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	2^341466+4429	102792	Lelio R Paula	09/2011
9502	2^341460-107	102790	Lelio R Paula	08/2011
9503	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
9504	2^341355+21	102759	Lelio R Paula	08/2011
9505	2^341319+224885	102748	Enzo Doria	07/2024
9506	(419^39181-1)/418	102739	Tom Wu	07/2024
9507	(6496^26947-1)/6495	102736	Serge Batalov	06/2022
9508	2^341246+40755	102726	Lelio R Paula	11/2016
9509	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
9510	7^121547+78	102720	Lelio R Paula	10/2016
9511	2^341223-461197	102719	Enzo Doria	06/2015
9512	27838^4893+4893^27838	102711	Hans Havermann	03/2019
9514	2^341190-20577	102709	Enzo Doria	06/2013
9513	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
9515	(25*10^102698+77)/3	102699	Robert Price	09/2022
9516	6^131976-65	102698	Lelio R Paula	10/2016
9517	2^341134+2533	102692	Henri Lifchitz	09/2005
9518	13^92184-54	102688	Lelio R Paula	10/2016
9519	2^341116-20873	102687	Enzo Doria	06/2013
9520	2^341094-19953	102680	Enzo Doria	06/2013
9521	23761^20950+20950^23761	102676	Hans Havermann	03/2019
9523	2^341053+129	102668	Lelio R Paula	08/2011
9522	(4724^27943-1)/4723	102668	Serge Batalov	06/2022
9525	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
9524	7^121471+94	102655	Lelio R Paula	10/2016
9527	2^341004-173	102653	Lelio R Paula	08/2011
9526	20^78901+3	102653	Lelio R Paula	10/2016
9528	(2^341001+1674)/2	102652	Stefano Morozzi	09/2020
9529	5^146853-52	102646	Lelio R Paula	10/2016
9530	2^340969-216931	102642	Enzo Doria	05/2014
9531	122^49196+121	102641	Norbert Schneider	10/2018
9532	2^340952+1870021	102637	Enzo Doria	05/2016
9533	5*2^340940-3	102634	Lelio R Paula	08/2014
9534	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
9535	(11*10^102629-23)/3	102630	Robert Price	09/2021
9536	3^215094+5*2^215094	102626	Jon Grantham	08/2023
9537	25876^9239+9239^25876	102615	Hans Havermann	02/2019
9538	(4*10^102612+83)/3	102613	Robert Price	02/2018
9539	(234^43313-1)/20184091	102611	Aurel Gibier	03/2025
9541	75^54717+74	102598	Norbert Schneider	01/2015
9540	(17*10^102597+13)/3	102598	Robert Price	01/2019
9542	2^340806-20393	102593	Enzo Doria	06/2013
9543	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
9544	6^131821+77	102577	Lelio R Paula	10/2016
9545	(203*10^102561-11)/3	102563	Robert Price	12/2020
9546	(67^56171-1)/2053280351166	102561	Paul Vanderveen	05/2025
9547	2^340688-29	102558	Henri Lifchitz	05/2005
9548	2^340685-109101	102557	Enzo Doria	04/2014
9549	65^56567-64	102552	Norbert Schneider	11/2014
9550	26230^8121+8121^26230	102550	Hans Havermann	03/2019
9551	(64*10^102547+161)/9	102548	Robert Price	08/2022
9552	(8*10^102541+49)/3	102542	Robert Price	05/2020
9553	(536*10^102533-23)/9	102535	Robert Price	02/2020
9554	2^340547-108897	102515	Enzo Doria	03/2014
9555	(2^340536+778)/2	102512	Stefano Morozzi	09/2020
9556	25592^10119+10119^25592	102500	Hans Havermann	02/2019
9557	(5*10^102492-23)/9	102492	Serge Batalov	11/2022
9558	7^121268+82	102484	Lelio R Paula	10/2016
9559	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
9560	2^340434-5955	102481	Lelio R Paula	11/2016
9561	(7*10^102480-19)/3	102481	Robert Price	10/2020
9562	(2^340381+47)/7	102465	Lelio R Paula	12/2013
9563	111^50095+110	102461	Norbert Schneider	04/2017
9564	180^45427-45427^180	102451	Norman Luhn	09/2024
9565	2^340291-20301	102438	Enzo Doria	06/2013
9566	12^94915+89	102431	Lelio R Paula	10/2016
9567	(106*10^102422+17)/3	102424	Robert Price	04/2021
9568	24466^15349+15349^24466	102417	Hans Havermann	03/2019
9569	2^340212+111546435	102415	Paul Bourdelais	10/2021
9570	2^340208-20373	102413	Enzo Doria	06/2013
9571	6^131598-17273	102404	Enzo Doria	02/2013
9572	(2^340132+1182)/2	102390	Stefano Morozzi	09/2020
9573	(2^340133+1166)/2	102390	Stefano Morozzi	09/2020
9574	2^340115-21181	102385	Enzo Doria	06/2013
9575	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
9576	(2^340064+3630)/2	102370	Stefano Morozzi	09/2020
9577	9348*31^68638+13	102369	Eric Chen	04/2024
9578	89^52511-88^52511	102365	Robert Price	06/2015
9579	3^214539-112756	102362	Enzo Doria	07/2014
9580	Phi(562221,2)/53723397926257372614541581386770268796893300042857	102361	Anonymous	06/2025
9581	23159^23450-23450^23159	102353	Norbert Schneider	12/2019
9582	2^340000-19877	102351	Enzo Doria	06/2013
9584	2^339990-114845	102348	Enzo Doria	05/2015
9583	311^41058-41058^311	102348	Norman Luhn	09/2024
9585	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
9586	20^78661-99	102341	Lelio R Paula	09/2016
9587	2^339951-19585	102336	Enzo Doria	05/2013
9588	(17*10^102335-167)/3	102336	Robert Price	05/2022
9589	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
9590	(236282#+121441)/(121441*25499429)	102332	Makoto Morimoto	08/2020
9591	5*10^102323-91	102324	Robert Price	03/2021
9593	2^339889+29327	102317	Yves Minet	06/2010
9592	(167*10^102315-17)/3	102317	Robert Price	03/2020
9594	26348^7641+7641^26348	102314	Hans Havermann	03/2019
9595	Phi(239414,10)/6333218543	102303	Makoto Kamada	08/2019
9596	2^339834-109493	102301	Enzo Doria	04/2014
9597	(16*10^102299-19)/3	102300	Robert Price	02/2019
9598	(11^98221-5^98221)/6	102286	Robert Price	01/2013
9599	3^214365+1820	102279	Lelio R Paula	10/2016
9600	31978^1579+1579^31978	102278	Hans Havermann	03/2019
9601	(89*10^102262-467)/9	102263	Robert Price	04/2022
9602	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
9603	2^339694-16995	102259	Lelio R Paula	09/2016
9604	(56*10^102255+691)/9	102256	Robert Price	05/2019
9605	122^49008+121	102249	Norbert Schneider	10/2018
9606	(2^339652+3178)/2	102246	Stefano Morozzi	09/2020
9607	7^120985-38	102245	Lelio R Paula	10/2016
9608	10^102244+122961	102245	Patrick De Geest	12/2016
9609	10^102244-27	102244	Lelio R Paula	09/2016
9610	7^120982-62	102242	Lelio R Paula	10/2016
9611	(2^339640+2670)/2	102242	Stefano Morozzi	09/2020
9612	4*6^131382-5	102236	Lelio R Paula	11/2014
9613	(2^339607+3290)/2	102232	Stefano Morozzi	02/2021
9614	2^339586-1091	102226	Yves Minet	11/2012
9615	11^98161-3072000	102225	Enzo Doria	12/2012
9616	9*7^120961-4	102225	Lelio R Paula	11/2014
9617	5*3^214250+2	102224	Serge Batalov	10/2010
9618	12^94713-59	102213	Lelio R Paula	10/2016
9619	12^94705+89	102204	Lelio R Paula	10/2016
9620	L(2*339475)%(2^339475)	102193	Henri Lifchitz	06/2025
9621	2^339407-177	102172	Lelio R Paula	08/2011
9622	4*10^102163-57	102164	Robert Price	10/2018
9623	2^339355+65	102157	Lelio R Paula	07/2011
9624	(28*10^102142-31)/3	102143	Robert Price	12/2019
9625	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
9626	(2^339268+1758)/2	102130	Stefano Morozzi	09/2020
9627	U(610865)	102130	Serge Batalov	07/2024
9628	s(178551)	102122	Robert Price	05/2020
9629	(797*10^102112-23)/9	102114	Robert Price	01/2022
9630	(5*10^102107+7)/3	102108	Tyler Busby	02/2023
9631	(2^339175+2790)/2	102102	Stefano Morozzi	02/2021
9634	2^339168+21	102100	Lelio R Paula	07/2011
9633	2^339167-108807	102100	Enzo Doria	03/2014
9632	(2^339169+42)/2	102100	Stefano Morozzi	09/2020
9635	2^339156+163	102097	Lelio R Paula	08/2011
9636	(2^339149+746)/2	102094	Stefano Morozzi	09/2020
9637	(25*10^102076-67)/3	102077	Robert Price	06/2019
9638	2^339081-4543	102074	Yves Minet	03/2019
9639	(3435^28867-1)/3434	102069	Serge Batalov	06/2022
9640	2*10^102062+77	102063	Robert Price	08/2020
9642	24327^15668+15668^24327	102053	Hans Havermann	02/2019
9641	10^102052+66793	102053	Patrick De Geest	09/2022
9644	10^102052-7000001	102052	Robert Price	06/2021
9643	10^102052-618623	102052	Patrick De Geest	09/2022
9645	2^339000-175635	102050	Stefano Morozzi	12/2021
9646	2^339000-151667	102050	Stefano Morozzi	12/2021
9647	2^338999+79289	102049	Stefano Morozzi	01/2022
9648	2^338998-63897	102049	Stefano Morozzi	12/2022
9649	2^338997+99659	102049	Stefano Morozzi	02/2023
9650	2^338994+188757	102048	Stefano Morozzi	05/2022
9651	2^338995+70785	102048	Stefano Morozzi	11/2022
9652	2^338994-12183	102048	Stefano Morozzi	12/2022
9653	2^338992+181591	102047	Stefano Morozzi	01/2022
9654	2^338992+136171	102047	Stefano Morozzi	03/2022
9655	2^338991-109435	102047	Stefano Morozzi	04/2022
9656	2^338991+193611	102047	Stefano Morozzi	09/2022
9657	2^338988-134619	102046	Stefano Morozzi	04/2022
9658	2^338987-62557	102046	Stefano Morozzi	12/2022
9659	2^338986-60141	102045	Stefano Morozzi	06/2022
9660	2^338986+98209	102045	Stefano Morozzi	11/2022
9661	2^338981+106391	102044	Stefano Morozzi	01/2022
9662	2^338982+34069	102044	Stefano Morozzi	03/2022
9663	2^338982-58781	102044	Stefano Morozzi	04/2022
9664	2^338980+70833	102044	Stefano Morozzi	11/2022
9665	2^338982-92111	102044	Stefano Morozzi	02/2023
9666	2^338977+83007	102043	Stefano Morozzi	02/2022
9667	2^338979-83601	102043	Stefano Morozzi	04/2022
9668	2^338975+28355	102042	Stefano Morozzi	01/2022
9669	2^338973+134619	102042	Stefano Morozzi	03/2022
9670	2^338974+183777	102042	Stefano Morozzi	03/2022
9671	2^338975+69293	102042	Stefano Morozzi	09/2022
9679	25080^11711+11711^25080	102041	Hans Havermann	02/2019
9672	2^338972+152343	102041	Stefano Morozzi	12/2021
9673	2^338972-180623	102041	Stefano Morozzi	02/2022
9674	2^338972+84441	102041	Stefano Morozzi	03/2022
9675	2^338971+64875	102041	Stefano Morozzi	05/2022
9676	2^338971+44985	102041	Stefano Morozzi	11/2022
9677	2^338971+145065	102041	Stefano Morozzi	11/2022
9678	2^338972-16635	102041	Stefano Morozzi	01/2023
9680	2^338968+53461	102040	Stefano Morozzi	01/2022
9681	2^338969+160175	102040	Stefano Morozzi	03/2022
9682	2^338967+13409	102040	Stefano Morozzi	04/2022
9683	2^338969+67635	102040	Stefano Morozzi	09/2022
9684	2^338969-15913	102040	Stefano Morozzi	01/2023
9685	2^338963-127455	102039	Stefano Morozzi	12/2021
9686	2^338963+132195	102039	Stefano Morozzi	02/2022
9687	2^338966+137919	102039	Stefano Morozzi	04/2022
9688	2^338963-87529	102039	Stefano Morozzi	12/2022
9689	2^338963-116859	102039	Stefano Morozzi	02/2023
9696	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
9690	2^338960+53935	102038	Stefano Morozzi	01/2022
9691	2^338962+83157	102038	Stefano Morozzi	02/2022
9692	2^338961+12341	102038	Stefano Morozzi	04/2022
9693	2^338960+63933	102038	Stefano Morozzi	05/2022
9694	2^338960+170791	102038	Stefano Morozzi	11/2022
9695	2^338962+21679	102038	Stefano Morozzi	11/2022
9697	2^338959-30919	102037	Stefano Morozzi	02/2022
9698	2^338959+164769	102037	Stefano Morozzi	05/2022
9699	2^338958-43161	102037	Stefano Morozzi	02/2023
9700	2^338954-177003	102036	Stefano Morozzi	12/2021
9701	2^338954+154207	102036	Stefano Morozzi	01/2022
9702	2^338956+182493	102036	Stefano Morozzi	02/2022
9703	2^338954+162715	102036	Stefano Morozzi	04/2022
9704	2^338955-158241	102036	Stefano Morozzi	04/2022
9705	2^338956-33395	102036	Stefano Morozzi	04/2022
9706	2^338954+190915	102036	Stefano Morozzi	06/2022
9707	2^338955+41643	102036	Stefano Morozzi	09/2022
9708	2^338954+194427	102036	Stefano Morozzi	09/2022
9709	2^338956+117967	102036	Stefano Morozzi	09/2022
9710	2^338956+195495	102036	Stefano Morozzi	11/2022
9711	2^338954-186371	102036	Stefano Morozzi	12/2022
9712	2^338950+175077	102035	Stefano Morozzi	12/2021
9713	2^338951-51687	102035	Stefano Morozzi	12/2021
9714	2^338951+66123	102035	Stefano Morozzi	06/2022
9715	2^338950+19317	102035	Stefano Morozzi	09/2022
9716	2^338951-161479	102035	Stefano Morozzi	12/2022
9717	2^338950-66335	102035	Stefano Morozzi	01/2023
9718	2^338951-41611	102035	Stefano Morozzi	02/2023
9719	2^338952-142887	102035	Stefano Morozzi	02/2023
9720	2^338949+85449	102034	Stefano Morozzi	03/2022
9721	2^338949-184585	102034	Stefano Morozzi	04/2022
9722	2^338949-88555	102034	Stefano Morozzi	12/2022
9723	2^338948+49393	102034	Stefano Morozzi	02/2023
9724	2^338949-17601	102034	Stefano Morozzi	02/2023
9725	2^338943+127103	102033	Stefano Morozzi	12/2021
9726	2^338944-84003	102033	Stefano Morozzi	04/2022
9727	2^338945+138605	102033	Stefano Morozzi	05/2022
9728	2^338943+95133	102033	Stefano Morozzi	11/2022
9729	2^338943+147435	102033	Stefano Morozzi	11/2022
9730	2^338943-116067	102033	Stefano Morozzi	01/2023
9731	2^338940+78607	102032	Stefano Morozzi	01/2022
9732	2^338942-86687	102032	Stefano Morozzi	12/2022
9733	2^338939+151569	102031	Stefano Morozzi	12/2021
9734	2^338938+183975	102031	Stefano Morozzi	03/2022
9735	2^338937-33429	102031	Stefano Morozzi	04/2022
9736	2^338939-183259	102031	Stefano Morozzi	04/2022
9737	2^338937-139951	102031	Stefano Morozzi	01/2023
9738	2^338938-40151	102031	Stefano Morozzi	01/2023
9739	2^338938+74449	102031	Stefano Morozzi	02/2023
9740	2^338935+179999	102030	Stefano Morozzi	01/2022
9741	2^338936+84147	102030	Stefano Morozzi	03/2022
9742	2^338935+171261	102030	Stefano Morozzi	11/2022
9743	2^338936-41355	102030	Stefano Morozzi	01/2023
9744	2^338931+2349	102029	Stefano Morozzi	12/2021
9745	2^338933+79935	102029	Stefano Morozzi	01/2022
9746	2^338930+33819	102029	Stefano Morozzi	03/2022
9747	2^338931-31555	102029	Stefano Morozzi	03/2022
9748	2^338933+64169	102029	Stefano Morozzi	05/2022
9749	2^338932-184965	102029	Stefano Morozzi	06/2022
9750	2^338932+66943	102029	Stefano Morozzi	09/2022

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Probable Primes Top 10000

(303322 PRPs in the top)