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	(88*10^128324-637)/9	128325	Robert Price	11/2020
4002	(491*10^128285+31)/9	128287	Robert Price	04/2022
4003	39103^1908+1908^39103	128281	Hans Havermann	04/2021
4004	2^426043+35	128252	Robert Price	11/2015
4005	(4*10^128244-19)/3	128245	Robert Price	03/2018
4006	35489^4102+4102^35489	128222	Hans Havermann	04/2021
4007	34721^4926+4926^34721	128208	Hans Havermann	04/2021
4008	(305*10^128198+1)/9	128200	Robert Price	02/2020
4009	2^425808-459959	128181	Enzo Doria	06/2015
4010	30632^15291+15291^30632	128178	Hans Havermann	04/2021
4011	35981^3648+3648^35981	128167	Hans Havermann	04/2021
4012	2^425627-113605	128127	Enzo Doria	08/2014
4013	(4*10^128109+119)/3	128110	Robert Price	12/2021
4014	(22*10^128094+53)/3	128095	Robert Price	07/2019
4015	(86*10^128086-221)/9	128087	Robert Price	09/2019
4016	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
4017	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
4018	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
4019	Phi(149401,10)/30037901719561	128003	Makoto Kamada	07/2022
4020	2^425205+4911	128000	Marek Hubal	02/2017
4021	29241^23836+23836^29241	127995	Hans Havermann	04/2021
4022	2^425118-113663	127974	Enzo Doria	08/2014
4023	(86*10^127967-329)/9	127968	Robert Price	01/2020
4024	2^425061+1869761	127957	Enzo Doria	05/2016
4025	746^44541+44541^746	127955	Norbert Schneider	07/2019
4026	30236^17043+17043^30236	127946	Hans Havermann	03/2021
4027	2^424938+212419	127920	Enzo Doria	08/2023
4028	2^424918-21141	127914	Enzo Doria	07/2013
4029	(62*10^127903+91)/9	127904	Robert Price	07/2021
4030	2^424864-29489	127897	Enzo Doria	08/2015
4031	30438^15893+15893^30438	127877	Hans Havermann	02/2021
4032	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
4033	28929^26258+26258^28929	127845	Hans Havermann	03/2021
4034	30563^15220+15220^30563	127828	Hans Havermann	03/2021
4035	2^424632-2786639	127827	Enzo Doria	03/2016
4036	10^127821-700001	127821	Robert Price	08/2021
4037	2^424577-113755	127811	Enzo Doria	09/2014
4038	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
4039	(56*10^127752+691)/9	127753	Robert Price	05/2019
4040	11^122629-720	127705	Enzo Doria	11/2012
4041	22*10^127645+3	127647	Robert Price	01/2020
4042	28715^27844+27844^28715	127631	Hans Havermann	03/2021
4043	(56*10^127612+187)/9	127613	Robert Price	10/2021
4044	(5*36^81995+821)/7	127609	Eric Chen	01/2021
4045	4*10^127562-39	127563	Robert Price	09/2020
4046	32595^8186+8186^32595	127547	Hans Havermann	03/2021
4047	2^423696-21429	127546	Enzo Doria	07/2013
4048	2^423664-1864559	127536	Enzo Doria	03/2016
4049	37889^2322+2322^37889	127530	Hans Havermann	03/2021
4050	37668^2429+2429^37668	127523	Hans Havermann	03/2021
4051	3^267267-4	127519	Henri Lifchitz	10/2014
4052	fibonacci(610144)-2	127513	Jon Grantham	08/2023
4053	(103*10^127491+17)/3	127493	Robert Price	08/2020
4054	29376^21869+21869^29376	127487	Hans Havermann	03/2021
4055	31186^12241+12241^31186	127483	Hans Havermann	02/2021
4056	(19^99689+5^99689)/24	127477	Robert Price	09/2013
4057	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
4058	30594^14645+14645^30594	127446	Hans Havermann	03/2021
4059	2^423328-21537	127435	Enzo Doria	07/2013
4060	(67*10^127413-7)/3	127415	Robert Price	01/2020
4061	(5*34^83193+700233)/11	127408	Eric Chen	08/2023
4062	(2*10^127407+73)/3	127407	Robert Price	09/2020
4063	(2^423165-7)/25	127384	Lelio R Paula	05/2015
4064	(7726^32768+1)/13917994151414876602369	127379	Kellen Shenton	04/2021
4065	(4*10^127349+17)/3	127350	Tyler Busby	01/2023
4066	29512^20647+20647^29512	127341	Hans Havermann	03/2021
4067	2^422987-3001935	127332	Paul Bourdelais	07/2023
4068	(112*10^127324+17)/3	127326	Robert Price	03/2020
4069	29565^20252+20252^29565	127321	Hans Havermann	03/2021
4070	fibonacci(609165)-3	127308	Jon Grantham	08/2023
4072	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
4071	(5^182099-3^182099)/2	127282	Kellen Shenton	05/2022
4073	(16*10^127259+197)/3	127260	Robert Price	04/2019
4074	(26*10^127240+61)/3	127241	Robert Price	10/2019
4075	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
4076	2^422515-114997	127190	Enzo Doria	06/2015
4077	5*10^127179-3	127180	Robert Price	07/2015
4078	31678^10343+10343^31678	127176	Hans Havermann	03/2021
4079	(44*10^127169-233)/9	127170	Robert Price	01/2019
4080	34947^4352+4352^34947	127162	Hans Havermann	03/2021
4081	6*10^127158+19	127159	Robert Price	11/2021
4082	30469^14902+14902^30469	127155	Hans Havermann	03/2021
4083	5*10^127153+77	127154	Robert Price	12/2018
4084	29941^17620+17620^29941	127130	Hans Havermann	02/2021
4085	31607^10516+10516^31607	127119	Hans Havermann	03/2021
4086	(19*10^127118-97)/3	127119	Robert Price	10/2021
4087	(29*10^127111+691)/9	127112	Robert Price	08/2021
4088	736^44335+44335^736	127104	Norbert Schneider	07/2019
4089	33040^7023+7023^33040	127090	Hans Havermann	03/2021
4090	(4*10^127081+167)/9	127081	Robert Price	03/2022
4091	29748^18661+18661^29748	127052	Hans Havermann	03/2021
4092	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
4093	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
4094	(14*10^127014-137)/3	127015	Robert Price	04/2021
4095	31436^10965+10965^31436	127002	Hans Havermann	03/2021
4096	28905^24758+24758^28905	127001	Hans Havermann	03/2021
4097	2^421860-113285	126993	Enzo Doria	07/2014
4098	(10^127030+7)/81234833/9230384921/6092460488946445358851	126991	Alfred Reich	07/2021
4099	(2^421827-7)/11	126982	Lelio R Paula	05/2015
4100	11^121910-840	126957	Enzo Doria	12/2012
4101	(56*10^126935+187)/9	126936	Robert Price	10/2021
4102	28915^24538+24538^28915	126933	Hans Havermann	03/2021
4103	(29*10^126928-77)/3	126929	Robert Price	02/2020
4104	(259*10^126919-1)/3	126921	Robert Price	12/2020
4105	10^126919+204567	126920	Patrick De Geest	05/2021
4106	(2^421617+100280245065)	126920	Paul Bourdelais	05/2022
4107	10^126919-100001	126919	Robert Price	07/2020
4108	28340^28503+28503^28340	126907	Norbert Schneider	02/2021
4109	2^421534-3001935	126895	Paul Bourdelais	07/2023
4110	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
4111	(5*10^126871-119)/3	126872	Robert Price	03/2018
4112	331^50339-10004	126846	Enzo Doria	07/2012
4113	2^421363-2790757	126843	Enzo Doria	03/2016
4114	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
4115	37938^2203+2203^37938	126828	Hans Havermann	03/2021
4116	(13*10^126819+77)/9	126820	Robert Price	07/2022
4117	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
4119	(14*10^126784-83)/3	126785	Robert Price	12/2018
4118	2^421169-3001935	126785	Paul Bourdelais	07/2023
4120	2^421161-286183	126783	Enzo Doria	06/2015
4121	(106*10^126726+17)/3	126728	Robert Price	04/2021
4122	30718^13347+13347^30718	126724	Hans Havermann	03/2021
4123	2^420939-113935	126716	Enzo Doria	10/2014
4124	11*23^93048+356	126708	Eric Chen	08/2023
4125	177^56363-2	126703	Lelio R Paula	10/2017
4126	2^420741-113659	126656	Enzo Doria	08/2014
4127	2^420694-21	126642	Lelio R Paula	05/2017
4128	(13*10^126638+437)/9	126639	Robert Price	04/2018
4129	(167*10^126637-17)/3	126639	Robert Price	03/2020
4130	4*10^126625+87	126626	Robert Price	08/2018
4131	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
4132	7*10^126600-99	126601	Robert Price	06/2019
4133	2^420424-59189	126561	Enzo Doria	10/2015
4134	28717^25534+25534^28717	126560	Hans Havermann	03/2021
4135	(86*10^126542+103)/9	126543	Robert Price	12/2021
4136	28922^23655+23655^28922	126503	Hans Havermann	03/2021
4137	2^420126+71893	126471	Enzo Doria	04/2016
4138	(43*10^126441+47)/9	126442	Robert Price	12/2018
4139	8*10^126408+71	126409	Robert Price	05/2022
4140	2^419866+1877059	126393	Enzo Doria	07/2016
4141	29315^20484+20484^29315	126390	Hans Havermann	03/2021
4142	29433^19676+19676^29433	126384	Hans Havermann	03/2021
4143	F(604711)	126377	Henri Lifchitz	02/2005
4144	2^419757+72707	126360	Enzo Doria	04/2016
4145	2^419720-21569	126349	Enzo Doria	07/2013
4146	2^419637+29	126324	Henri Lifchitz	02/2006
4147	31004^11865+11865^31004	126319	Hans Havermann	03/2021
4148	2^419612+1876741	126316	Enzo Doria	07/2016
4149	2^419520+2793271	126289	Enzo Doria	03/2016
4150	(2^419447-5)/369	126264	Lelio R Paula	05/2014
4151	2^419328-1859939	126231	Enzo Doria	03/2016
4152	2^419282-1851507	126217	Enzo Doria	08/2015
4153	(133*10^126212+17)/3	126214	Robert Price	11/2021
4154	2^419251+1866143	126208	Enzo Doria	03/2016
4155	11^121185+2	126202	Robert Price	05/2014
4156	28203^28352+28352^28203	126175	Norbert Schneider	01/2021
4157	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
4158	2^418851+23	126087	Robert Price	09/2015
4159	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
4160	2^418829+167	126081	Lelio R Paula	01/2012
4161	31037^11530+11530^31037	126067	Hans Havermann	03/2021
4162	4*10^126064-69	126065	Robert Price	01/2022
4163	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
4164	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
4165	(35*10^126048-323)/9	126049	Robert Price	10/2021
4166	33016^6551+6551^33016	126000	Hans Havermann	03/2021
4167	2^418548-111546435	125996	Paul Bourdelais	10/2021
4168	34736^4227+4227^34736	125954	Hans Havermann	03/2021
4169	2^418319-109501	125927	Enzo Doria	04/2014
4170	2^418316-112373	125926	Enzo Doria	06/2014
4171	40398^1309+1309^40398	125919	Hans Havermann	03/2021
4172	(8*10^125894-29)/3	125895	Robert Price	07/2018
4173	(26*10^125886-413)/9	125887	Robert Price	05/2018
4174	10^(262938+1)-710^62938-1	125877	Robert Price	07/2023
4175	55*10^125847+9	125849	Robert Price	03/2022
4176	4*10^125832+57	125833	Robert Price	05/2022
4177	2^417968+1869811	125821	Enzo Doria	06/2016
4178	2^417902+63	125802	Lelio R Paula	09/2015
4179	(10^125792-91)/9	125792	Serge Batalov	12/2014
4180	30438^13573+13573^30438	125791	Hans Havermann	03/2021
4181	32867^6714+6714^32867	125782	Hans Havermann	03/2021
4182	31155^10892+10892^31155	125777	Hans Havermann	03/2021
4183	(35*10^125754-593)/9	125755	Robert Price	07/2018
4184	30455^13464+13464^30455	125754	Hans Havermann	03/2021
4185	(32*10^125751-77)/9	125752	Robert Price	06/2018
4186	2^417704+77011	125742	Enzo Doria	05/2016
4187	29755^16816+16816^29755	125737	Hans Havermann	03/2021
4188	(22*10^125734+203)/9	125735	Robert Price	10/2021
4189	29918^15915+15915^29918	125710	Hans Havermann	03/2021
4190	(10^125706+149)/3	125706	Serge Batalov	12/2014
4191	28531^25368+25368^28531	125659	Hans Havermann	03/2021
4192	2^417419-115309	125656	Enzo Doria	07/2015
4193	(46*10^125642+593)/9	125643	Robert Price	04/2022
4194	2^417300+77281	125620	Enzo Doria	05/2016
4195	30638^12537+12537^30638	125561	Hans Havermann	03/2021
4196	2^417095-1657	125559	Yves Minet	07/2014
4197	30162^14525+14525^30162	125538	Hans Havermann	03/2021
4198	(56*10^125535+583)/9	125536	Robert Price	08/2021
4199	(23*10^125517-179)/3	125518	Robert Price	06/2022
4200	9*10^125516+29	125517	Robert Price	03/2022
4201	(88*10^125492-637)/9	125493	Robert Price	11/2020
4202	28958^21525+21525^28958	125474	Hans Havermann	02/2021
4204	2^416773-25	125462	Lelio R Paula	09/2015
4203	(10^125482+7)/162685667/1639829194459	125462	Alfred Reich	07/2021
4205	33889^5032+5032^33889	125449	Hans Havermann	03/2021
4206	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
4207	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
4208	(289511#+1896)/(23^3797801939911849)	125434	Makoto Morimoto	06/2019
4209	2^416641-2*416641+1	125422	Robert Price	05/2018
4210	33392^5697+5697^33392	125409	Hans Havermann	03/2021
4211	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
4212	2^416530+1870429	125389	Enzo Doria	05/2016
4213	(56*10^125385+691)/9	125386	Robert Price	05/2019
4214	27953^28198+28198^27953	125381	Norbert Schneider	01/2021
4215	31074^10837+10837^31074	125381	Hans Havermann	03/2021
4216	33745^5194+5194^33745	125380	Hans Havermann	03/2021
4217	2^416490+1875109	125376	Enzo Doria	09/2016
4218	28360^26331+26331^28360	125365	Hans Havermann	03/2021
4219	2^416416-114929	125354	Enzo Doria	05/2015
4220	(77*10^125330-293)/9	125331	Robert Price	09/2019
4221	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
4222	2^416134+1865899	125269	Enzo Doria	03/2016
4223	153^57337-152	125264	Norbert Schneider	12/2018
4224	(599*10^125224+13)/9	125226	Robert Price	02/2022
4225	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
4226	30054^14657+14657^30054	125207	Hans Havermann	03/2021
4227	(23^91943-1)/22	125201	Robert Price	01/2012
4228	2^415884-933075	125194	Paul Bourdelais	06/2021
4229	43125^27010-106	125185	Enzo Doria	08/2012
4230	(38*10^125166+349)/9	125167	Robert Price	10/2018
4231	10^125166-5001	125166	Robert Price	12/2021
4232	2^415765-112603	125158	Enzo Doria	06/2014
4233	8*10^125088-13	125089	Robert Price	08/2019
4234	(25*10^125076-13)/3	125077	Robert Price	09/2019
4235	(11*10^125054+73)/3	125055	Robert Price	08/2021
4236	(29*10^125021-113)/3	125022	Robert Price	10/2019
4237	2^415290-113591	125015	Enzo Doria	08/2014
4238	2^415276-460919	125011	Enzo Doria	06/2015
4239	2^415259+77243	125006	Enzo Doria	05/2016
4240	(67*10^124990+77)/9	124991	Robert Price	10/2021
4241	2^415144-3683	124971	Yves Minet	10/2011
4242	2^415092+111546435	124956	Paul Bourdelais	10/2021
4243	31936^8173+8173^31936	124946	Hans Havermann	03/2021
4244	5^178715-4	124916	Tyler NeSmith	07/2021
4245	29767^15700+15700^29767	124900	Hans Havermann	03/2021
4246	2^414874+79	124890	Lelio R Paula	01/2015
4247	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
4248	2^414618+79459	124813	Enzo Doria	06/2016
4249	(61*10^124809-1)/3	124811	Robert Price	01/2020
4250	(29*10^124765-71)/3	124766	Robert Price	07/2021

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Probable Primes Top 10000

(293510 PRPs in the top)