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 ?
4001	(10^110503-1)/9+510^99423+510^11079	110503	Makoto Morimoto	09/2020
4002	(10^110503-1)/9+7(10^23617-1)/910^43443	110503	Makoto Morimoto	09/2020
4003	(10^110503-1)/9+8(10^30251-1)/910^40126	110503	Makoto Morimoto	09/2020
4004	3(10^110503-1)/9+110^106036+1*10^4466	110503	Makoto Morimoto	09/2020
4005	3(10^110503-1)/9+110^58962+1*10^51540	110503	Makoto Morimoto	09/2020
4006	3(10^110503-1)/9+110^78213+1*10^32289	110503	Makoto Morimoto	09/2020
4007	3(10^110503-1)/9+210^76898+2*10^33604	110503	Makoto Morimoto	09/2020
4008	3(10^110503-1)/9-110^100802-1*10^9700	110503	Makoto Morimoto	09/2020
4009	3(10^110503-1)/9-110^76355-1*10^34147	110503	Makoto Morimoto	09/2020
4010	3(10^110503-1)/9-210^105704-2*10^4798	110503	Makoto Morimoto	09/2020
4011	7(10^110503-1)/9+1(10^27685-1)/9*10^41409	110503	Makoto Morimoto	09/2020
4012	7(10^110503-1)/9+1(10^91035-1)/9*10^9734	110503	Makoto Morimoto	09/2020
4013	7(10^110503-1)/9-1(10^23717-1)/9*10^43393	110503	Makoto Morimoto	09/2020
4014	7(10^110503-1)/9-110^57906-1*10^52596	110503	Makoto Morimoto	09/2020
4015	7(10^110503-1)/9-110^72287-1*10^38215	110503	Makoto Morimoto	09/2020
4016	7(10^110503-1)/9-2(10^53823-1)/9*10^28340	110503	Makoto Morimoto	09/2020
4017	7(10^110503-1)/9-2(10^88659-1)/9*10^10922	110503	Makoto Morimoto	09/2020
4018	7(10^110503-1)/9-3(10^79921-1)/9*10^15291	110503	Makoto Morimoto	09/2020
4019	7(10^110503-1)/9-310^60024-3*10^50478	110503	Makoto Morimoto	09/2020
4020	7(10^110503-1)/9-4(10^103091-1)/9*10^3706	110503	Makoto Morimoto	09/2020
4021	7(10^110503-1)/9-410^103658-4*10^6844	110503	Makoto Morimoto	09/2020
4022	7(10^110503-1)/9-410^78188-4*10^32314	110503	Makoto Morimoto	09/2020
4023	7(10^110503-1)/9-5(10^35035-1)/9*10^37734	110503	Makoto Morimoto	09/2020
4024	7(10^110503-1)/9-6(10^67347-1)/9*10^21578	110503	Makoto Morimoto	09/2020
4025	7(10^110503-1)/9-610^60391-6*10^50111	110503	Makoto Morimoto	09/2020
4026	(10^110503-1)-4(10^96247-1)/910^7128	110503	Makoto Morimoto	09/2020
4027	(10^110503-1)-410^74037-410^36465	110503	Makoto Morimoto	09/2020
4028	(10^110503-1)-410^77787-410^32715	110503	Makoto Morimoto	09/2020
4029	(10^110503-1)-410^91179-410^19323	110503	Makoto Morimoto	09/2020
4030	(10^110503-1)-5(10^99143-1)/910^5680	110503	Makoto Morimoto	09/2020
4031	(10^110503-1)-7(10^85075-1)/910^12714	110503	Makoto Morimoto	09/2020
4032	(10^110503-1)-710^100712-710^9790	110503	Makoto Morimoto	09/2020
4033	(10^110503-1)-710^76427-710^34075	110503	Makoto Morimoto	09/2020
4034	(10^110503-1)-710^90451-710^20051	110503	Makoto Morimoto	09/2020
4035	(10^110503-1)-810^106252-810^4250	110503	Makoto Morimoto	09/2020
4036	(11*10^110496+49)/3	110497	Robert Price	07/2018
4037	25447^21958+21958^25447	110481	Hans Havermann	11/2020
4038	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
4039	7*10^110468-23	110469	Robert Price	07/2019
4040	2^366853+5711	110434	Lelio R Paula	05/2017
4041	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
4042	2^366816+315	110423	Lelio R Paula	05/2017
4043	2^366775-2787037	110411	Enzo Doria	03/2016
4044	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
4045	2^366751+2797553	110404	Enzo Doria	03/2016
4046	25276^23331+23331^25276	110404	Hans Havermann	10/2020
4047	2^366748+255	110403	Lelio R Paula	05/2017
4048	2^366738-2985	110400	Yves Minet	09/2014
4049	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
4050	(2^366722+1314)/2	110395	Stefano Morozzi	02/2021
4051	2^366716+1871791	110393	Enzo Doria	05/2016
4052	2^366649+1871687	110373	Enzo Doria	05/2016
4053	2^366629-351205	110367	Enzo Doria	06/2015
4054	2^366558+1874479	110345	Enzo Doria	06/2016
4055	25132^24581+24581^25132	110345	Hans Havermann	10/2020
4056	(2^366539+770)/2	110339	Stefano Morozzi	09/2020
4057	26368^15285+15285^26368	110331	Hans Havermann	10/2020
4058	(23*10^110290+19)/3	110291	Robert Price	07/2019
4059	18^87853-4409	110280	Enzo Doria	03/2013
4060	28490^7419+7419^28490	110267	Hans Havermann	11/2020
4061	2^366218-23	110243	Lelio R Paula	02/2013
4062	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
4063	2^366178-343991	110231	Enzo Doria	07/2015
4064	25777^18798+18798^25777	110174	Hans Havermann	10/2020
4065	2^365944+1871341	110161	Enzo Doria	05/2016
4066	2^365838-461267	110129	Enzo Doria	07/2015
4067	30152^4491+4491^30152	110126	Hans Havermann	11/2020
4068	10^110111-40001	110111	Robert Price	01/2021
4069	2^365763-6555	110106	Lelio R Paula	04/2017
4070	(2^365689+2^182845+1)/5	110083		11/2006
4071	2^365666-459161	110077	Enzo Doria	05/2015
4072	3*10^110076-7	110077	Robert Price	08/2015
4073	13^98785-72	110041	Lelio R Paula	03/2017
4074	(25^78707+1)/26	110027	Robert Price	06/2013
4075	(16*10^110014-73)/3	110015	Robert Price	07/2020
4076	(7*10^110006-151)/9	110006	Robert Price	02/2018
4077	6^141361-7	110001	Lelio R Paula	11/2014
4078	20^84536+81	109984	Lelio R Paula	03/2017
4079	5*2^365347-9	109982	Lelio R Paula	09/2014
4080	9*6^141303+7	109957	Lelio R Paula	11/2014
4081	27635^9522+9522^27635	109953	Hans Havermann	11/2020
4082	78^58099+77	109929	Norbert Schneider	02/2015
4083	2*10^109928-7	109929	Robert Price	10/2015
4084	30580^3933+3933^30580	109927	Hans Havermann	11/2020
4085	26380^14689+14689^26380	109926	Hans Havermann	11/2020
4086	(2^365161+1130)/2	109925	Stefano Morozzi	09/2020
4087	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
4088	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
4089	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
4090	(2^365069+3774)/2	109897	Stefano Morozzi	02/2021
4091	29652^5083+5083^29652	109894	Mark Rodenkirch	10/2020
4092	(2^365049+722)/2	109891	Stefano Morozzi	09/2020
4093	18^87533-11	109878	Lelio R Paula	04/2017
4094	2^364982-5	109871	Henri Lifchitz	04/2006
4095	3*10^109861+59	109862	Robert Price	08/2018
4096	5*10^109860-69	109861	Robert Price	02/2021
4097	2^364936-1867979	109857	Enzo Doria	04/2016
4098	27013^11652+11652^27013	109846	Hans Havermann	10/2020
4099	2^364867-112087	109836	Enzo Doria	06/2014
4100	4^182415-85061	109825	Mike Oakes	06/2011
4101	(2^364809+1034)/2	109819	Stefano Morozzi	09/2020
4102	25708^18675+18675^25708	109806	Hans Havermann	10/2020
4103	(17^89227+16^89227)/33	109788	Robert Price	08/2013
4104	2^364687-187	109782	Lelio R Paula	01/2012
4105	2^364644+67	109769	Lelio R Paula	01/2012
4106	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
4107	(2^364616+5)/9	109760	Lelio R Paula	01/2014
4108	(55*10^109759+89)/9	109760	Robert Price	03/2019
4109	12^101694+73	109747	Lelio R Paula	03/2017
4110	13^98518-66	109744	Lelio R Paula	03/2017
4111	2^364478-113261	109719	Enzo Doria	07/2014
4112	(2^364513+1)/(3*44290516579)	109719	Gord Palameta	08/2018
4113	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
4114	27814^8777+8777^27814	109681	Hans Havermann	10/2020
4115	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
4116	3^229824+340	109654	Lelio R Paula	03/2017
4117	(2*10^109645-71)/3	109645	Robert Price	12/2017
4118	2^364169-112813	109626	Enzo Doria	06/2014
4119	28822^6359+6359^28822	109622	Hans Havermann	11/2020
4120	10^109615+21	109616	Lelio R Paula	03/2017
4121	10^109615-456267	109615	Patrick De Geest	03/2017
4122	2^364094-113	109604	Lelio R Paula	01/2012
4123	25251^21898+21898^25251	109600	Hans Havermann	11/2020
4124	(4^182026+11)/3	109591	Robert Price	02/2017
4125	2^364041-6883	109588	Lelio R Paula	09/2011
4126	12^101545+11	109586	Lelio R Paula	03/2017
4127	26536^13475+13475^26536	109582	Hans Havermann	11/2020
4128	2^363842-2787101	109528	Enzo Doria	03/2016
4129	(2^363812+3570)/2	109519	Stefano Morozzi	09/2020
4130	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
4131	2^363769+5711	109506	Lelio R Paula	04/2017
4132	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
4133	p(22245)#/2-8	109462	Robert Price	01/2017
4134	2^363556+55	109442	Lelio R Paula	01/2012
4135	(2^363437+1682)/2	109406	Stefano Morozzi	09/2020
4136	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
4137	2^363406+1871569	109397	Enzo Doria	05/2016
4138	(2^363370+1338)/2	109385	Stefano Morozzi	02/2021
4139	(2^363349+7)/9	109378	Lelio R Paula	01/2014
4140	3^229236+100	109374	Lelio R Paula	03/2017
4141	(2^363315+3258)/2	109369	Stefano Morozzi	02/2021
4142	2^363268-58695	109355	Lelio R Paula	04/2017
4143	2^363191-112321	109332	Enzo Doria	06/2014
4144	26231^14718+14718^26231	109327	Hans Havermann	10/2020
4145	25461^19672+19672^25461	109326	Hans Havermann	10/2020
4146	4*10^109316-63	109317	Robert Price	10/2018
4147	2^363120+3	109311	Donovan Johnson	04/2006
4148	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
4149	2^363042-114641	109287	Enzo Doria	04/2015
4150	2^363020-112793	109280	Enzo Doria	06/2014
4151	(85*10^109253+203)/9	109254	Robert Price	09/2020
4152	24990^23431+23431^24990	109202	Hans Havermann	10/2020
4153	(2^362746+3738)/2	109198	Stefano Morozzi	09/2020
4154	(2^362716+1282)/2	109189	Stefano Morozzi	01/2021
4155	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
4156	25060^22737+22737^25060	109180	Hans Havermann	10/2020
4157	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
4158	5^156181+38	109166	Lelio R Paula	02/2017
4159	(2^362623+3618)/2	109161	Stefano Morozzi	09/2020
4160	25138^21993+21993^25138	109157	Hans Havermann	10/2020
4161	4*10^109142+91	109143	Robert Price	08/2018
4163	3^228750+68	109142	Lelio R Paula	03/2017
4162	(2^362561+786)/2	109142	Stefano Morozzi	09/2020
4164	2*10^109100-49	109101	Robert Price	09/2020
4165	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
4166	65^60167-64^60167	109078	Robert Price	08/2013
4167	7*3^228589-2	109066	Lelio R Paula	09/2014
4168	24874^24243+24243^24874	109063	Hans Havermann	11/2020
4169	(17*10^109059-161)/9	109060	Robert Price	02/2021
4170	29158^5495+5495^29158	109050	Hans Havermann	11/2020
4171	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
4172	2*7^129008+9	109025	Lelio R Paula	11/2014
4173	88*10^109022+7	109024	Robert Price	03/2020
4174	28194^7337+7337^28194	108985	Hans Havermann	10/2020
4175	(5*10^108960+91)/3	108961	Robert Price	04/2018
4176	2^361957+76367	108960	Enzo Doria	05/2016
4177	2^361873-1411	108935	Yves Minet	01/2013
4178	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
4179	115^52842-114	108892	Norbert Schneider	07/2018
4180	13^97745-24	108883	Lelio R Paula	03/2017
4181	(2^361696+2562)/2	108882	Stefano Morozzi	09/2020
4182	17^88475+8	108864	Lelio R Paula	04/2017
4183	2^361567+51	108843	Lelio R Paula	01/2012
4184	2^361563-109501	108842	Enzo Doria	04/2014
4185	12^100852+83	108838	Lelio R Paula	03/2017
4186	2^361497+767	108822	Lelio R Paula	01/2012
4187	28019^7630+7630^28019	108785	Hans Havermann	10/2020
4188	24723^24758-24758^24723	108765	Norbert Schneider	11/2020
4189	2^361280-112349	108757	Enzo Doria	06/2014
4190	2^361271-5955	108754	Lelio R Paula	04/2017
4191	12^100757+19	108736	Lelio R Paula	03/2017
4192	25368^19333+19333^25368	108735	Hans Havermann	11/2020
4193	(2^361195+3618)/2	108731	Stefano Morozzi	09/2020
4194	14^94849-61	108710	Lelio R Paula	05/2017
4195	27267^9700+9700^27267	108708	Hans Havermann	11/2020
4196	(19^85009-5^85009)/14	108705	Robert Price	07/2013
4197	24832^23853+23853^24832	108704	Hans Havermann	11/2020
4198	27502^8963+8963^27502	108701	Hans Havermann	11/2020
4199	25807^16278+16278^25807	108689	Hans Havermann	11/2020
4200	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
4201	2^360973+1299	108664	Lelio R Paula	04/2017
4202	2^360959-109101	108660	Enzo Doria	04/2014
4203	6*5^155454+7	108659	Lelio R Paula	11/2014
4204	10^108656+79	108657	Lelio R Paula	02/2017
4205	10^108656-50001	108656	Patrick De Geest	03/2017
4206	2^360918-35	108648	Lelio R Paula	01/2012
4207	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
4208	3*10^108624-49	108625	Robert Price	07/2018
4209	(2^360831+666)/2	108621	Stefano Morozzi	09/2020
4210	(134*10^108610+7)/3	108612	Robert Price	02/2020
4211	2*10^108609+29	108610	Robert Price	02/2021
4212	(2^360742+3222)/2	108594	Stefano Morozzi	09/2020
4213	2^360706-458903	108584	Enzo Doria	04/2015
4214	31112^3087+3087^31112	108567	Hans Havermann	11/2020
4215	2^360641-113185	108564	Enzo Doria	07/2014
4216	2^360618+75019	108557	Enzo Doria	04/2016
4217	(14*10^108545-221)/9	108546	Robert Price	04/2018
4218	(44*10^108544-233)/9	108545	Robert Price	01/2019
4219	3*5^155286+2	108541	Lelio R Paula	11/2014
4220	7^128422+4	108530	Lelio R Paula	11/2014
4221	7^128421-80	108529	Lelio R Paula	03/2017
4222	2^360497+53807	108521	Yves Minet	07/2010
4223	2^360468-4559	108512	Yves Minet	03/2019
4224	(2^360451+578)/2	108507	Stefano Morozzi	09/2020
4225	2^360366+1459	108481	Lelio R Paula	09/2011
4226	2^360364-1499	108481	Yves Minet	05/2013
4227	25662^16871+16871^25662	108477	Hans Havermann	10/2020
4228	25009^21748+21748^25009	108475	Hans Havermann	10/2020
4229	14^94642-23	108472	Lelio R Paula	05/2017
4230	(197*10^108446-11)/3	108448	Robert Price	03/2020
4231	(2^360229+1290)/2	108440	Stefano Morozzi	01/2021
4232	4*10^108412+9	108413	Robert Price	05/2015
4233	(259*10^108409-1)/3	108411	Robert Price	12/2020
4234	(2^360122+1194)/2	108408	Stefano Morozzi	09/2020
4235	133^51042-132	108406	Norbert Schneider	02/2019
4236	2^360093-351103	108399	Enzo Doria	06/2015
4237	2^360042+723	108384	Lelio R Paula	01/2012
4238	85^56164-2	108364	Lelio R Paula	10/2013
4239	2^359937-29323	108352	Enzo Doria	07/2015
4240	(2^359922+1762)/2	108348	Stefano Morozzi	09/2020
4241	(2^359903+758)/2	108342	Stefano Morozzi	09/2020
4242	2^359898-19997	108341	Enzo Doria	06/2013
4243	(2^359886+2122)/2	108337	Stefano Morozzi	09/2020
4244	2*5^154948-7	108305	Lelio R Paula	11/2014
4245	10^108303+13	108304	Lelio R Paula	02/2017
4246	10^108303-207959	108303	Patrick De Geest	03/2017
4247	7*10^108300+69	108301	Robert Price	07/2019
4248	2^359730+753	108290	Lelio R Paula	12/2011
4249	(8*10^108273+13)/3	108274	Robert Price	06/2018
4250	2^359650-19797	108266	Enzo Doria	06/2013

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Probable Primes Top 10000

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