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	2^321716-2786939	96847	Enzo Doria	03/2016
9502	22496^20181+20181^22496	96844	Hans Havermann	03/2020
9503	2^321701-113053	96842	Enzo Doria	07/2014
9504	2^321700-28635	96842	Lelio R Paula	06/2016
9505	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
9506	6*10^96835+13	96836	Robert Price	10/2021
9507	6^124433-124433	96828	Robert Price	01/2014
9508	2^321631+69	96821	Lelio R Paula	12/2012
9509	(27109^21841-1)/27108	96820	Serge Batalov	06/2022
9510	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
9511	(5052^26141-1)/5051	96809	Serge Batalov	06/2022
9512	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
9513	(59*10^96798+31)/9	96799	Robert Price	09/2015
9514	(2^321536+2062)/2	96792	Stefano Morozzi	09/2020
9515	223319#+231223	96790	Makoto Morimoto	02/2016
9516	2^321519-28635	96787	Lelio R Paula	06/2016
9517	2^321487-1867237	96778	Enzo Doria	03/2016
9518	2^321461-63	96770	Lelio R Paula	12/2012
9519	(16053^23011-1)/16052	96770	Serge Batalov	06/2022
9520	2^321439+123	96763	Lelio R Paula	12/2012
9521	2^321434+709	96762	Lelio R Paula	02/2013
9522	2^321419+22703	96757	Enzo Doria	09/2023
9523	(2^321415+554)/2	96756	Stefano Morozzi	09/2020
9524	14^84413+89	96749	Lelio R Paula	07/2016
9525	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
9526	13^86847+96	96743	Lelio R Paula	06/2016
9527	9*2^321336-7	96733	Lelio R Paula	08/2014
9528	(209*10^96722-17)/3	96724	Robert Price	05/2017
9529	(54163^20431-1)/54162	96710	Serge Batalov	06/2022
9530	2^321237-4615	96702	Yves Minet	05/2019
9531	(27273^21799-1)/27272	96691	Serge Batalov	06/2022
9532	2^321187-1159	96687	Yves Minet	11/2012
9533	2^321182-1850081	96686	Enzo Doria	08/2015
9535	23359^13768+13768^23359	96680	Hans Havermann	06/2020
9534	(65630^20071-1)/65629	96680	Serge Batalov	06/2022
9536	2^321116-112829	96666	Enzo Doria	06/2014
9537	2^321108-109499	96664	Enzo Doria	04/2014
9538	2^321098+2793859	96661	Enzo Doria	03/2016
9539	(2^321100+1170)/2	96661	Stefano Morozzi	09/2020
9540	2^321057+4097	96648	Lelio R Paula	06/2016
9541	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
9542	22743^17750+17750^22743	96640	Hans Havermann	04/2020
9543	22882^16679+16679^22882	96612	Hans Havermann	02/2020
9544	23452^13163+13163^23452	96608	Hans Havermann	02/2020
9545	(1042^32009-1)/1041	96596	Serge Batalov	06/2022
9546	(85*10^96594-373)/9	96595	Robert Price	05/2021
9547	(2^320863+666)/2	96590	Stefano Morozzi	09/2020
9548	p(19849)#/2-64	96581	Robert Price	04/2017
9549	2^320817+189	96576	Lelio R Paula	12/2012
9550	2^320816-4685	96576	Yves Minet	05/2019
9552	(361*10^96567-163)/9	96569	Robert Price	10/2017
9551	(19*10^96568+137)/3	96569	Robert Price	03/2022
9553	2^320788-110327	96567	Enzo Doria	05/2014
9554	(3065^27697-1)/3064	96561	Serge Batalov	06/2022
9555	2^320764+793	96560	Lelio R Paula	02/2013
9556	(2^320752+1842)/2	96556	Stefano Morozzi	02/2021
9557	(48331^20611-1)/48330	96542	Serge Batalov	06/2022
9558	(107746^19321-1)/(107746^139-1)	96532	Ryan Propper	11/2023
9559	(50595^20521-1)/50594	96529	Serge Batalov	06/2022
9560	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
9561	23288^13947+13947^23288	96517	Hans Havermann	07/2020
9563	2^320616-78795	96516	Lelio R Paula	03/2016
9562	(19*10^96520+287)/9/109/409	96516	Alfred Reich	11/2022
9564	2^320612-461939	96514	Enzo Doria	07/2015
9565	(21245^22303-1)/21244	96507	Serge Batalov	06/2022
9566	10^96504+987654321	96505	Robert Price	12/2019
9567	10^96504+71887	96505	Patrick De Geest	02/2020
9568	22654^18195+18195^22654	96505	Hans Havermann	07/2020
9569	10^96504-139277	96504	Patrick De Geest	02/2020
9570	(218^41263-1)/217	96490	Serge Batalov	06/2022
9571	(47220^20641-1)/47219	96474	Serge Batalov	06/2022
9572	5*2^320431+7	96461	Lelio R Paula	08/2014
9573	19^75431-90	96458	Lelio R Paula	06/2016
9574	(11853^23677-1)/11852	96452	Serge Batalov	06/2022
9575	(2^320386+2814)/2	96446	Stefano Morozzi	02/2021
9576	(2^320370+3)/67	96440	Lelio R Paula	10/2013
9577	3*10^96431-17	96432	Robert Price	03/2021
9578	2^320309+1871477	96423	Enzo Doria	05/2016
9579	(10412^24001-1)/10411	96421	Serge Batalov	06/2022
9580	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
9581	(29*10^96407-23)/3	96408	Robert Price	03/2022
9582	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
9583	2^320232-173	96400	Lelio R Paula	12/2012
9584	175^42975-2	96395	Lelio R Paula	10/2017
9585	(2^320170+2718)/2	96381	Stefano Morozzi	09/2020
9586	10^96377+199911	96378	Patrick De Geest	12/2016
9587	10^96377-20001	96377	Robert Price	11/2016
9588	(18079^22639-1)/18078	96374	Serge Batalov	06/2022
9590	2^320124-2790449	96367	Enzo Doria	03/2016
9589	10^96366+19197	96367	Patrick De Geest	08/2021
9592	10^96366-10000000001	96366	Robert Price	04/2021
9591	10^96366-287367	96366	Patrick De Geest	08/2021
9593	(26351^21799-1)/26350	96365	Serge Batalov	06/2022
9594	22488^19255+19255^22488	96351	Hans Havermann	11/2019
9595	23248^13939+13939^23248	96346	Hans Havermann	11/2019
9596	(5928^25537-1)/5927	96345	Serge Batalov	06/2022
9598	2^320043-108775	96343	Enzo Doria	04/2014
9597	24989^7168+7168^24989	96343	Hans Havermann	11/2019
9599	10^96338+424939	96339	Patrick De Geest	03/2016
9600	10^96338-9281	96338	Robert Price	09/2015
9601	(8527^24509-1)/8526	96336	Serge Batalov	06/2022
9602	(3*2^320008+1)/7	96332	Lelio R Paula	09/2013
9603	(2444^28433-1)/2443	96331	Serge Batalov	06/2022
9604	(48690^20551-1)/48689	96327	Serge Batalov	06/2022
9605	(61935^20101-1)/61934	96318	Serge Batalov	06/2022
9606	25699^5596+5596^25699	96317	Hans Havermann	07/2020
9607	(7*10^96312+83)/9	96312	Tyler Busby	01/2023
9608	(11*10^96298+529)/9	96299	Robert Price	09/2021
9610	26502^4297+4297^26502	96287	Hans Havermann	07/2020
9609	(54180^20341-1)/54179	96287	Serge Batalov	06/2022
9611	2^319838+4257	96281	Lelio R Paula	03/2016
9612	2^319830-16995	96279	Lelio R Paula	03/2016
9613	6^123713+143	96268	Lelio R Paula	05/2016
9614	(28*10^96265-97)/3	96266	Robert Price	07/2016
9615	(3799^26893-1)/3798	96265	Serge Batalov	06/2022
9617	103^47825-102	96264	Norbert Schneider	10/2016
9616	(54041^20341-1)/54040	96264	Serge Batalov	06/2022
9618	(2^319777+2082)/2	96263	Stefano Morozzi	09/2020
9619	(2^319771+3686)/2	96261	Stefano Morozzi	09/2020
9620	2^319713-81	96244	Lelio R Paula	11/2012
9621	2^319711+213413	96243	Enzo Doria	09/2023
9622	(55459*2^319706+1)/20167	96242	Lelio R Paula	07/2014
9623	22834^16393+16393^22834	96238	Hans Havermann	05/2020
9624	8*10^96236+27	96237	Robert Price	09/2021
9625	12^89153-43	96213	Lelio R Paula	06/2016
9626	(25048^21871-1)/25047	96202	Serge Batalov	06/2022
9628	(2*10^96195-59)/3	96195	Robert Price	05/2017
9627	9*10^96194-77	96195	Robert Price	08/2020
9629	2^319545+147	96193	Lelio R Paula	11/2012
9630	23357^13128+13128^23357	96189	Hans Havermann	02/2020
9631	(19838^22381-1)/19837	96179	Serge Batalov	06/2022
9632	(221^41023-1)/220	96172	Serge Batalov	06/2022
9633	25952^5073+5073^25952	96160	Hans Havermann	12/2019
9634	(50891^20431-1)/50890	96157	Serge Batalov	06/2022
9635	(50^56597+1)/51	96155	Robert Price	03/2014
9636	22313^20374+20374^22313	96149	Hans Havermann	12/2019
9637	22279^20668+20668^22279	96141	Hans Havermann	11/2019
9638	(41*10^96137-59)/9	96138	Robert Price	10/2017
9639	2^319353-110343	96135	Enzo Doria	05/2014
9640	11^92309-42	96130	Lelio R Paula	05/2016
9641	(21675^22171-1)/21674	96129	Serge Batalov	06/2022
9642	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
9643	(7*10^96112+143)/3	96113	Robert Price	04/2016
9644	26731^3940+3940^26731	96112	Hans Havermann	07/2020
9645	22640^17583+17583^22640	96109	Hans Havermann	07/2020
9646	(19178^22441-1)/19177	96107	Serge Batalov	06/2022
9647	2^319237+65835	96100	Lelio R Paula	03/2016
9648	2^319194-1841	96087	Yves Minet	03/2013
9649	23949^10280+10280^23949	96084	Hans Havermann	07/2020
9650	(1927^29251-1)/1926	96083	Serge Batalov	06/2022
9651	20^73847-31	96078	Lelio R Paula	05/2016
9652	(60229^20101-1)/60228	96075	Serge Batalov	06/2022
9653	(28044^21601-1)/28043	96074	Serge Batalov	06/2022
9654	50^56543-49	96065	Norbert Schneider	09/2018
9655	2^319107-109555	96061	Enzo Doria	04/2014
9656	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
9657	2^319098-112157	96059	Enzo Doria	06/2014
9658	15^81673+94	96055	Lelio R Paula	07/2016
9659	(85761^19471-1)/85760	96052	Serge Batalov	06/2022
9660	2^319074+1871749	96051	Enzo Doria	05/2016
9661	25670^5517+5517^25670	96050	Hans Havermann	06/2020
9662	6*10^96037+19	96038	Robert Price	11/2021
9663	2^319007-112111	96031	Enzo Doria	06/2014
9664	(57987^20161-1)/57986	96029	Serge Batalov	06/2022
9666	2^318946-1421	96013	Yves Minet	01/2013
9665	(68310^19861-1)/68309	96013	Serge Batalov	06/2022
9667	(20294^22291-1)/20293	96012	Serge Batalov	06/2022
9668	(304^38669-1)/303	96008	Serge Batalov	06/2022
9669	(1840^29401-1)/1839	95986	Serge Batalov	06/2022
9670	22830^16003+16003^22830	95982	Hans Havermann	02/2020
9671	2^318834-110411	95979	Enzo Doria	05/2014
9672	2^318831-1965	95978	Lelio R Paula	03/2016
9673	(5*10^95976+7)/3	95977	Erik Branger	03/2014
9674	(12797^23369-1)/12796	95975	Serge Batalov	06/2022
9675	(10534^23857-1)/10533	95963	Serge Batalov	06/2022
9676	22871^15696+15696^22871	95962	Hans Havermann	01/2020
9677	(2^318760+858)/2	95957	Stefano Morozzi	02/2021
9678	23167^13860+13860^23167	95953	Hans Havermann	01/2020
9679	(823^32911-1)/822	95946	Serge Batalov	06/2022
9681	5*3^201089-8	95945	Lelio R Paula	08/2014
9680	(81783^19531-1)/81782	95945	Serge Batalov	06/2022
9682	2^318711-139	95942	Lelio R Paula	11/2012
9683	2^318635-1167	95919	Lelio R Paula	03/2016
9684	15^81555+16	95917	Lelio R Paula	07/2016
9685	(37*10^95895+377)/9	95896	Robert Price	10/2017
9686	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
9687	45^57997+196072	95882	Enzo Doria	10/2023
9688	2^318496-97305	95877	Lelio R Paula	03/2016
9689	22129^21496+21496^22129	95871	Hans Havermann	07/2020
9691	2^318466+15015	95868	Lelio R Paula	03/2016
9690	24847^7216+7216^24847	95868	Hans Havermann	07/2020
9692	23706^11065+11065^23706	95866	Hans Havermann	07/2020
9693	(2863^27733-1)/2862	95865	Serge Batalov	06/2022
9694	6^123187-173129	95859	Mike Oakes	04/2011
9695	2^318423-487	95855	Yves Minet	03/2012
9696	10^95848+443709	95849	Patrick De Geest	10/2022
9697	10^95848-5000000001	95848	Robert Price	09/2022
9698	10^95848-61971	95848	Patrick De Geest	10/2022
9699	(2^318359+678)/2	95836	Stefano Morozzi	09/2020
9700	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
9701	(8060^24533-1)/8059	95831	Serge Batalov	06/2022
9702	(9853^23993-1)/9852	95814	Serge Batalov	06/2022
9704	(2^318267+2550)/2	95808	Stefano Morozzi	09/2020
9703	(5048^25873-1)/5047	95808	Serge Batalov	06/2022
9706	4*10^95799+13	95800	Robert Price	02/2021
9705	(65533^19891-1)/65532	95800	Serge Batalov	06/2022
9707	2^318203+211343	95789	Enzo Doria	08/2023
9708	45369!2+1024	95787	Robert Price	02/2015
9709	3^200758-86	95786	Lelio R Paula	05/2016
9710	(2^318271+1)/(346031404238891654090604244843)	95781	Gord Palameta	12/2018
9711	(2^318171+2030)/2	95779	Stefano Morozzi	09/2020
9712	3*10^95776-59	95777	Robert Price	10/2017
9713	(82970^19471-1)/82969	95772	Serge Batalov	06/2022
9714	193^41901-2	95768	Lelio R Paula	10/2017
9715	(2^318124+2502)/2	95765	Stefano Morozzi	09/2020
9716	(12900^23297-1)/12899	95761	Serge Batalov	06/2022
9717	4*10^95752-71	95753	Robert Price	11/2017
9718	(16955^22639-1)/16954	95743	Serge Batalov	06/2022
9719	(81795^19489-1)/81794	95740	Serge Batalov	06/2022
9720	(2742^27847-1)/2741	95737	Serge Batalov	06/2022
9721	(6072^25303-1)/6071	95726	Serge Batalov	06/2022
9722	23640^11197+11197^23640	95721	Hans Havermann	12/2019
9723	10^95712+89329	95713	Patrick De Geest	09/2022
9725	10^95712-4000001	95712	Robert Price	07/2021
9724	10^95712-989313	95712	Patrick De Geest	09/2022
9726	(60657^20011-1)/60656	95706	Serge Batalov	06/2022
9727	((10^47850-1)10000/9+6421)10^47850+(10^47850-1)/9	95704	Hans Havermann	05/2019
9728	(509203*2^317881-1)/52805	95693	Lelio R Paula	04/2015
9729	(26161^21661-1)/26160	95687	Serge Batalov	06/2022
9730	(2^317853+1086)/2	95683	Stefano Morozzi	09/2020
9731	4*10^95672+91	95673	Robert Price	11/2017
9732	6*10^95665+43	95666	Robert Price	07/2020
9733	(20819^22153-1)/20818	95663	Serge Batalov	06/2022
9734	(64464^19891-1)/64463	95658	Serge Batalov	06/2022
9735	(934^32203-1)/933	95652	Serge Batalov	06/2022
9736	(11*10^95641-113)/3	95642	Robert Price	01/2017
9737	(72330^19681-1)/72329	95632	Serge Batalov	06/2022
9738	(13224^23203-1)/13223	95624	Serge Batalov	06/2022
9739	(18211^22441-1)/18210	95602	Serge Batalov	06/2022
9740	(71975^19681-1)/71974	95590	Serge Batalov	06/2022
9741	(13*10^95588+11)/3	95589	Robert Price	05/2015
9742	Phi(191188,10)/191189	95587	Maksym Voznyy	11/2015
9743	(13368^23167-1)/13367	95585	Serge Batalov	06/2022
9744	(25874^21661-1)/25873	95583	Serge Batalov	06/2022
9745	3^200325+70	95580	Lelio R Paula	05/2016
9746	(25*10^95574-7)/9	95575	Robert Price	12/2014
9747	(2^317485-3)/21313	95569	Lelio R Paula	06/2013
9748	2^317464+31	95567	Lelio R Paula	11/2012
9749	(2^317451+2114)/2	95562	Stefano Morozzi	09/2020
9750	7^113073+82	95558	Lelio R Paula	04/2016

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