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 ?
9501	89^52511-88^52511	102365	Robert Price	06/2015
9502	3^214539-112756	102362	Enzo Doria	07/2014
9503	Phi(562221,2)/53723397926257372614541581386770268796893300042857	102361	Anonymous	06/2025
9504	23159^23450-23450^23159	102353	Norbert Schneider	12/2019
9505	2^340000-19877	102351	Enzo Doria	06/2013
9507	2^339990-114845	102348	Enzo Doria	05/2015
9506	311^41058-41058^311	102348	Norman Luhn	09/2024
9508	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
9509	20^78661-99	102341	Lelio R Paula	09/2016
9510	2^339951-19585	102336	Enzo Doria	05/2013
9511	(17*10^102335-167)/3	102336	Robert Price	05/2022
9512	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
9513	(236282#+121441)/(121441*25499429)	102332	Makoto Morimoto	08/2020
9514	5*10^102323-91	102324	Robert Price	03/2021
9516	2^339889+29327	102317	Yves Minet	06/2010
9515	(167*10^102315-17)/3	102317	Robert Price	03/2020
9517	26348^7641+7641^26348	102314	Hans Havermann	03/2019
9518	Phi(239414,10)/6333218543	102303	Makoto Kamada	08/2019
9519	2^339834-109493	102301	Enzo Doria	04/2014
9520	(16*10^102299-19)/3	102300	Robert Price	02/2019
9521	(11^98221-5^98221)/6	102286	Robert Price	01/2013
9522	3^214365+1820	102279	Lelio R Paula	10/2016
9523	31978^1579+1579^31978	102278	Hans Havermann	03/2019
9524	(89*10^102262-467)/9	102263	Robert Price	04/2022
9525	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
9526	2^339694-16995	102259	Lelio R Paula	09/2016
9527	(56*10^102255+691)/9	102256	Robert Price	05/2019
9528	122^49008+121	102249	Norbert Schneider	10/2018
9529	(2^339652+3178)/2	102246	Stefano Morozzi	09/2020
9530	7^120985-38	102245	Lelio R Paula	10/2016
9531	10^102244+122961	102245	Patrick De Geest	12/2016
9532	10^102244-27	102244	Lelio R Paula	09/2016
9533	7^120982-62	102242	Lelio R Paula	10/2016
9534	(2^339640+2670)/2	102242	Stefano Morozzi	09/2020
9535	4*6^131382-5	102236	Lelio R Paula	11/2014
9536	(2^339607+3290)/2	102232	Stefano Morozzi	02/2021
9537	2^339586-1091	102226	Yves Minet	11/2012
9538	11^98161-3072000	102225	Enzo Doria	12/2012
9539	9*7^120961-4	102225	Lelio R Paula	11/2014
9540	5*3^214250+2	102224	Serge Batalov	10/2010
9541	12^94713-59	102213	Lelio R Paula	10/2016
9542	12^94705+89	102204	Lelio R Paula	10/2016
9543	L(2*339475)%(2^339475)	102193	Henri Lifchitz	06/2025
9544	2^339407-177	102172	Lelio R Paula	08/2011
9545	4*10^102163-57	102164	Robert Price	10/2018
9546	2^339355+65	102157	Lelio R Paula	07/2011
9547	(28*10^102142-31)/3	102143	Robert Price	12/2019
9548	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
9549	(2^339268+1758)/2	102130	Stefano Morozzi	09/2020
9550	U(610865)	102130	Serge Batalov	07/2024
9551	s(178551)	102122	Robert Price	05/2020
9552	(797*10^102112-23)/9	102114	Robert Price	01/2022
9553	(5*10^102107+7)/3	102108	Tyler Busby	02/2023
9554	(2^339175+2790)/2	102102	Stefano Morozzi	02/2021
9557	2^339168+21	102100	Lelio R Paula	07/2011
9556	2^339167-108807	102100	Enzo Doria	03/2014
9555	(2^339169+42)/2	102100	Stefano Morozzi	09/2020
9558	2^339156+163	102097	Lelio R Paula	08/2011
9559	(2^339149+746)/2	102094	Stefano Morozzi	09/2020
9560	(25*10^102076-67)/3	102077	Robert Price	06/2019
9561	2^339081-4543	102074	Yves Minet	03/2019
9562	(3435^28867-1)/3434	102069	Serge Batalov	06/2022
9563	2*10^102062+77	102063	Robert Price	08/2020
9564	24327^15668+15668^24327	102053	Hans Havermann	02/2019
9565	10^102052+66793	102053	Patrick De Geest	09/2022
9567	10^102052-7000001	102052	Robert Price	06/2021
9566	10^102052-618623	102052	Patrick De Geest	09/2022
9568	2^339000-175635	102050	Stefano Morozzi	12/2021
9569	2^339000-151667	102050	Stefano Morozzi	12/2021
9570	2^338999+79289	102049	Stefano Morozzi	01/2022
9571	2^338998-63897	102049	Stefano Morozzi	12/2022
9572	2^338997+99659	102049	Stefano Morozzi	02/2023
9573	2^338994+188757	102048	Stefano Morozzi	05/2022
9574	2^338995+70785	102048	Stefano Morozzi	11/2022
9575	2^338994-12183	102048	Stefano Morozzi	12/2022
9576	2^338992+181591	102047	Stefano Morozzi	01/2022
9577	2^338992+136171	102047	Stefano Morozzi	03/2022
9578	2^338991-109435	102047	Stefano Morozzi	04/2022
9579	2^338991+193611	102047	Stefano Morozzi	09/2022
9580	2^338988-134619	102046	Stefano Morozzi	04/2022
9581	2^338987-62557	102046	Stefano Morozzi	12/2022
9582	2^338986-60141	102045	Stefano Morozzi	06/2022
9583	2^338986+98209	102045	Stefano Morozzi	11/2022
9584	2^338981+106391	102044	Stefano Morozzi	01/2022
9585	2^338982+34069	102044	Stefano Morozzi	03/2022
9586	2^338982-58781	102044	Stefano Morozzi	04/2022
9587	2^338980+70833	102044	Stefano Morozzi	11/2022
9588	2^338982-92111	102044	Stefano Morozzi	02/2023
9589	2^338977+83007	102043	Stefano Morozzi	02/2022
9590	2^338979-83601	102043	Stefano Morozzi	04/2022
9591	2^338975+28355	102042	Stefano Morozzi	01/2022
9592	2^338973+134619	102042	Stefano Morozzi	03/2022
9593	2^338974+183777	102042	Stefano Morozzi	03/2022
9594	2^338975+69293	102042	Stefano Morozzi	09/2022
9602	25080^11711+11711^25080	102041	Hans Havermann	02/2019
9595	2^338972+152343	102041	Stefano Morozzi	12/2021
9596	2^338972-180623	102041	Stefano Morozzi	02/2022
9597	2^338972+84441	102041	Stefano Morozzi	03/2022
9598	2^338971+64875	102041	Stefano Morozzi	05/2022
9599	2^338971+44985	102041	Stefano Morozzi	11/2022
9600	2^338971+145065	102041	Stefano Morozzi	11/2022
9601	2^338972-16635	102041	Stefano Morozzi	01/2023
9603	2^338968+53461	102040	Stefano Morozzi	01/2022
9604	2^338969+160175	102040	Stefano Morozzi	03/2022
9605	2^338967+13409	102040	Stefano Morozzi	04/2022
9606	2^338969+67635	102040	Stefano Morozzi	09/2022
9607	2^338969-15913	102040	Stefano Morozzi	01/2023
9608	2^338963-127455	102039	Stefano Morozzi	12/2021
9609	2^338963+132195	102039	Stefano Morozzi	02/2022
9610	2^338966+137919	102039	Stefano Morozzi	04/2022
9611	2^338963-87529	102039	Stefano Morozzi	12/2022
9612	2^338963-116859	102039	Stefano Morozzi	02/2023
9619	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
9613	2^338960+53935	102038	Stefano Morozzi	01/2022
9614	2^338962+83157	102038	Stefano Morozzi	02/2022
9615	2^338961+12341	102038	Stefano Morozzi	04/2022
9616	2^338960+63933	102038	Stefano Morozzi	05/2022
9617	2^338960+170791	102038	Stefano Morozzi	11/2022
9618	2^338962+21679	102038	Stefano Morozzi	11/2022
9620	2^338959-30919	102037	Stefano Morozzi	02/2022
9621	2^338959+164769	102037	Stefano Morozzi	05/2022
9622	2^338958-43161	102037	Stefano Morozzi	02/2023
9623	2^338954-177003	102036	Stefano Morozzi	12/2021
9624	2^338954+154207	102036	Stefano Morozzi	01/2022
9625	2^338956+182493	102036	Stefano Morozzi	02/2022
9626	2^338954+162715	102036	Stefano Morozzi	04/2022
9627	2^338955-158241	102036	Stefano Morozzi	04/2022
9628	2^338956-33395	102036	Stefano Morozzi	04/2022
9629	2^338954+190915	102036	Stefano Morozzi	06/2022
9630	2^338955+41643	102036	Stefano Morozzi	09/2022
9631	2^338954+194427	102036	Stefano Morozzi	09/2022
9632	2^338956+117967	102036	Stefano Morozzi	09/2022
9633	2^338956+195495	102036	Stefano Morozzi	11/2022
9634	2^338954-186371	102036	Stefano Morozzi	12/2022
9635	2^338950+175077	102035	Stefano Morozzi	12/2021
9636	2^338951-51687	102035	Stefano Morozzi	12/2021
9637	2^338951+66123	102035	Stefano Morozzi	06/2022
9638	2^338950+19317	102035	Stefano Morozzi	09/2022
9639	2^338951-161479	102035	Stefano Morozzi	12/2022
9640	2^338950-66335	102035	Stefano Morozzi	01/2023
9641	2^338951-41611	102035	Stefano Morozzi	02/2023
9642	2^338952-142887	102035	Stefano Morozzi	02/2023
9643	2^338949+85449	102034	Stefano Morozzi	03/2022
9644	2^338949-184585	102034	Stefano Morozzi	04/2022
9645	2^338949-88555	102034	Stefano Morozzi	12/2022
9646	2^338948+49393	102034	Stefano Morozzi	02/2023
9647	2^338949-17601	102034	Stefano Morozzi	02/2023
9648	2^338943+127103	102033	Stefano Morozzi	12/2021
9649	2^338944-84003	102033	Stefano Morozzi	04/2022
9650	2^338945+138605	102033	Stefano Morozzi	05/2022
9651	2^338943+95133	102033	Stefano Morozzi	11/2022
9652	2^338943+147435	102033	Stefano Morozzi	11/2022
9653	2^338943-116067	102033	Stefano Morozzi	01/2023
9654	2^338940+78607	102032	Stefano Morozzi	01/2022
9655	2^338942-86687	102032	Stefano Morozzi	12/2022
9656	2^338939+151569	102031	Stefano Morozzi	12/2021
9657	2^338938+183975	102031	Stefano Morozzi	03/2022
9658	2^338937-33429	102031	Stefano Morozzi	04/2022
9659	2^338939-183259	102031	Stefano Morozzi	04/2022
9660	2^338937-139951	102031	Stefano Morozzi	01/2023
9661	2^338938-40151	102031	Stefano Morozzi	01/2023
9662	2^338938+74449	102031	Stefano Morozzi	02/2023
9663	2^338935+179999	102030	Stefano Morozzi	01/2022
9664	2^338936+84147	102030	Stefano Morozzi	03/2022
9665	2^338935+171261	102030	Stefano Morozzi	11/2022
9666	2^338936-41355	102030	Stefano Morozzi	01/2023
9667	2^338931+2349	102029	Stefano Morozzi	12/2021
9668	2^338933+79935	102029	Stefano Morozzi	01/2022
9669	2^338930+33819	102029	Stefano Morozzi	03/2022
9670	2^338931-31555	102029	Stefano Morozzi	03/2022
9671	2^338933+64169	102029	Stefano Morozzi	05/2022
9672	2^338932-184965	102029	Stefano Morozzi	06/2022
9673	2^338932+66943	102029	Stefano Morozzi	09/2022
9674	2^338932+92995	102029	Stefano Morozzi	09/2022
9675	2^338931+97001	102029	Stefano Morozzi	11/2022
9676	2^338932-165453	102029	Stefano Morozzi	01/2023
9677	2^338933-40899	102029	Stefano Morozzi	01/2023
9678	2^338928+2367	102028	Stefano Morozzi	12/2021
9679	2^338927+52779	102028	Stefano Morozzi	01/2022
9680	2^338927-79539	102028	Stefano Morozzi	02/2022
9681	2^338929+60819	102028	Stefano Morozzi	03/2022
9682	2^338928-156959	102028	Stefano Morozzi	03/2022
9683	2^338927-63919	102028	Stefano Morozzi	12/2022
9684	2^338925+106631	102027	Stefano Morozzi	01/2022
9685	2^338926+80235	102027	Stefano Morozzi	01/2022
9686	2^338926+41607	102027	Stefano Morozzi	09/2022
9687	2^338925+195435	102027	Stefano Morozzi	11/2022
9688	2^338924-92885	102027	Stefano Morozzi	02/2023
9689	2^338922-27291	102026	Stefano Morozzi	12/2021
9690	2^338919-103849	102025	Stefano Morozzi	01/2022
9691	2^338919+130221	102025	Stefano Morozzi	01/2022
9692	2^338918-91967	102025	Stefano Morozzi	02/2023
9693	2^338917+561057	102025	Boyan Hu	03/2024
9694	2^338914-79121	102024	Stefano Morozzi	02/2022
9695	2^338916+134047	102024	Stefano Morozzi	03/2022
9696	2^338914-11315	102024	Stefano Morozzi	12/2022
9697	2^338910+81027	102023	Stefano Morozzi	01/2022
9698	2^338912+179821	102023	Stefano Morozzi	01/2022
9699	2^338909+100769	102022	Stefano Morozzi	11/2021
9700	2^338908-100839	102022	Stefano Morozzi	12/2021
9701	2^338909-25951	102022	Stefano Morozzi	12/2021
9702	2^338909+66845	102022	Stefano Morozzi	09/2022
9703	2^338907+73509	102022	Stefano Morozzi	11/2022
9704	2^338906-25823	102021	Stefano Morozzi	12/2021
9705	2^338904+75951	102021	Stefano Morozzi	12/2021
9706	2^338906+6685	102021	Stefano Morozzi	01/2022
9707	2^338905+160365	102021	Stefano Morozzi	03/2022
9708	2^338906+92617	102021	Stefano Morozzi	09/2022
9709	2^338904+47065	102021	Stefano Morozzi	11/2022
9710	2^338905+70427	102021	Stefano Morozzi	11/2022
9711	2^338905-163975	102021	Stefano Morozzi	12/2022
9712	2^338903+4155	102020	Stefano Morozzi	01/2022
9713	2^338901+55571	102020	Stefano Morozzi	01/2022
9714	2^338901-55479	102020	Stefano Morozzi	02/2022
9715	2^338903+33555	102020	Stefano Morozzi	03/2022
9716	2^338901+39777	102020	Stefano Morozzi	05/2022
9717	2^338903+165981	102020	Stefano Morozzi	06/2022
9718	2^338901-34863	102020	Stefano Morozzi	06/2022
9719	2^338899-150051	102019	Stefano Morozzi	12/2021
9720	2^338899+125951	102019	Stefano Morozzi	12/2021
9721	2^338898+179623	102019	Stefano Morozzi	01/2022
9722	2^338899-154467	102019	Stefano Morozzi	02/2022
9723	2^338898-60753	102019	Stefano Morozzi	06/2022
9724	2^338898+68635	102019	Stefano Morozzi	09/2022
9725	2^338897-85963	102019	Stefano Morozzi	12/2022
9726	2^338898+174129	102019	Stefano Morozzi	02/2023
9727	2^338894-133295	102018	Stefano Morozzi	04/2022
9728	2^338894+165573	102018	Stefano Morozzi	06/2022
9729	2^338894-60957	102018	Stefano Morozzi	06/2022
9730	2^338894-89463	102018	Stefano Morozzi	01/2023
9740	2^338891-18885	102017	Enzo Doria	05/2013
9731	2^338891+26499	102017	Stefano Morozzi	12/2021
9732	2^338891-2625	102017	Stefano Morozzi	12/2021
9733	2^338893+128727	102017	Stefano Morozzi	01/2022
9734	2^338890-52965	102017	Stefano Morozzi	01/2022
9735	2^338892-55467	102017	Stefano Morozzi	02/2022
9736	2^338892-83393	102017	Stefano Morozzi	04/2022
9737	2^338893+13649	102017	Stefano Morozzi	05/2022
9738	2^338892+117957	102017	Stefano Morozzi	09/2022
9739	2^338892-14643	102017	Stefano Morozzi	01/2023
9741	2^338887+154029	102016	Stefano Morozzi	01/2022
9742	2^338889-104293	102016	Stefano Morozzi	02/2022
9743	2^338887+147741	102016	Stefano Morozzi	11/2022
9744	2^338889+195975	102016	Stefano Morozzi	11/2022
9745	2^338889-117873	102016	Stefano Morozzi	02/2023
9746	2^338886+177159	102015	Stefano Morozzi	12/2021
9747	2^338885+40425	102015	Stefano Morozzi	06/2022
9748	2^338884-13053	102015	Stefano Morozzi	12/2022
9749	2^338885-112569	102015	Stefano Morozzi	12/2022
9750	2^338880+11341	102014	Stefano Morozzi	03/2022

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Probable Primes Top 10000

(303103 PRPs in the top)