77	102063	Robert Price	08/2020
9336	24327^15668+15668^24327	102053	Hans Havermann	02/2019
9337	10^102052+66793	102053	Patrick De Geest	09/2022
9339	10^102052-7000001	102052	Robert Price	06/2021
9338	10^102052-618623	102052	Patrick De Geest	09/2022
9340	2^339000-175635	102050	Stefano Morozzi	12/2021
9341	2^339000-151667	102050	Stefano Morozzi	12/2021
9342	2^338999+79289	102049	Stefano Morozzi	01/2022
9343	2^338998-63897	102049	Stefano Morozzi	12/2022
9344	2^338997+99659	102049	Stefano Morozzi	02/2023
9345	2^338994+188757	102048	Stefano Morozzi	05/2022
9346	2^338995+70785	102048	Stefano Morozzi	11/2022
9347	2^338994-12183	102048	Stefano Morozzi	12/2022
9348	2^338992+181591	102047	Stefano Morozzi	01/2022
9349	2^338992+136171	102047	Stefano Morozzi	03/2022
9350	2^338991-109435	102047	Stefano Morozzi	04/2022
9351	2^338991+193611	102047	Stefano Morozzi	09/2022
9352	2^338988-134619	102046	Stefano Morozzi	04/2022
9353	2^338987-62557	102046	Stefano Morozzi	12/2022
9354	2^338986-60141	102045	Stefano Morozzi	06/2022
9355	2^338986+98209	102045	Stefano Morozzi	11/2022
9356	2^338981+106391	102044	Stefano Morozzi	01/2022
9357	2^338982+34069	102044	Stefano Morozzi	03/2022
9358	2^338982-58781	102044	Stefano Morozzi	04/2022
9359	2^338980+70833	102044	Stefano Morozzi	11/2022
9360	2^338982-92111	102044	Stefano Morozzi	02/2023
9361	2^338977+83007	102043	Stefano Morozzi	02/2022
9362	2^338979-83601	102043	Stefano Morozzi	04/2022
9363	2^338975+28355	102042	Stefano Morozzi	01/2022
9364	2^338973+134619	102042	Stefano Morozzi	03/2022
9365	2^338974+183777	102042	Stefano Morozzi	03/2022
9366	2^338975+69293	102042	Stefano Morozzi	09/2022
9374	25080^11711+11711^25080	102041	Hans Havermann	02/2019
9367	2^338972+152343	102041	Stefano Morozzi	12/2021
9368	2^338972-180623	102041	Stefano Morozzi	02/2022
9369	2^338972+84441	102041	Stefano Morozzi	03/2022
9370	2^338971+64875	102041	Stefano Morozzi	05/2022
9371	2^338971+44985	102041	Stefano Morozzi	11/2022
9372	2^338971+145065	102041	Stefano Morozzi	11/2022
9373	2^338972-16635	102041	Stefano Morozzi	01/2023
9375	2^338968+53461	102040	Stefano Morozzi	01/2022
9376	2^338969+160175	102040	Stefano Morozzi	03/2022
9377	2^338967+13409	102040	Stefano Morozzi	04/2022
9378	2^338969+67635	102040	Stefano Morozzi	09/2022
9379	2^338969-15913	102040	Stefano Morozzi	01/2023
9380	2^338963-127455	102039	Stefano Morozzi	12/2021
9381	2^338963+132195	102039	Stefano Morozzi	02/2022
9382	2^338966+137919	102039	Stefano Morozzi	04/2022
9383	2^338963-87529	102039	Stefano Morozzi	12/2022
9384	2^338963-116859	102039	Stefano Morozzi	02/2023
9391	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
9385	2^338960+53935	102038	Stefano Morozzi	01/2022
9386	2^338962+83157	102038	Stefano Morozzi	02/2022
9387	2^338961+12341	102038	Stefano Morozzi	04/2022
9388	2^338960+63933	102038	Stefano Morozzi	05/2022
9389	2^338960+170791	102038	Stefano Morozzi	11/2022
9390	2^338962+21679	102038	Stefano Morozzi	11/2022
9392	2^338959-30919	102037	Stefano Morozzi	02/2022
9393	2^338959+164769	102037	Stefano Morozzi	05/2022
9394	2^338958-43161	102037	Stefano Morozzi	02/2023
9395	2^338954-177003	102036	Stefano Morozzi	12/2021
9396	2^338954+154207	102036	Stefano Morozzi	01/2022
9397	2^338956+182493	102036	Stefano Morozzi	02/2022
9398	2^338954+162715	102036	Stefano Morozzi	04/2022
9399	2^338955-158241	102036	Stefano Morozzi	04/2022
9400	2^338956-33395	102036	Stefano Morozzi	04/2022
9401	2^338954+190915	102036	Stefano Morozzi	06/2022
9402	2^338955+41643	102036	Stefano Morozzi	09/2022
9403	2^338954+194427	102036	Stefano Morozzi	09/2022
9404	2^338956+117967	102036	Stefano Morozzi	09/2022
9405	2^338956+195495	102036	Stefano Morozzi	11/2022
9406	2^338954-186371	102036	Stefano Morozzi	12/2022
9407	2^338950+175077	102035	Stefano Morozzi	12/2021
9408	2^338951-51687	102035	Stefano Morozzi	12/2021
9409	2^338951+66123	102035	Stefano Morozzi	06/2022
9410	2^338950+19317	102035	Stefano Morozzi	09/2022
9411	2^338951-161479	102035	Stefano Morozzi	12/2022
9412	2^338950-66335	102035	Stefano Morozzi	01/2023
9413	2^338951-41611	102035	Stefano Morozzi	02/2023
9414	2^338952-142887	102035	Stefano Morozzi	02/2023
9415	2^338949+85449	102034	Stefano Morozzi	03/2022
9416	2^338949-184585	102034	Stefano Morozzi	04/2022
9417	2^338949-88555	102034	Stefano Morozzi	12/2022
9418	2^338948+49393	102034	Stefano Morozzi	02/2023
9419	2^338949-17601	102034	Stefano Morozzi	02/2023
9420	2^338943+127103	102033	Stefano Morozzi	12/2021
9421	2^338944-84003	102033	Stefano Morozzi	04/2022
9422	2^338945+138605	102033	Stefano Morozzi	05/2022
9423	2^338943+95133	102033	Stefano Morozzi	11/2022
9424	2^338943+147435	102033	Stefano Morozzi	11/2022
9425	2^338943-116067	102033	Stefano Morozzi	01/2023
9426	2^338940+78607	102032	Stefano Morozzi	01/2022
9427	2^338942-86687	102032	Stefano Morozzi	12/2022
9428	2^338939+151569	102031	Stefano Morozzi	12/2021
9429	2^338938+183975	102031	Stefano Morozzi	03/2022
9430	2^338937-33429	102031	Stefano Morozzi	04/2022
9431	2^338939-183259	102031	Stefano Morozzi	04/2022
9432	2^338937-139951	102031	Stefano Morozzi	01/2023
9433	2^338938-40151	102031	Stefano Morozzi	01/2023
9434	2^338938+74449	102031	Stefano Morozzi	02/2023
9435	2^338935+179999	102030	Stefano Morozzi	01/2022
9436	2^338936+84147	102030	Stefano Morozzi	03/2022
9437	2^338935+171261	102030	Stefano Morozzi	11/2022
9438	2^338936-41355	102030	Stefano Morozzi	01/2023
9439	2^338931+2349	102029	Stefano Morozzi	12/2021
9440	2^338933+79935	102029	Stefano Morozzi	01/2022
9441	2^338930+33819	102029	Stefano Morozzi	03/2022
9442	2^338931-31555	102029	Stefano Morozzi	03/2022
9443	2^338933+64169	102029	Stefano Morozzi	05/2022
9444	2^338932-184965	102029	Stefano Morozzi	06/2022
9445	2^338932+66943	102029	Stefano Morozzi	09/2022
9446	2^338932+92995	102029	Stefano Morozzi	09/2022
9447	2^338931+97001	102029	Stefano Morozzi	11/2022
9448	2^338932-165453	102029	Stefano Morozzi	01/2023
9449	2^338933-40899	102029	Stefano Morozzi	01/2023
9450	2^338928+2367	102028	Stefano Morozzi	12/2021
9451	2^338927+52779	102028	Stefano Morozzi	01/2022
9452	2^338927-79539	102028	Stefano Morozzi	02/2022
9453	2^338929+60819	102028	Stefano Morozzi	03/2022
9454	2^338928-156959	102028	Stefano Morozzi	03/2022
9455	2^338927-63919	102028	Stefano Morozzi	12/2022
9456	2^338925+106631	102027	Stefano Morozzi	01/2022
9457	2^338926+80235	102027	Stefano Morozzi	01/2022
9458	2^338926+41607	102027	Stefano Morozzi	09/2022
9459	2^338925+195435	102027	Stefano Morozzi	11/2022
9460	2^338924-92885	102027	Stefano Morozzi	02/2023
9461	2^338922-27291	102026	Stefano Morozzi	12/2021
9462	2^338919-103849	102025	Stefano Morozzi	01/2022
9463	2^338919+130221	102025	Stefano Morozzi	01/2022
9464	2^338918-91967	102025	Stefano Morozzi	02/2023
9465	2^338917+561057	102025	Boyan Hu	03/2024
9466	2^338914-79121	102024	Stefano Morozzi	02/2022
9467	2^338916+134047	102024	Stefano Morozzi	03/2022
9468	2^338914-11315	102024	Stefano Morozzi	12/2022
9469	2^338910+81027	102023	Stefano Morozzi	01/2022
9470	2^338912+179821	102023	Stefano Morozzi	01/2022
9471	2^338909+100769	102022	Stefano Morozzi	11/2021
9472	2^338908-100839	102022	Stefano Morozzi	12/2021
9473	2^338909-25951	102022	Stefano Morozzi	12/2021
9474	2^338909+66845	102022	Stefano Morozzi	09/2022
9475	2^338907+73509	102022	Stefano Morozzi	11/2022
9476	2^338906-25823	102021	Stefano Morozzi	12/2021
9477	2^338904+75951	102021	Stefano Morozzi	12/2021
9478	2^338906+6685	102021	Stefano Morozzi	01/2022
9479	2^338905+160365	102021	Stefano Morozzi	03/2022
9480	2^338906+92617	102021	Stefano Morozzi	09/2022
9481	2^338904+47065	102021	Stefano Morozzi	11/2022
9482	2^338905+70427	102021	Stefano Morozzi	11/2022
9483	2^338905-163975	102021	Stefano Morozzi	12/2022
9484	2^338903+4155	102020	Stefano Morozzi	01/2022
9485	2^338901+55571	102020	Stefano Morozzi	01/2022
9486	2^338901-55479	102020	Stefano Morozzi	02/2022
9487	2^338903+33555	102020	Stefano Morozzi	03/2022
9488	2^338901+39777	102020	Stefano Morozzi	05/2022
9489	2^338903+165981	102020	Stefano Morozzi	06/2022
9490	2^338901-34863	102020	Stefano Morozzi	06/2022
9491	2^338899-150051	102019	Stefano Morozzi	12/2021
9492	2^338899+125951	102019	Stefano Morozzi	12/2021
9493	2^338898+179623	102019	Stefano Morozzi	01/2022
9494	2^338899-154467	102019	Stefano Morozzi	02/2022
9495	2^338898-60753	102019	Stefano Morozzi	06/2022
9496	2^338898+68635	102019	Stefano Morozzi	09/2022
9497	2^338897-85963	102019	Stefano Morozzi	12/2022
9498	2^338898+174129	102019	Stefano Morozzi	02/2023
9499	2^338894-133295	102018	Stefano Morozzi	04/2022
9500	2^338894+165573	102018	Stefano Morozzi	06/2022

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Probable Primes Top 10000

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