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 ?
5001	(91*10^112098-1)/9	112100	Robert Price	04/2015
5002	(68*10^112087-149)/9	112088	Robert Price	07/2022
5003	2^372310-85061	112077	Paul Bourdelais	02/2012
5004	(10^112067+53)/9	112067	Serge Batalov	07/2015
5005	(2^372237+2082)/2	112055	Stefano Morozzi	09/2020
5006	75^59760+2	112054	Lelio R Paula	08/2013
5007	(2^372200+1710)/2	112044	Stefano Morozzi	09/2020
5008	(10^112048+7)/8747/373157	112039	Alfred Reich	06/2021
5009	(2^372181+2250)/2	112038	Stefano Morozzi	01/2021
5010	(2^372161+2574)/2	112032	Stefano Morozzi	09/2020
5011	8*10^112018-49	112019	Robert Price	08/2019
5013	2^372108+74221	112016	Enzo Doria	04/2016
5012	(2^372109+2046)/2	112016	Stefano Morozzi	09/2020
5014	8*10^112011-73	112012	Robert Price	01/2022
5015	(184*10^112007-1)/3	112009	Robert Price	02/2020
5016	5*10^112003+81	112004	Robert Price	03/2019
5017	215^48018+48018^215	112000	Norbert Schneider	10/2018
5018	25549^24148+24148^25549	111979	Hans Havermann	02/2021
5019	2^371970-459491	111975	Enzo Doria	05/2015
5020	41^69427-40^69427	111971	Robert Price	07/2012
5021	(2^371782+358)/2	111918	Stefano Morozzi	01/2021
5022	(34*10^111902-547)/9	111903	Robert Price	03/2021
5023	(10^111902+71)/9	111902	Serge Batalov	07/2015
5024	(2^371625+1610)/2	111870	Stefano Morozzi	09/2020
5025	29080^7027+7027^29080	111865	Hans Havermann	01/2021
5026	31307^3730+3730^31307	111820	Hans Havermann	02/2021
5027	2^371440-112865	111815	Enzo Doria	06/2014
5028	2^371426-459161	111811	Enzo Doria	05/2015
5029	25768^21771+21771^25768	111779	Hans Havermann	02/2021
5030	28022^9747+9747^28022	111777	Hans Havermann	02/2021
5031	(94*10^111770+11)/3	111772	Robert Price	04/2020
5032	2^371276-461267	111766	Enzo Doria	07/2015
5033	6*10^111760+43	111761	Robert Price	07/2020
5034	98079!4-1024	111747	Robert Price	11/2019
5035	(2^371186+3162)/2	111738	Stefano Morozzi	09/2020
5036	2^371098-113261	111712	Enzo Doria	07/2014
5037	(7*10^111706-61)/9	111706	Erik Branger	01/2011
5038	2^371044+1869391	111696	Enzo Doria	05/2016
5039	26310^17581+17581^26310	111688	Hans Havermann	01/2021
5040	88^57416+87	111645	Norbert Schneider	11/2015
5041	2^370829-109693	111631	Enzo Doria	04/2014
5042	15^94906-2	111619	Lelio R Paula	11/2013
5043	25835^20904+20904^25835	111614	Hans Havermann	02/2021
5044	(2^370726+1198)/2	111600	Stefano Morozzi	09/2020
5045	27758^10479+10479^27758	111597	Hans Havermann	02/2021
5046	2^370695-4627	111591	Yves Minet	05/2019
5047	7*10^111579-87	111580	Robert Price	06/2020
5049	2^370643-37	111575	Yves Minet	01/2012
5048	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
5050	2^370610-3911	111565	Yves Minet	04/2017
5051	(154*10^111549+17)/9	111551	Robert Price	06/2022
5052	26200^18097+18097^26200	111550	Hans Havermann	01/2021
5053	286^45405+45405^286	111532	Norbert Schneider	04/2015
5054	4*5^159563-9	111531	Lelio R Paula	11/2014
5055	5*10^111528-21	111529	Robert Price	12/2021
5056	(4^185225+23)/3	111517	Robert Price	10/2018
5057	2^370393-2797093	111500	Enzo Doria	03/2016
5058	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
5059	(2^370371+554)/2	111493	Stefano Morozzi	09/2020
5060	6^143273-5	111489	Paul Bourdelais	01/2021
5061	2^370292-2791979	111469	Enzo Doria	03/2016
5062	(14*10^111443-11)/3	111444	Robert Price	08/2022
5063	2^370177-461551	111435	Enzo Doria	07/2015
5064	(2^370169+1706)/2	111432	Stefano Morozzi	09/2020
5065	109^54683-108	111413	Norbert Schneider	02/2017
5066	(83*10^111406-173)/9	111407	Robert Price	04/2021
5067	(2^370043+1010)/2	111394	Stefano Morozzi	09/2020
5068	32961^2396+2396^32961	111392	Hans Havermann	10/2020
5069	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
5070	(23*10^111380-29)/3	111381	Robert Price	03/2022
5071	2^369974+733	111374	Lelio R Paula	05/2013
5072	121^53470+120	111367	Norbert Schneider	10/2018
5073	2^369915-286267	111356	Enzo Doria	07/2015
5074	(62*10^111347-629)/9	111348	Robert Price	07/2021
5075	2^369855-1615	111338	Lelio R Paula	05/2017
5076	7*10^111325+3	111326	Robert Price	08/2015
5077	51^65176+2	111293	Lelio R Paula	08/2013
5078	2^369643-1865767	111274	Enzo Doria	03/2016
5079	2^369603+885	111262	Lelio R Paula	05/2017
5080	25555^22564+22564^25555	111252	Hans Havermann	10/2020
5081	L(532277)	111240	Renaud Lifchitz	03/2004
5082	105^55033-2	111233	Lelio R Paula	10/2017
5083	(35*10^111232-737)/9	111233	Robert Price	07/2018
5084	26970^13307+13307^26970	111227	Hans Havermann	10/2020
5085	25419^23716+23716^25419	111210	Hans Havermann	10/2020
5086	9*10^111201-29	111202	Robert Price	09/2019
5087	2^369392+29835	111199	Lelio R Paula	05/2017
5088	3^233059+16	111198	Robert Price	03/2020
5089	2^369354-3413	111187	Yves Minet	12/2016
5090	2^369296-27	111170	Lelio R Paula	02/2013
5091	2^369239-109837	111153	Enzo Doria	05/2014
5092	2^369224-291839	111148	Enzo Doria	07/2015
5093	2^369216+2798881	111146	Enzo Doria	04/2016
5094	26842^13817+13817^26842	111137	Hans Havermann	11/2020
5095	(5*10^111119-191)/3	111120	Robert Price	05/2021
5096	(29*10^111112-23)/3	111113	Robert Price	03/2022
5097	10^111111+163849	111112	Patrick De Geest	03/2017
5098	10^111111-312911	111111	Patrick De Geest	03/2017
5099	2^369092-216923	111108	Enzo Doria	05/2014
5100	2^369081-55	111105	Lelio R Paula	02/2013
5101	(2^369047+3618)/2	111094	Stefano Morozzi	09/2020
5102	88^57124-87	111077	Norbert Schneider	11/2015
5103	2^368980+753	111075	Lelio R Paula	05/2013
5104	2^368946-3623	111064	Yves Minet	03/2017
5105	2^368929+29835	111059	Lelio R Paula	05/2017
5106	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
5107	111^54298+110	111057	Norbert Schneider	04/2017
5108	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
5109	35799^1262+1262^35799	111015	Hans Havermann	10/2020
5110	(298*10^111004+11)/3	111006	Robert Price	11/2020
5111	27648^10349+10349^27648	111004	Hans Havermann	11/2020
5112	28899^6932+6932^28899	110997	Hans Havermann	11/2020
5113	2^368641-460303	110972	Enzo Doria	06/2015
5114	2^368619-109087	110966	Enzo Doria	04/2014
5115	(74*10^110961+313)/9	110962	Robert Price	06/2019
5116	25258^24711+24711^25258	110956	Hans Havermann	11/2020
5117	(2^368539+1290)/2	110941	Stefano Morozzi	01/2021
5118	3*2^368489+7	110927	Lelio R Paula	09/2014
5119	(14*10^110922+61)/3	110923	Robert Price	12/2018
5120	97411!4-2	110913	Robert Price	07/2017
5121	(301*10^110903+23)/9	110905	Robert Price	06/2021
5122	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
5123	25830^19619+19619^25830	110880	Hans Havermann	10/2020
5124	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
5125	26022^18191+18191^26022	110850	Hans Havermann	10/2020
5126	(2^368211+2250)/2	110843	Stefano Morozzi	01/2021
5127	(37*10^110813+251)/9	110814	Robert Price	09/2021
5128	2^368050-64875	110795	Lelio R Paula	05/2017
5129	2^368048+25	110794	Lelio R Paula	02/2013
5130	(2^368017+2262)/2	110784	Stefano Morozzi	02/2021
5131	69^60239-2	110771	Lelio R Paula	10/2013
5132	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
5133	2^367924-69	110757	Lelio R Paula	02/2013
5134	(23*10^110738+61)/3	110739	Robert Price	01/2022
5135	(2^367779+3750)/2	110713	Stefano Morozzi	01/2021
5136	2^367709-109723	110692	Enzo Doria	04/2014
5137	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
5138	(2^367626+3514)/2	110667	Stefano Morozzi	09/2020
5139	(1288676*34^72242-455)/33	110642	Eric Chen	03/2023
5140	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
5141	140^51515-139	110558	Norbert Schneider	04/2019
5142	2^367215+1879223	110543	Enzo Doria	09/2016
5143	25782^19375+19375^25782	110534	Hans Havermann	10/2020
5144	26117^17058+17058^26117	110526	Hans Havermann	10/2020
5145	2^367141+41	110521	Lelio R Paula	02/2013
5146	2^367126+29835	110516	Lelio R Paula	05/2017
5147	(10^110503-1)/9+2(10^59183-1)/910^25660	110503	Makoto Morimoto	09/2020
5148	(10^110503-1)/9+2(10^65511-1)/910^22496	110503	Makoto Morimoto	09/2020
5149	(10^110503-1)/9+210^108327+210^2175	110503	Makoto Morimoto	09/2020
5150	(10^110503-1)/9+210^66251+210^44251	110503	Makoto Morimoto	09/2020
5151	(10^110503-1)/9+3(10^28813-1)/910^40845	110503	Makoto Morimoto	09/2020
5152	(10^110503-1)/9+3(10^82573-1)/910^13965	110503	Makoto Morimoto	09/2020
5153	(10^110503-1)/9+4(10^43305-1)/910^33599	110503	Makoto Morimoto	09/2020
5154	(10^110503-1)/9+510^70327+510^40175	110503	Makoto Morimoto	09/2020
5155	(10^110503-1)/9+510^99423+510^11079	110503	Makoto Morimoto	09/2020
5156	(10^110503-1)/9+7(10^23617-1)/910^43443	110503	Makoto Morimoto	09/2020
5157	(10^110503-1)/9+8(10^30251-1)/910^40126	110503	Makoto Morimoto	09/2020
5158	3(10^110503-1)/9+110^106036+1*10^4466	110503	Makoto Morimoto	09/2020
5159	3(10^110503-1)/9+110^58962+1*10^51540	110503	Makoto Morimoto	09/2020
5160	3(10^110503-1)/9+110^78213+1*10^32289	110503	Makoto Morimoto	09/2020
5161	3(10^110503-1)/9+210^76898+2*10^33604	110503	Makoto Morimoto	09/2020
5162	3(10^110503-1)/9-110^100802-1*10^9700	110503	Makoto Morimoto	09/2020
5163	3(10^110503-1)/9-110^76355-1*10^34147	110503	Makoto Morimoto	09/2020
5164	3(10^110503-1)/9-210^105704-2*10^4798	110503	Makoto Morimoto	09/2020
5165	7(10^110503-1)/9+1(10^27685-1)/9*10^41409	110503	Makoto Morimoto	09/2020
5166	7(10^110503-1)/9+1(10^91035-1)/9*10^9734	110503	Makoto Morimoto	09/2020
5167	7(10^110503-1)/9-1(10^23717-1)/9*10^43393	110503	Makoto Morimoto	09/2020
5168	7(10^110503-1)/9-110^57906-1*10^52596	110503	Makoto Morimoto	09/2020
5169	7(10^110503-1)/9-110^72287-1*10^38215	110503	Makoto Morimoto	09/2020
5170	7(10^110503-1)/9-2(10^53823-1)/9*10^28340	110503	Makoto Morimoto	09/2020
5171	7(10^110503-1)/9-2(10^88659-1)/9*10^10922	110503	Makoto Morimoto	09/2020
5172	7(10^110503-1)/9-3(10^79921-1)/9*10^15291	110503	Makoto Morimoto	09/2020
5173	7(10^110503-1)/9-310^60024-3*10^50478	110503	Makoto Morimoto	09/2020
5174	7(10^110503-1)/9-4(10^103091-1)/9*10^3706	110503	Makoto Morimoto	09/2020
5175	7(10^110503-1)/9-410^103658-4*10^6844	110503	Makoto Morimoto	09/2020
5176	7(10^110503-1)/9-410^78188-4*10^32314	110503	Makoto Morimoto	09/2020
5177	7(10^110503-1)/9-5(10^35035-1)/9*10^37734	110503	Makoto Morimoto	09/2020
5178	7(10^110503-1)/9-6(10^67347-1)/9*10^21578	110503	Makoto Morimoto	09/2020
5179	7(10^110503-1)/9-610^60391-6*10^50111	110503	Makoto Morimoto	09/2020
5180	(10^110503-1)-4(10^96247-1)/910^7128	110503	Makoto Morimoto	09/2020
5181	(10^110503-1)-410^74037-410^36465	110503	Makoto Morimoto	09/2020
5182	(10^110503-1)-410^77787-410^32715	110503	Makoto Morimoto	09/2020
5183	(10^110503-1)-410^91179-410^19323	110503	Makoto Morimoto	09/2020
5184	(10^110503-1)-5(10^99143-1)/910^5680	110503	Makoto Morimoto	09/2020
5185	(10^110503-1)-7(10^85075-1)/910^12714	110503	Makoto Morimoto	09/2020
5186	(10^110503-1)-710^100712-710^9790	110503	Makoto Morimoto	09/2020
5187	(10^110503-1)-710^76427-710^34075	110503	Makoto Morimoto	09/2020
5188	(10^110503-1)-710^90451-710^20051	110503	Makoto Morimoto	09/2020
5189	(10^110503-1)-810^106252-810^4250	110503	Makoto Morimoto	09/2020
5190	(11*10^110496+49)/3	110497	Robert Price	07/2018
5191	25447^21958+21958^25447	110481	Hans Havermann	11/2020
5192	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
5193	7*10^110468-23	110469	Robert Price	07/2019
5194	2^366853+5711	110434	Lelio R Paula	05/2017
5195	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
5196	2^366816+315	110423	Lelio R Paula	05/2017
5197	2^366775-2787037	110411	Enzo Doria	03/2016
5198	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
5199	2^366751+2797553	110404	Enzo Doria	03/2016
5200	25276^23331+23331^25276	110404	Hans Havermann	10/2020
5201	2^366748+255	110403	Lelio R Paula	05/2017
5202	2^366738-2985	110400	Yves Minet	09/2014
5203	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
5204	(2^366722+1314)/2	110395	Stefano Morozzi	02/2021
5205	2^366716+1871791	110393	Enzo Doria	05/2016
5206	2^366649+1871687	110373	Enzo Doria	05/2016
5207	2^366629-351205	110367	Enzo Doria	06/2015
5208	(31*10^110363+257)/9	110364	Robert Price	12/2021
5209	(17*19^86292-215)/18	110347	Eric Chen	01/2023
5211	2^366558+1874479	110345	Enzo Doria	06/2016
5210	25132^24581+24581^25132	110345	Hans Havermann	10/2020
5212	(2^366539+770)/2	110339	Stefano Morozzi	09/2020
5213	26368^15285+15285^26368	110331	Hans Havermann	10/2020
5214	(23*10^110290+19)/3	110291	Robert Price	07/2019
5215	18^87853-4409	110280	Enzo Doria	03/2013
5216	28490^7419+7419^28490	110267	Hans Havermann	11/2020
5217	2^366218-23	110243	Lelio R Paula	02/2013
5218	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
5219	2^366178-343991	110231	Enzo Doria	07/2015
5220	25777^18798+18798^25777	110174	Hans Havermann	10/2020
5221	2^365944+1871341	110161	Enzo Doria	05/2016
5222	2^365838-461267	110129	Enzo Doria	07/2015
5223	30152^4491+4491^30152	110126	Hans Havermann	11/2020
5224	10^110111+464019	110112	Patrick De Geest	05/2021
5225	10^110111-40001	110111	Robert Price	01/2021
5226	2^365763-6555	110106	Lelio R Paula	04/2017
5227	(2^365689+2^182845+1)/5	110083		11/2006
5228	2^365666-459161	110077	Enzo Doria	05/2015
5229	3*10^110076-7	110077	Robert Price	08/2015
5230	13^98785-72	110041	Lelio R Paula	03/2017
5231	(25^78707+1)/26	110027	Robert Price	06/2013
5232	(7*10^110027-277)/9	110027	Robert Price	02/2022
5233	(16*10^110014-73)/3	110015	Robert Price	07/2020
5234	(7*10^110006-151)/9	110006	Robert Price	02/2018
5235	6^141361-7	110001	Lelio R Paula	11/2014
5236	20^84536+81	109984	Lelio R Paula	03/2017
5237	5*2^365347-9	109982	Lelio R Paula	09/2014
5238	9*6^141303+7	109957	Lelio R Paula	11/2014
5239	27635^9522+9522^27635	109953	Hans Havermann	11/2020
5240	78^58099+77	109929	Norbert Schneider	02/2015
5241	2*10^109928-7	109929	Robert Price	10/2015
5242	30580^3933+3933^30580	109927	Hans Havermann	11/2020
5243	26380^14689+14689^26380	109926	Hans Havermann	11/2020
5244	(2^365161+1130)/2	109925	Stefano Morozzi	09/2020
5245	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
5246	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
5247	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
5248	(2^365069+3774)/2	109897	Stefano Morozzi	02/2021
5249	29652^5083+5083^29652	109894	Mark Rodenkirch	10/2020
5250	(2^365049+722)/2	109891	Stefano Morozzi	09/2020

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