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 ?
7751	9*10^97247-29	97248	Robert Price	05/2017
7752	24382^9735+9735^24382	97244	Hans Havermann	02/2020
7753	(31*10^97242+41)/9	97243	Robert Price	04/2015
7754	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
7755	12^90098-41	97233	Lelio R Paula	07/2016
7756	2^322928-216929	97212	Enzo Doria	05/2014
7757	(16731^23017-1)/16730	97209	Serge Batalov	06/2022
7758	3*10^97205-61	97206	Robert Price	04/2021
7759	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
7760	(35*10^97194-341)/9	97195	Robert Price	08/2021
7761	(4872^26357-1)/4871	97194	Serge Batalov	06/2022
7762	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
7763	(2^322789+2214)/2	97169	Stefano Morozzi	09/2020
7764	2^322725+75761	97150	Enzo Doria	04/2016
7765	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
7766	(2175^29101-1)/2174	97121	Serge Batalov	06/2022
7767	22402^21639+21639^22402	97118	Hans Havermann	07/2020
7768	23399^14128+14128^23399	97108	Hans Havermann	06/2020
7769	(2892^28057-1)/2891	97108	Serge Batalov	06/2022
7770	(9578^24391-1)/9577	97104	Serge Batalov	06/2022
7771	(2^322525+2606)/2	97090	Stefano Morozzi	09/2020
7772	(9563^24391-1)/9562	97087	Serge Batalov	06/2022
7773	(41*10^97085+373)/9	97086	Robert Price	04/2017
7774	(2^322473+854)/2	97074	Stefano Morozzi	02/2021
7775	2^322413+77	97056	Lelio R Paula	12/2012
7776	2^322406+177	97054	Lelio R Paula	12/2012
7777	(349^38167-1)/348	97050	Serge Batalov	06/2022
7778	(14*10^97044+31)/9	97045	Robert Price	02/2015
7779	2^322302+255255	97023	Lelio R Paula	07/2016
7780	(1302^31147-1)/1301	97008	Serge Batalov	06/2022
7781	2^322196-113093	96991	Enzo Doria	07/2014
7782	(2^322169+2690)/2	96983	Stefano Morozzi	09/2020
7783	(49*10^96980+221)/9	96981	Robert Price	02/2022
7784	9*10^96968-47	96969	Robert Price	11/2021
7785	(5895^25717-1)/5894	96962	Serge Batalov	06/2022
7786	(27473^21841-1)/27472	96946	Serge Batalov	06/2022
7787	23109^15668+15668^23109	96943	Hans Havermann	07/2020
7788	2^322000-1861469	96932	Enzo Doria	03/2016
7789	2^321971-112747	96923	Enzo Doria	06/2014
7790	23754^12023+12023^23754	96917	Hans Havermann	07/2020
7791	11^93062-92	96915	Lelio R Paula	06/2016
7792	(37871^21169-1)/37870	96914	Serge Batalov	06/2022
7793	(2^321922+2214)/2	96908	Stefano Morozzi	09/2020
7794	(2^321900+2086)/2	96902	Stefano Morozzi	09/2020
7795	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
7796	3^203051+34	96880	Lelio R Paula	05/2016
7797	2*10^96867-51	96868	Robert Price	11/2017
7798	(2^321779+2618)/2	96865	Stefano Morozzi	09/2020
7799	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
7800	2^321716-2786939	96847	Enzo Doria	03/2016
7801	22496^20181+20181^22496	96844	Hans Havermann	03/2020
7802	2^321701-113053	96842	Enzo Doria	07/2014
7803	2^321700-28635	96842	Lelio R Paula	06/2016
7804	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
7805	6*10^96835+13	96836	Robert Price	10/2021
7806	6^124433-124433	96828	Robert Price	01/2014
7807	2^321631+69	96821	Lelio R Paula	12/2012
7808	(27109^21841-1)/27108	96820	Serge Batalov	06/2022
7809	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
7810	(5052^26141-1)/5051	96809	Serge Batalov	06/2022
7811	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
7812	(59*10^96798+31)/9	96799	Robert Price	09/2015
7813	(2^321536+2062)/2	96792	Stefano Morozzi	09/2020
7814	223319#+231223	96790	Makoto Morimoto	02/2016
7815	2^321519-28635	96787	Lelio R Paula	06/2016
7816	2^321487-1867237	96778	Enzo Doria	03/2016
7817	2^321461-63	96770	Lelio R Paula	12/2012
7818	(16053^23011-1)/16052	96770	Serge Batalov	06/2022
7819	2^321439+123	96763	Lelio R Paula	12/2012
7820	2^321434+709	96762	Lelio R Paula	02/2013
7821	(2^321415+554)/2	96756	Stefano Morozzi	09/2020
7822	14^84413+89	96749	Lelio R Paula	07/2016
7823	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
7824	13^86847+96	96743	Lelio R Paula	06/2016
7825	9*2^321336-7	96733	Lelio R Paula	08/2014
7826	(209*10^96722-17)/3	96724	Robert Price	05/2017
7827	(54163^20431-1)/54162	96710	Serge Batalov	06/2022
7828	2^321237-4615	96702	Yves Minet	05/2019
7829	(27273^21799-1)/27272	96691	Serge Batalov	06/2022
7830	2^321187-1159	96687	Yves Minet	11/2012
7831	2^321182-1850081	96686	Enzo Doria	08/2015
7833	23359^13768+13768^23359	96680	Hans Havermann	06/2020
7832	(65630^20071-1)/65629	96680	Serge Batalov	06/2022
7834	2^321116-112829	96666	Enzo Doria	06/2014
7835	2^321108-109499	96664	Enzo Doria	04/2014
7836	2^321098+2793859	96661	Enzo Doria	03/2016
7837	(2^321100+1170)/2	96661	Stefano Morozzi	09/2020
7838	2^321057+4097	96648	Lelio R Paula	06/2016
7839	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
7840	22743^17750+17750^22743	96640	Hans Havermann	04/2020
7841	22882^16679+16679^22882	96612	Hans Havermann	02/2020
7842	23452^13163+13163^23452	96608	Hans Havermann	02/2020
7843	(1042^32009-1)/1041	96596	Serge Batalov	06/2022
7844	(85*10^96594-373)/9	96595	Robert Price	05/2021
7845	(2^320863+666)/2	96590	Stefano Morozzi	09/2020
7846	p(19849)#/2-64	96581	Robert Price	04/2017
7847	2^320817+189	96576	Lelio R Paula	12/2012
7848	2^320816-4685	96576	Yves Minet	05/2019
7850	(361*10^96567-163)/9	96569	Robert Price	10/2017
7849	(19*10^96568+137)/3	96569	Robert Price	03/2022
7851	2^320788-110327	96567	Enzo Doria	05/2014
7852	(3065^27697-1)/3064	96561	Serge Batalov	06/2022
7853	2^320764+793	96560	Lelio R Paula	02/2013
7854	(2^320752+1842)/2	96556	Stefano Morozzi	02/2021
7855	(48331^20611-1)/48330	96542	Serge Batalov	06/2022
7856	(50595^20521-1)/50594	96529	Serge Batalov	06/2022
7857	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
7858	23288^13947+13947^23288	96517	Hans Havermann	07/2020
7859	2^320616-78795	96516	Lelio R Paula	03/2016
7860	2^320612-461939	96514	Enzo Doria	07/2015
7861	(21245^22303-1)/21244	96507	Serge Batalov	06/2022
7862	10^96504+987654321	96505	Robert Price	12/2019
7863	10^96504+71887	96505	Patrick De Geest	02/2020
7864	22654^18195+18195^22654	96505	Hans Havermann	07/2020
7865	10^96504-139277	96504	Patrick De Geest	02/2020
7866	(218^41263-1)/217	96490	Serge Batalov	06/2022
7867	(47220^20641-1)/47219	96474	Serge Batalov	06/2022
7868	5*2^320431+7	96461	Lelio R Paula	08/2014
7869	19^75431-90	96458	Lelio R Paula	06/2016
7870	(11853^23677-1)/11852	96452	Serge Batalov	06/2022
7871	(2^320386+2814)/2	96446	Stefano Morozzi	02/2021
7872	(2^320370+3)/67	96440	Lelio R Paula	10/2013
7873	3*10^96431-17	96432	Robert Price	03/2021
7874	2^320309+1871477	96423	Enzo Doria	05/2016
7875	(10412^24001-1)/10411	96421	Serge Batalov	06/2022
7876	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
7877	(29*10^96407-23)/3	96408	Robert Price	03/2022
7878	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
7879	2^320232-173	96400	Lelio R Paula	12/2012
7880	175^42975-2	96395	Lelio R Paula	10/2017
7881	(2^320170+2718)/2	96381	Stefano Morozzi	09/2020
7882	10^96377+199911	96378	Patrick De Geest	12/2016
7883	10^96377-20001	96377	Robert Price	11/2016
7884	(18079^22639-1)/18078	96374	Serge Batalov	06/2022
7886	2^320124-2790449	96367	Enzo Doria	03/2016
7885	10^96366+19197	96367	Patrick De Geest	08/2021
7888	10^96366-10000000001	96366	Robert Price	04/2021
7887	10^96366-287367	96366	Patrick De Geest	08/2021
7889	(26351^21799-1)/26350	96365	Serge Batalov	06/2022
7890	22488^19255+19255^22488	96351	Hans Havermann	11/2019
7891	23248^13939+13939^23248	96346	Hans Havermann	11/2019
7892	(5928^25537-1)/5927	96345	Serge Batalov	06/2022
7894	2^320043-108775	96343	Enzo Doria	04/2014
7893	24989^7168+7168^24989	96343	Hans Havermann	11/2019
7895	10^96338+424939	96339	Patrick De Geest	03/2016
7896	10^96338-9281	96338	Robert Price	09/2015
7897	(8527^24509-1)/8526	96336	Serge Batalov	06/2022
7898	(3*2^320008+1)/7	96332	Lelio R Paula	09/2013
7899	(2444^28433-1)/2443	96331	Serge Batalov	06/2022
7900	(48690^20551-1)/48689	96327	Serge Batalov	06/2022
7901	(61935^20101-1)/61934	96318	Serge Batalov	06/2022
7902	25699^5596+5596^25699	96317	Hans Havermann	07/2020
7903	(11*10^96298+529)/9	96299	Robert Price	09/2021
7905	26502^4297+4297^26502	96287	Hans Havermann	07/2020
7904	(54180^20341-1)/54179	96287	Serge Batalov	06/2022
7906	2^319838+4257	96281	Lelio R Paula	03/2016
7907	2^319830-16995	96279	Lelio R Paula	03/2016
7908	6^123713+143	96268	Lelio R Paula	05/2016
7909	(28*10^96265-97)/3	96266	Robert Price	07/2016
7910	(3799^26893-1)/3798	96265	Serge Batalov	06/2022
7912	103^47825-102	96264	Norbert Schneider	10/2016
7911	(54041^20341-1)/54040	96264	Serge Batalov	06/2022
7913	(2^319777+2082)/2	96263	Stefano Morozzi	09/2020
7914	(2^319771+3686)/2	96261	Stefano Morozzi	09/2020
7915	2^319713-81	96244	Lelio R Paula	11/2012
7916	(55459*2^319706+1)/20167	96242	Lelio R Paula	07/2014
7917	22834^16393+16393^22834	96238	Hans Havermann	05/2020
7918	8*10^96236+27	96237	Robert Price	09/2021
7919	12^89153-43	96213	Lelio R Paula	06/2016
7920	(25048^21871-1)/25047	96202	Serge Batalov	06/2022
7922	(2*10^96195-59)/3	96195	Robert Price	05/2017
7921	9*10^96194-77	96195	Robert Price	08/2020
7923	2^319545+147	96193	Lelio R Paula	11/2012
7924	23357^13128+13128^23357	96189	Hans Havermann	02/2020
7925	(19838^22381-1)/19837	96179	Serge Batalov	06/2022
7926	(221^41023-1)/220	96172	Serge Batalov	06/2022
7927	25952^5073+5073^25952	96160	Hans Havermann	12/2019
7928	(50891^20431-1)/50890	96157	Serge Batalov	06/2022
7929	(50^56597+1)/51	96155	Robert Price	03/2014
7930	22313^20374+20374^22313	96149	Hans Havermann	12/2019
7931	22279^20668+20668^22279	96141	Hans Havermann	11/2019
7932	(41*10^96137-59)/9	96138	Robert Price	10/2017
7933	2^319353-110343	96135	Enzo Doria	05/2014
7934	11^92309-42	96130	Lelio R Paula	05/2016
7935	(21675^22171-1)/21674	96129	Serge Batalov	06/2022
7936	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
7937	(7*10^96112+143)/3	96113	Robert Price	04/2016
7938	26731^3940+3940^26731	96112	Hans Havermann	07/2020
7939	22640^17583+17583^22640	96109	Hans Havermann	07/2020
7940	(19178^22441-1)/19177	96107	Serge Batalov	06/2022
7941	2^319237+65835	96100	Lelio R Paula	03/2016
7942	2^319194-1841	96087	Yves Minet	03/2013
7943	23949^10280+10280^23949	96084	Hans Havermann	07/2020
7944	(1927^29251-1)/1926	96083	Serge Batalov	06/2022
7945	20^73847-31	96078	Lelio R Paula	05/2016
7946	(60229^20101-1)/60228	96075	Serge Batalov	06/2022
7947	(28044^21601-1)/28043	96074	Serge Batalov	06/2022
7948	50^56543-49	96065	Norbert Schneider	09/2018
7949	2^319107-109555	96061	Enzo Doria	04/2014
7950	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
7951	2^319098-112157	96059	Enzo Doria	06/2014
7952	15^81673+94	96055	Lelio R Paula	07/2016
7953	(85761^19471-1)/85760	96052	Serge Batalov	06/2022
7954	2^319074+1871749	96051	Enzo Doria	05/2016
7955	25670^5517+5517^25670	96050	Hans Havermann	06/2020
7956	6*10^96037+19	96038	Robert Price	11/2021
7957	2^319007-112111	96031	Enzo Doria	06/2014
7958	(57987^20161-1)/57986	96029	Serge Batalov	06/2022
7960	2^318946-1421	96013	Yves Minet	01/2013
7959	(68310^19861-1)/68309	96013	Serge Batalov	06/2022
7961	(20294^22291-1)/20293	96012	Serge Batalov	06/2022
7962	(304^38669-1)/303	96008	Serge Batalov	06/2022
7963	(1840^29401-1)/1839	95986	Serge Batalov	06/2022
7964	22830^16003+16003^22830	95982	Hans Havermann	02/2020
7965	2^318834-110411	95979	Enzo Doria	05/2014
7966	2^318831-1965	95978	Lelio R Paula	03/2016
7967	(5*10^95976+7)/3	95977	Erik Branger	03/2014
7968	(12797^23369-1)/12796	95975	Serge Batalov	06/2022
7969	(10534^23857-1)/10533	95963	Serge Batalov	06/2022
7970	22871^15696+15696^22871	95962	Hans Havermann	01/2020
7971	(2^318760+858)/2	95957	Stefano Morozzi	02/2021
7972	23167^13860+13860^23167	95953	Hans Havermann	01/2020
7973	(823^32911-1)/822	95946	Serge Batalov	06/2022
7975	5*3^201089-8	95945	Lelio R Paula	08/2014
7974	(81783^19531-1)/81782	95945	Serge Batalov	06/2022
7976	2^318711-139	95942	Lelio R Paula	11/2012
7977	2^318635-1167	95919	Lelio R Paula	03/2016
7978	15^81555+16	95917	Lelio R Paula	07/2016
7979	(37*10^95895+377)/9	95896	Robert Price	10/2017
7980	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
7981	2^318496-97305	95877	Lelio R Paula	03/2016
7982	22129^21496+21496^22129	95871	Hans Havermann	07/2020
7984	2^318466+15015	95868	Lelio R Paula	03/2016
7983	24847^7216+7216^24847	95868	Hans Havermann	07/2020
7985	23706^11065+11065^23706	95866	Hans Havermann	07/2020
7986	(2863^27733-1)/2862	95865	Serge Batalov	06/2022
7987	6^123187-173129	95859	Mike Oakes	04/2011
7988	2^318423-487	95855	Yves Minet	03/2012
7989	(2^318359+678)/2	95836	Stefano Morozzi	09/2020
7990	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
7991	(8060^24533-1)/8059	95831	Serge Batalov	06/2022
7992	(9853^23993-1)/9852	95814	Serge Batalov	06/2022
7994	(2^318267+2550)/2	95808	Stefano Morozzi	09/2020
7993	(5048^25873-1)/5047	95808	Serge Batalov	06/2022
7996	4*10^95799+13	95800	Robert Price	02/2021
7995	(65533^19891-1)/65532	95800	Serge Batalov	06/2022
7997	45369!2+1024	95787	Robert Price	02/2015
7998	3^200758-86	95786	Lelio R Paula	05/2016
7999	(2^318271+1)/(346031404238891654090604244843)	95781	Gord Palameta	12/2018
8000	(2^318171+2030)/2	95779	Stefano Morozzi	09/2020

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