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	2^303698-1847231	91423	Enzo Doria	07/2015
9502	(38^28933-1)^2-2	91416	Norbert Schneider	06/2016
9503	25660^3643+3643^25660	91388	Hans Havermann	08/2020
9504	2^303554+77299	91379	Enzo Doria	05/2016
9505	2^303542+12705	91376	Lelio R Paula	02/2016
9506	31^61269-2	91375	Lelio R Paula	09/2013
9507	(2^303525+2774)/2	91370	Stefano Morozzi	01/2021
9508	2^303516-64875	91368	Lelio R Paula	02/2016
9509	(2^303497+1266)/2	91362	Stefano Morozzi	09/2020
9510	(2^303497+3710)/2	91362	Stefano Morozzi	09/2020
9511	(31*10^91352+257)/9	91353	Robert Price	12/2021
9512	21856^15121+15121^21856	91349	Hans Havermann	09/2020
9513	(24737*2^303428+1)/3	91345	Lelio R Paula	06/2014
9514	(21181*2^303357+1)/32361	91320	Lelio R Paula	06/2014
9515	23081^9046+9046^23081	91319	Hans Havermann	09/2020
9516	2^303344-2786969	91316	Enzo Doria	03/2016
9517	6^117346+65	91313	Lelio R Paula	05/2016
9518	2^303321+855	91309	Lelio R Paula	02/2016
9519	(2^303315+3746)/2	91307	Stefano Morozzi	01/2021
9520	12^84606+47	91306	Lelio R Paula	06/2016
9521	2^303288+1874311	91299	Enzo Doria	06/2016
9522	197^39788-2	91293	Lelio R Paula	10/2017
9523	11^87663-1710	91292	Enzo Doria	12/2012
9524	(4*10^91284-61)/3	91285	Robert Price	12/2021
9526	2^303224+2533	91280	Henri Lifchitz	05/2005
9525	(2^303226+1830)/2	91280	Stefano Morozzi	02/2021
9527	6^117302+143	91279	Lelio R Paula	05/2016
9528	3^191306-112880	91277	Enzo Doria	07/2014
9529	(10052^22807-1)/10051	91276	Serge Batalov	08/2020
9530	2^303207+12915	91275	Lelio R Paula	02/2016
9531	2^303191-111259	91270	Enzo Doria	05/2014
9532	81539!4+32	91267	Robert Price	09/2019
9533	(2^303116+3570)/2	91247	Stefano Morozzi	09/2020
9534	10^91230+9^(91230+1)	91231	Robert Price	08/2016
9535	10^91230+7921	91231	Patrick De Geest	11/2016
9536	10^91230-911141	91230	Patrick De Geest	11/2016
9537	10^91229+348793	91230	Patrick De Geest	07/2019
9538	10^91229-2471	91229	Patrick De Geest	01/2019
9540	2996^26241+26241^2996	91228	Norbert Schneider	01/2020
9539	2^303249-494953	91228	Harrison Mesh	06/2022
9542	10^91225+5271	91226	Patrick De Geest	01/2019
9541	2816^26445+26445^2816	91226	Norbert Schneider	02/2020
9544	6^117232-17423	91225	Enzo Doria	02/2013
9543	10^91225-147219	91225	Patrick De Geest	07/2019
9545	7*10^91215+3	91216	Erik Branger	11/2009
9546	10^91215+230611	91216	Patrick De Geest	07/2019
9547	10^91215-4539	91215	Patrick De Geest	01/2019
9548	(2^303007+606)/2	91214	Stefano Morozzi	09/2020
9549	9*10^91212-47	91213	Robert Price	11/2021
9550	(2^302998+3102)/2	91212	Stefano Morozzi	09/2020
9551	10^91210+2421	91211	Patrick De Geest	01/2019
9552	10^91210-1737	91210	Patrick De Geest	01/2019
9553	97*10^91205-3	91207	Robert Price	01/2017
9554	2^302979-161181	91206	Enzo Doria	04/2013
9555	(166*10^91199-7)/3	91201	Robert Price	11/2020
9556	2^302949+81	91197	Henri Lifchitz	02/2007
9557	10^91194+200361	91195	Patrick De Geest	07/2019
9559	4*6^117192-5	91194	Lelio R Paula	10/2014
9558	10^91194-8663	91194	Patrick De Geest	01/2019
9560	2^302918+99	91188	Lelio R Paula	11/2012
9561	10^91186+268111	91187	Patrick De Geest	07/2019
9562	10^91186-7763	91186	Patrick De Geest	01/2019
9563	10^91181+550471	91182	Patrick De Geest	07/2019
9564	(26*10^91181-83)/3	91182	Robert Price	12/2021
9565	10^91181-1367	91181	Patrick De Geest	01/2019
9566	10^91178+71883	91179	Patrick De Geest	07/2019
9567	10^91178-4719	91178	Patrick De Geest	01/2019
9568	24686^4935+4935^24686	91173	Hans Havermann	08/2020
9569	10^91165+3043	91166	Patrick De Geest	01/2019
9570	10^91165-399413	91165	Patrick De Geest	07/2019
9571	(19*10^91167+107)/9/11/11/151	91164	Alfred Reich	11/2022
9572	10^91156+3861	91157	Patrick De Geest	01/2019
9573	10^91156-231497	91156	Patrick De Geest	07/2019
9574	2^302797+1869587	91151	Enzo Doria	05/2016
9575	265^37614+37614^265	91148	Norbert Schneider	01/2015
9576	7^107852+82	91146	Lelio R Paula	04/2016
9577	(38*10^91144-11)/9	91145	Robert Price	05/2015
9578	(55*10^91142+377)/9	91143	Robert Price	10/2017
9579	10^91128+9961	91129	Patrick De Geest	01/2019
9581	249^38030+38030^249	91128	Norbert Schneider	01/2015
9580	10^91128-189153	91128	Patrick De Geest	07/2019
9582	(2^302718+2814)/2	91127	Stefano Morozzi	02/2021
9583	6^117094-211049	91117	Mike Oakes	05/2011
9584	21353^18472+18472^21353	91103	Hans Havermann	05/2020
9586	2^302602-1867181	91093	Enzo Doria	03/2016
9585	10^91092+56127	91093	Patrick De Geest	07/2019
9587	10^91092-9107	91092	Patrick De Geest	01/2019
9588	(1017*2^302592-1)/53	91091	Lelio R Paula	04/2015
9589	15^77445-16	91083	Lelio R Paula	07/2016
9590	21656^16053+16053^21656	91076	Hans Havermann	05/2020
9591	2^302505+81	91064	Henri Lifchitz	02/2007
9592	2^302496-112349	91061	Enzo Doria	06/2014
9593	(2^302475+1790)/2	91054	Stefano Morozzi	01/2021
9594	17^73999-72	91052	Lelio R Paula	07/2016
9595	10^91047+9331	91048	Patrick De Geest	01/2019
9596	10^91047-671169	91047	Patrick De Geest	07/2019
9597	10^91044+2077	91045	Patrick De Geest	01/2019
9598	10^91044-136359	91044	Patrick De Geest	07/2019
9599	10^91041+9349	91042	Patrick De Geest	01/2019
9600	10^91041-7823	91041	Patrick De Geest	01/2019
9601	10^91040+4077	91041	Patrick De Geest	01/2019
9602	10^91040-119421	91040	Patrick De Geest	07/2019
9603	10^91037+2769	91038	Patrick De Geest	01/2019
9604	10^91037-22649	91037	Patrick De Geest	07/2019
9605	(16*10^91032+41)/3	91033	Robert Price	10/2017
9606	10^91023+58039	91024	Patrick De Geest	07/2019
9607	10^91023-6471	91023	Patrick De Geest	01/2019
9608	10^91018+7873	91019	Patrick De Geest	01/2019
9609	10^91018-333177	91018	Patrick De Geest	07/2019
9610	10^91017+68767	91018	Patrick De Geest	07/2019
9611	10^91017-428327	91017	Patrick De Geest	07/2019
9612	10^91016+73111	91017	Patrick De Geest	07/2019
9613	10^91016-7973	91016	Patrick De Geest	01/2019
9614	1949^27666+27666^1949	91016	Norbert Schneider	04/2020
9615	2^302332+577294575	91012	Lelio R Paula	08/2016
9616	10^91004+9073	91005	Patrick De Geest	01/2019
9617	10^91004-491519	91004	Patrick De Geest	07/2019
9618	10^91003+74269	91004	Patrick De Geest	07/2019
9619	10^91003-3903	91003	Patrick De Geest	01/2019
9620	2^302274+74209	90994	Enzo Doria	04/2016
9621	10^90991+81147	90992	Patrick De Geest	07/2019
9622	10^90991-6279	90991	Patrick De Geest	01/2019
9623	10^90983+1393	90984	Patrick De Geest	01/2019
9624	11*10^90982+9	90984	Robert Price	08/2020
9625	10^90983-562383	90983	Patrick De Geest	07/2019
9626	(311^36497-1)/310	90976	Eric Chen	09/2017
9627	(2^302210+1014)/2	90974	Stefano Morozzi	09/2020
9628	(3^190668+2)/89	90970	Lelio R Paula	04/2013
9629	2^302188+90195	90968	Lelio R Paula	02/2016
9630	(53*10^90965-71)/9	90966	Robert Price	09/2015
9631	10^90965+573987	90966	Patrick De Geest	07/2019
9632	10^90965-6833	90965	Patrick De Geest	01/2019
9633	10^90964+48789	90965	Patrick De Geest	07/2019
9634	10^90964-52103	90964	Patrick De Geest	07/2019
9635	10^90963+191889	90964	Patrick De Geest	07/2019
9636	10^90963-3659	90963	Patrick De Geest	01/2019
9637	10^90962+7657	90963	Patrick De Geest	01/2019
9638	10^90962-215633	90962	Patrick De Geest	07/2019
9639	10^90961+67471	90962	Patrick De Geest	07/2019
9640	10^90961-211043	90961	Patrick De Geest	07/2019
9641	10^90960+1072117	90961	Patrick De Geest	07/2019
9642	10^90959+8791	90960	Patrick De Geest	01/2019
9643	10^90960-610659	90960	Patrick De Geest	07/2019
9644	10^90959-275213	90959	Patrick De Geest	07/2019
9645	(2^302129+3110)/2	90950	Stefano Morozzi	09/2020
9647	10^90948+9867	90949	Patrick De Geest	01/2019
9646	21665^15774+15774^21665	90949	Hans Havermann	04/2020
9648	10^90948-109239	90948	Patrick De Geest	07/2019
9649	2^302113+74105	90946	Enzo Doria	04/2016
9650	2^302102-6555	90942	Lelio R Paula	02/2016
9651	10^90930+95223	90931	Patrick De Geest	07/2019
9652	10^90930-3623	90930	Patrick De Geest	01/2019
9653	156(10^(422731)-1)/101-1	90925	Robert Price	05/2014
9654	3^190568+38	90925	Lelio R Paula	04/2016
9655	10^90917+179863	90918	Patrick De Geest	07/2019
9656	10^90917-6693	90917	Patrick De Geest	01/2019
9657	2^302009-16449	90914	Enzo Doria	04/2013
9658	10^90908+3181	90909	Patrick De Geest	01/2019
9659	10^90908-139511	90908	Patrick De Geest	07/2019
9660	10^90904+106947	90905	Patrick De Geest	07/2019
9661	10^90904-5169	90904	Patrick De Geest	01/2019
9662	10^90903+120963	90904	Patrick De Geest	07/2019
9663	10^90902+2613	90903	Patrick De Geest	01/2019
9664	10^90903-190737	90903	Patrick De Geest	07/2019
9665	25174^4083+4083^25174	90903	Hans Havermann	08/2020
9666	10^90902-952329	90902	Patrick De Geest	07/2019
9667	(17*2^301951-1)/165	90896	Lelio R Paula	02/2014
9668	3^190497+74	90891	Lelio R Paula	04/2016
9669	(24737*2^301896+1)/399	90882	Lelio R Paula	06/2014
9670	10^90880+5707	90881	Patrick De Geest	01/2019
9671	10^90880-152993	90880	Patrick De Geest	07/2019
9672	18^72397+89	90878	Lelio R Paula	06/2016
9673	(2^301876+762)/2	90874	Stefano Morozzi	09/2020
9674	134^42719-133	90868	Norbert Schneider	03/2019
9675	6^116769-47	90864	Lelio R Paula	05/2016
9676	10^90858+233433	90859	Patrick De Geest	07/2019
9677	10^90858-8301	90858	Patrick De Geest	01/2019
9678	24298^5483+5483^24298	90851	Hans Havermann	08/2020
9679	10^90849+40141	90850	Patrick De Geest	07/2019
9680	10^90849-4721	90849	Patrick De Geest	01/2019
9681	2^301712-465	90825	Lelio R Paula	02/2016
9682	2^301693-69	90819	Lelio R Paula	11/2012
9683	2^301683-301683^2	90816	Henri Lifchitz	05/2005
9684	10^90807+7279	90808	Patrick De Geest	01/2019
9685	10^90807-162263	90807	Patrick De Geest	07/2019
9686	6*10^90803+79	90804	Robert Price	09/2020
9687	10^90800-6453	90800	Patrick De Geest	11/2018
9688	11^87187-1710	90796	Enzo Doria	12/2012
9689	5*10^90793+21	90794	Robert Price	01/2017
9690	(22*10^90792-13)/9	90793	Robert Price	03/2015
9691	2^301591-1615	90788	Lelio R Paula	02/2016
9692	(52^52901+1)/53	90777	Paul Bourdelais	08/2017
9693	2^301546-109037	90775	Enzo Doria	04/2014
9694	10^90772+4029	90773	Patrick De Geest	11/2018
9695	10^90772-36627	90772	Patrick De Geest	07/2019
9696	10^90771+67737	90772	Patrick De Geest	07/2019
9697	10^90771-441003	90771	Patrick De Geest	07/2019
9698	10^90770+28941	90771	Patrick De Geest	07/2019
9699	10^90770-431	90770	Patrick De Geest	11/2018
9700	14^79195-3	90768	Lelio R Paula	06/2016
9701	10^90766+877	90767	Patrick De Geest	11/2018
9702	2^301517-1861693	90766	Enzo Doria	11/2015
9703	10^90766-109241	90766	Patrick De Geest	07/2019
9704	10^90765+485361	90766	Patrick De Geest	07/2019
9705	10^90765-4797	90765	Patrick De Geest	11/2018
9706	10^90757+7573	90758	Patrick De Geest	11/2018
9707	10^90757-554979	90757	Patrick De Geest	07/2019
9708	10^90756+438109	90757	Patrick De Geest	07/2019
9709	10^90756-8727	90756	Patrick De Geest	11/2018
9710	10^90749+823	90750	Patrick De Geest	11/2018
9713	2^301460-173	90749	Lelio R Paula	11/2012
9711	10^90748+4213	90749	Patrick De Geest	11/2018
9712	10^90749-130413	90749	Patrick De Geest	07/2019
9714	10^90748-75411	90748	Patrick De Geest	07/2019
9715	10^90747+438471	90748	Patrick De Geest	07/2019
9716	10^90747-9279	90747	Patrick De Geest	11/2018
9717	(85*10^90745-103)/9	90746	Robert Price	10/2017
9718	(2^301439+1206)/2	90742	Stefano Morozzi	09/2020
9719	10^90726+4077	90727	Patrick De Geest	11/2018
9720	10^90726-504951	90726	Patrick De Geest	07/2019
9722	10^90721+181	90722	Patrick De Geest	11/2018
9721	(2^301372+2722)/2	90722	Stefano Morozzi	09/2020
9723	10^90721-177149	90721	Patrick De Geest	07/2019
9724	(2^301317+1146)/2	90706	Stefano Morozzi	09/2020
9725	2^301312-89	90704	Lelio R Paula	11/2012
9726	10^90696+6349	90697	Patrick De Geest	11/2018
9727	2^301285-129	90696	Lelio R Paula	11/2012
9728	10^90696-635049	90696	Patrick De Geest	07/2019
9729	2^301282-109991	90695	Enzo Doria	04/2014
9730	10^90690+8877	90691	Patrick De Geest	11/2018
9731	10^90690-227433	90690	Patrick De Geest	07/2019
9732	10^90683+61411	90684	Patrick De Geest	07/2019
9733	(2^301244+1738)/2	90684	Stefano Morozzi	09/2020
9734	10^90683-2577	90683	Patrick De Geest	11/2018
9735	2^301228-1854269	90679	Enzo Doria	09/2015
9736	10^90674+138453	90675	Patrick De Geest	10/2022
9737	10^90674-5000001	90674	Robert Price	12/2021
9738	10^90674-59451	90674	Patrick De Geest	10/2022
9740	(151*10^90669-1)/3	90671	Robert Price	04/2017
9739	(2^301201+2046)/2	90671	Stefano Morozzi	09/2020
9742	(32*10^90669+13)/9	90670	Robert Price	04/2015
9741	10^90669+9793	90670	Patrick De Geest	11/2018
9743	10^90669-223931	90669	Patrick De Geest	07/2019
9744	(2^301191+2510)/2	90668	Stefano Morozzi	09/2020
9745	5*10^90666-63	90667	Robert Price	04/2021
9746	10^90665+10989	90666	Patrick De Geest	07/2019
9747	10^90665-3087	90665	Patrick De Geest	11/2018
9748	2^301177-227713	90664	Harrison Mesh	06/2022
9749	10^90662+89637	90663	Patrick De Geest	07/2019
9750	10^90662-9519	90662	Patrick De Geest	11/2018

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Probable Primes Top 10000

(291910 PRPs in the top)