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	(2^235099-2^117550+1)/5	70772		11/2006
9502	19^55325-6	70748	Lelio R Paula	08/2014
9503	257^29356+29356^257	70746	Norbert Schneider	10/2014
9504	22*10^70729+3	70731	Robert Price	10/2017
9505	2^234956+11715	70729	Lelio R Paula	05/2012
9506	(7*10^70727-43)/9	70727	Robert Price	10/2014
9507	(2^234897+3906)/2	70711	Stefano Morozzi	01/2020
9508	2^234890-30341	70709	Enzo Doria	11/2012
9509	17^57461+14	70703	Lelio R Paula	01/2015
9510	18281^7366+7366^18281	70697	Hans Havermann	09/2019
9511	(9179*2^234834-1)/5	70696	Lelio R Paula	04/2015
9512	2*10^70688+51	70689	Robert Price	10/2017
9513	123^33822-122	70685	Norbert Schneider	01/2015
9514	7*10^70680-99	70681	Robert Price	11/2017
9515	(2^234784+3646)/2	70677	Stefano Morozzi	01/2020
9516	(21*2^234772-1)/2095	70672	Lelio R Paula	01/2014
9517	(2^234762+1498)/2	70671	Stefano Morozzi	01/2020
9518	(24355^16111-1)/24354	70668	Serge Batalov	08/2020
9519	(2^234723+3690)/2	70659	Stefano Morozzi	01/2020
9520	(2^234718+3798)/2	70657	Stefano Morozzi	01/2020
9521	(2^234680+2902)/2	70646	Stefano Morozzi	01/2020
9522	(29*2^234686-1)/21145	70645	Lelio R Paula	01/2014
9523	(15*2^234688-1)/5278141	70643	Lelio R Paula	01/2014
9525	2^234655-67	70639	Lelio R Paula	02/2012
9524	(79*10^70638-61)/9	70639	Robert Price	10/2015
9526	2^234652-173	70638	Lelio R Paula	02/2012
9527	2^234618-3645	70628	Lelio R Paula	05/2012
9528	(2^234610-5)/19	70624	Lelio R Paula	05/2012
9529	4*5^101038+9	70624	Lelio R Paula	10/2014
9530	2^234603+71963	70623	Enzo Doria	04/2016
9531	2^234600-113129	70622	Enzo Doria	07/2014
9532	(2^234601+1446)/2	70622	Stefano Morozzi	01/2020
9533	2^234586+9	70618	Lelio R Paula	02/2012
9534	3^148008+26	70618	Robert Price	11/2013
9535	(7*10^70616-151)/9	70616	Robert Price	09/2017
9536	65^38947+32	70608	Lelio R Paula	01/2016
9537	(2^234517+2750)/2	70597	Stefano Morozzi	01/2020
9538	18363^6988+6988^18363	70594	Hans Havermann	10/2019
9539	(2^234488-3)/11	70587	Lelio R Paula	05/2012
9540	(3*2^234451+1)/35	70576	Lelio R Paula	08/2012
9541	(8848^17881-1)/8847	70570	Serge Batalov	08/2020
9542	Phi(159495,10)	70560	Maksym Voznyy	09/2015
9543	2^234383-4035	70557	Lelio R Paula	05/2012
9544	(2^234364+3618)/2	70551	Stefano Morozzi	01/2020
9545	(2^234333+3482)/2	70541	Stefano Morozzi	01/2020
9546	2^234315-111241	70536	Enzo Doria	05/2014
9547	14^61526+97	70517	Lelio R Paula	01/2015
9548	14742^16915+16915^14742	70512	Norbert Schneider	10/2019
9549	(2^234203+3306)/2	70502	Stefano Morozzi	01/2020
9550	(3*2^234170+1)/13	70492	Lelio R Paula	08/2012
9551	51^41281-50^41281	70491	Robert Price	02/2013
9552	2^234141-112123	70484	Enzo Doria	06/2014
9553	2^234139+12285	70483	Lelio R Paula	04/2012
9554	2^234133-3163	70482	Yves Minet	04/2009
9555	2^234115+83	70476	Lelio R Paula	02/2012
9556	2^234114-1595	70476	Lelio R Paula	05/2012
9557	24^51061-23^51061	70475	Robert Price	07/2012
9558	(2^234099+2538)/2	70471	Stefano Morozzi	01/2020
9559	19471^16428-2	70467	Faysal YAtim	09/2005
9560	7^83381+12	70466	Robert Price	01/2014
9561	(2^234080+3922)/2	70465	Stefano Morozzi	01/2020
9562	2^234067-111427	70462	Enzo Doria	05/2014
9563	(266*10^70457+1)/3	70459	Robert Price	02/2016
9564	(31*2^234041-1)/97	70453	Lelio R Paula	01/2014
9565	(2^234030+642)/2	70450	Stefano Morozzi	01/2020
9566	2^234026+12909	70449	Lelio R Paula	04/2012
9567	(2^234021+3510)/2	70448	Stefano Morozzi	01/2020
9568	2^233965-19	70431	Lelio R Paula	02/2012
9569	(11152^17401-1)/11151	70424	Serge Batalov	08/2020
9570	(5*2^233932-1)/179	70419	Lelio R Paula	01/2014
9571	2^233908-17109	70414	Enzo Doria	05/2013
9572	695^24772+24772^695	70402	Norbert Schneider	09/2016
9573	3*5^100719-2	70401	Lelio R Paula	10/2014
9574	(2^233862+1878)/2	70400	Stefano Morozzi	01/2020
9575	(2^233843+3330)/2	70394	Stefano Morozzi	01/2020
9576	2^233829-111355	70390	Enzo Doria	05/2014
9577	(19775^16384+1)/2	70388	Henri Lifchitz	03/2007
9578	7*3^147519+8	70386	Lelio R Paula	04/2014
9579	141^32749-2	70385	Lelio R Paula	10/2017
9580	5*7^83265+2	70368	Lelio R Paula	10/2014
9581	(23*10^70363+97)/3	70364	Robert Price	02/2017
9582	(23*2^233749-1)/35325	70363	Lelio R Paula	01/2014
9583	5^100652-13916	70353	Enzo Doria	02/2013
9584	45^42555-2	70353	Lelio R Paula	08/2013
9585	(3084^20161-1)/3083	70341	Serge Batalov	08/2020
9586	2^233661-61	70339	Lelio R Paula	02/2012
9587	(2^233641+1014)/2	70333	Stefano Morozzi	01/2020
9588	(2^233614+1074)/2	70325	Stefano Morozzi	01/2020
9589	(2^233592+2986)/2	70318	Stefano Morozzi	01/2020
9590	2^233523-112249	70298	Enzo Doria	06/2014
9591	5*3^147324-8	70293	Lelio R Paula	04/2014
9592	2^233488-13065	70287	Enzo Doria	11/2012
9593	(3^147322+8)/42851	70286	Lelio R Paula	06/2012
9594	(13301^17041-1)/13300	70271	Serge Batalov	08/2020
9595	(22*10^70259+161)/3	70260	Robert Price	02/2017
9597	2^233388+465	70257	Lelio R Paula	11/2012
9596	14^61299+59	70257	Lelio R Paula	01/2015
9598	2^233383+94065	70256	Lelio R Paula	04/2012
9599	49471!3-6561	70253	Robert Price	11/2015
9600	7^83121+6^(83121-1)	70246	Robert Price	03/2016
9601	(197*10^70241-11)/3	70243	Robert Price	10/2017
9602	23*10^70240-7	70242	Robert Price	03/2016
9603	(2^233301+2730)/2	70231	Stefano Morozzi	01/2020
9604	(71*10^70227-53)/9	70228	Robert Price	10/2015
9605	19825^3486+3486^19825	70227	Hans Havermann	10/2019
9606	10815^17408+17408^10815	70225	Norbert Schneider	05/2019
9607	(2^233247-9)/17	70214	Lelio R Paula	05/2012
9608	(11^67421-2^67421)/9	70211	Robert Price	01/2013
9609	(23*10^70209-41)/9	70210	Robert Price	03/2015
9610	(29*10^70194-11)/9	70195	Robert Price	04/2015
9611	3^147109+196	70189	Lelio R Paula	05/2014
9612	(34*10^70191-7)/9/3/40583/573047	70181	Makoto Morimoto	05/2016
9613	9^73538+8^(73538+1)	70174	Robert Price	06/2016
9614	2*5^100391+7	70171	Lelio R Paula	10/2014
9615	99^35156-2	70159	Lelio R Paula	08/2013
9616	(68*10^70148+7)/3	70150	Robert Price	03/2016
9617	11^67360-6030	70149	Enzo Doria	01/2013
9618	(35*10^70130-377)/9	70131	Robert Price	12/2017
9619	49391!3+3^49391	70128	Robert Price	09/2015
9620	(229*10^70122-1)/3	70124	Robert Price	12/2016
9621	7^82975-92	70123	Lelio R Paula	07/2014
9622	(19099^16381-1)/19098	70123	Serge Batalov	08/2020
9623	20294^2853+2853^20294	70122	Hans Havermann	10/2019
9624	65^38670+58	70106	Lelio R Paula	01/2016
9625	105^34684+34684^105	70103	Serge Batalov	05/2014
9626	18597^5882+5882^18597	70102	Hans Havermann	10/2019
9627	134^32955-133	70099	Norbert Schneider	03/2015
9630	2^232836-227903	70091	Enzo Doria	12/2012
9629	2^232837-1859173	70091	Enzo Doria	03/2016
9628	17778^8761+8761^17778	70091	Hans Havermann	10/2019
9631	3*2^232820+5	70087	Lelio R Paula	04/2014
9633	2^232799+90195	70080	Lelio R Paula	02/2013
9632	2^232799-112237	70080	Enzo Doria	06/2014
9634	17894^8247+8247^17894	70079	Hans Havermann	09/2019
9635	(2^232766+954)/2	70070	Stefano Morozzi	01/2020
9636	2^232759+262145	70068	Lelio R Paula	04/2012
9637	16817^14670+14670^16817	70067	Hans Havermann	09/2019
9638	3*2^232750+7	70066	Lelio R Paula	04/2014
9639	(7019^18217-1)/7018	70064	Serge Batalov	08/2020
9640	(3330^19891-1)/3329	70062	Serge Batalov	08/2020
9641	12^64918-11	70059	Lelio R Paula	01/2015
9642	7^82899-12	70058	Lelio R Paula	09/2013
9643	(22*10^70051-13)/9	70052	Robert Price	03/2015
9644	16428^16615-16615^16428	70042	Norbert Schneider	11/2019
9645	(2^232685-7)/2514625	70039	Lelio R Paula	04/2012
9646	(2^232653+1494)/2	70036	Stefano Morozzi	01/2020
9647	18^55786-5363	70027	Enzo Doria	03/2013
9648	(2^(77537*3+1)+243)/7	70023	Kevin Acres	11/2013
9649	2^232602+169	70021	Lelio R Paula	02/2012
9650	(137^32768+29^32768)/2	70016	Jeppe Stig Nielsen	04/2018
9651	2^232580+72133	70014	Enzo Doria	04/2016
9652	(4095^19381-1)/4094	70006	Serge Batalov	08/2020
9653	4*6^89958-7	70002	Lelio R Paula	09/2014
9654	10^70000+80487	70001	Milton L. Brown	05/2006
9655	10^69999+134857	70000	Patrick De Geest	02/2007
9656	10^70000-9273	70000	Patrick De Geest	08/2009
9657	(79*10^69999-7)/9	70000	Robert Price	01/2015
9658	((2^43112609)/10^38420)%10^70000	70000	Michael Vang	10/2016
9659	(2^756839/10^36014)%10^70000	70000	Michael Vang	12/2016
9660	(2^74207281/10^32641)%10^70000	70000	Michael Vang	12/2016
9661	10^69999-88251	69999	Patrick De Geest	08/2009
9662	2^232507+1089	69992	Lelio R Paula	04/2012
9663	(2^232506+498)/2	69991	Stefano Morozzi	01/2020
9664	(17*2^232445+1)/5	69974	Lelio R Paula	08/2012
9665	(529^25693+1)/530	69972	Richard Fischer	12/2017
9666	(2^232416+498)/2	69964	Stefano Morozzi	01/2020
9667	(2^232410+2794)/2	69963	Stefano Morozzi	01/2020
9668	7^82778+48	69956	Lelio R Paula	09/2013
9670	7*2^232381+3	69955	Lelio R Paula	04/2014
9669	19305^4204+4204^19305	69955	Hans Havermann	10/2019
9671	2^232362-110541	69948	Enzo Doria	05/2014
9672	19442^3957+3957^19442	69940	Hans Havermann	09/2019
9673	2^232326-112391	69938	Enzo Doria	06/2014
9674	3^146575+236	69935	Lelio R Paula	09/2013
9675	30^47341-29	69929	Norbert Schneider	02/2014
9676	(2^232294+1218)/2	69928	Stefano Morozzi	01/2020
9677	5^100040-68	69925	Lelio R Paula	09/2013
9678	9946^17491+17491^9946	69923	Norbert Schneider	07/2019
9679	16351^16592-16592^16351	69912	Norbert Schneider	11/2019
9680	(2^232139+3746)/2	69881	Stefano Morozzi	01/2020
9681	(2^232132+2566)/2	69879	Stefano Morozzi	01/2020
9682	(35*10^69866-593)/9	69867	Robert Price	08/2017
9683	2^232045-17295	69853	Lelio R Paula	04/2012
9684	(2^231987+78557)/95	69834	Lelio R Paula	05/2012
9685	2^231955+74243	69826	Yves Minet	03/2011
9686	(2^231949+3290)/2	69824	Stefano Morozzi	01/2020
9687	2^231946-15873	69823	Enzo Doria	04/2013
9688	18^55618+95	69816	Lelio R Paula	09/2013
9689	6^89712+5^(89712-1)	69810	Robert Price	02/2016
9690	(2^231876+670)/2	69802	Stefano Morozzi	01/2020
9691	2^231870+135	69800	Lelio R Paula	02/2012
9692	(23*2^231827-1)/4179	69785	Lelio R Paula	01/2014
9693	2^231778+54615	69773	Lelio R Paula	04/2012
9694	(19*2^231780+1)/235	69772	Lelio R Paula	08/2012
9695	(2^231775+2430)/2	69771	Stefano Morozzi	01/2020
9696	(381^27031-1)/380	69763	Serge Batalov	08/2020
9697	14^60866+27	69761	Lelio R Paula	09/2013
9698	13^62619-44	69755	Lelio R Paula	09/2013
9699	(2^231715-509203)/35	69752	Lelio R Paula	05/2012
9700	2^231711-110467	69752	Enzo Doria	05/2014
9702	(19^54547+18^54547)/37	69751	Robert Price	08/2013
9701	(2^231707+998)/2	69751	Stefano Morozzi	01/2020
9703	(3823^19471-1)/3822	69750	Serge Batalov	08/2020
9704	(23*2^231697-1)/45	69748	Lelio R Paula	01/2014
9705	2^231696-1861499	69748	Enzo Doria	03/2016
9706	2^231684-147	69744	Lelio R Paula	02/2012
9707	(23*2^231686-1)/1183	69743	Lelio R Paula	01/2014
9708	4*10^69723-93	69724	Robert Price	07/2020
9709	2^231591-477397	69716	Paul Bourdelais	03/2013
9710	16916^13209+13209^16916	69709	Hans Havermann	09/2019
9711	16568^16095+16095^16568	69697	Hans Havermann	09/2019
9712	11^66916-420	69686	Enzo Doria	08/2012
9713	5^99680-13706	69674	Enzo Doria	02/2013
9714	(8*10^69674-53)/9	69674	Robert Price	11/2014
9715	(44*10^69663-413)/9	69664	Robert Price	10/2017
9716	18950^4743+4743^18950	69662	Hans Havermann	10/2019
9717	(77*10^69656-23)/9	69657	Robert Price	10/2015
9718	(2^231385+3710)/2	69654	Stefano Morozzi	01/2020
9719	6^89509+131	69652	Lelio R Paula	09/2013
9720	(2^231364+3030)/2	69648	Stefano Morozzi	01/2020
9721	(78557*2^231349+1)/35	69647	Lelio R Paula	06/2014
9722	(11*10^69645+19)/3	69646	Robert Price	03/2016
9723	11^66875-28	69644	Lelio R Paula	09/2013
9724	2^231347+71483	69643	Enzo Doria	04/2016
9725	(14^60763+3^60763)/17	69641	Robert Price	04/2013
9726	(2^231340+3126)/2	69640	Stefano Morozzi	01/2020
9727	(4*10^69626+173)/3	69627	Robert Price	01/2017
9728	2^231289+255	69625	Lelio R Paula	04/2012
9729	(7155^18061-1)/7154	69615	Serge Batalov	08/2020
9730	19794^3287+3287^19794	69612	Hans Havermann	09/2019
9731	2^231234-112913	69609	Enzo Doria	06/2014
9732	(265*10^69602-7)/3	69604	Robert Price	07/2016
9733	2^231182-112841	69593	Enzo Doria	06/2014
9734	(15*2^231129+1)/23	69577	Lelio R Paula	08/2012
9735	3^145806-28	69568	Lelio R Paula	09/2013
9736	(265*10^69554-7)/3	69556	Robert Price	07/2016
9737	2^231052-113159	69554	Enzo Doria	07/2014
9738	(10^9+1)(10^129+1)(10^831+1)*(10^107199+1)/1001/(10^387+1)/(10^2493+1)/(10^35733+1)	69552	Makoto Kamada	03/2019
9739	11^66784-8	69549	Lelio R Paula	09/2013
9740	Phi(104409,10)/2296999	69546	Maksym Voznyy	07/2015
9741	(2^231023+1758)/2	69545	Stefano Morozzi	01/2020
9742	2^231016-110523	69543	Enzo Doria	05/2014
9743	2^231014+577294575	69543	Lelio R Paula	02/2016
9744	(2^230982+970)/2	69533	Stefano Morozzi	01/2020
9745	14^60658+67	69522	Lelio R Paula	09/2013
9746	(2^230898+2422)/2	69507	Stefano Morozzi	01/2020
9747	5^99418+36	69491	Lelio R Paula	06/2013
9748	(5596^18541-1)/5595	69486	Serge Batalov	08/2020
9749	7^82203-30	69470	Lelio R Paula	09/2013
9750	(63^38609-1)/62	69469	Paul Bourdelais	08/2017

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Probable Primes Top 10000

(271023 PRPs in the top)