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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
5002	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
5003	30639^19136+19136^30639	131192	Hans Havermann	04/2021
5004	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
5005	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
5006	2^435773+1875557	131181	Enzo Doria	06/2016
5008	(16*10^131180+167)/3	131181	Robert Price	06/2019
5007	(26*10^131180-77)/3	131181	Robert Price	11/2019
5009	(25*10^131144-7)/9	131145	Robert Price	05/2018
5010	29299^29358-29358^29299	131138	Norbert Schneider	03/2022
5011	2^435612-2789939	131133	Enzo Doria	12/2015
5012	33976^7231+7231^33976	131121	Hans Havermann	03/2021
5013	33715^7746+7746^33715	131121	Hans Havermann	03/2021
5014	66^72047-65^72047	131093	Robert Price	09/2013
5015	(5*10^131090+37)/3	131091	Robert Price	03/2018
5016	2^435468+75631	131089	Enzo Doria	04/2016
5017	37^83588-2	131083	Lelio R Paula	08/2015
5018	(4^217720+11)/3	131081	Robert Price	02/2017
5019	30407^20448+20448^30407	131074	Hans Havermann	04/2021
5020	(22*10^131070+179)/3	131071	Robert Price	02/2022
5021	28831^29388-29388^28831	131067	Frank Doornink	05/2024
5022	29487^27836+27836^29487	131059	Hans Havermann	04/2021
5023	29962^23615+23615^29962	131030	Hans Havermann	03/2021
5024	2^435202-113193	131009	Enzo Doria	07/2014
5025	41705^1384+1384^41705	131002	Hans Havermann	04/2021
5026	9*10^130998-19	130999	Robert Price	07/2019
5027	36243^4108+4108^36243	130969	Hans Havermann	04/2021
5028	(445^49433+1)/446	130914	Jinyuan Wang	05/2024
5029	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
5030	2^434835-111937	130899	Enzo Doria	05/2014
5031	(62*10^130895-629)/9	130896	Robert Price	07/2021
5032	2^434807+225	130890	Henri Lifchitz	11/2024
5033	2^434685+72257	130854	Enzo Doria	04/2016
5034	(7*10^130825+113)/3	130826	Robert Price	02/2018
5035	2^434539-29317	130810	Enzo Doria	07/2015
5036	(74*10^130791+637)/9	130792	Robert Price	01/2022
5037	2^434469-114259	130789	Enzo Doria	01/2015
5038	(5*10^130763+103)/9	130763	Robert Price	04/2022
5039	2^434246+33	130722	Robert Price	11/2015
5040	30156^21599+21599^30156	130710	Hans Havermann	04/2021
5041	(17*10^130695-161)/9	130696	Robert Price	02/2021
5042	30513^19148+19148^30513	130661	Hans Havermann	03/2021
5043	29736^24761+24761^29736	130654	Hans Havermann	04/2021
5044	9*10^130638+41	130639	Robert Price	08/2020
5045	2^433911-91	130621	Lelio R Paula	06/2017
5046	30786^17449+17449^30786	130588	Hans Havermann	03/2021
5047	2^433744-114419	130570	Enzo Doria	02/2015
5049	2^433708+1869451	130560	Enzo Doria	05/2016
5048	2^433710+93	130560	Lelio R Paula	06/2017
5050	7*10^130535-27	130536	Robert Price	11/2022
5051	(9629^32768+1)/120501441265666	130520	Kellen Shenton	05/2021
5052	804*34^85220+713	130516	Eric Chen	08/2023
5053	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
5054	3^273521+10	130503	Tyler NeSmith	01/2021
5055	41659^1356+1356^41659	130487	Hans Havermann	03/2021
5056	4*10^130480+9	130481	Robert Price	05/2015
5057	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
5058	3*2^433422+5	130474	Jon Grantham	07/2023
5059	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
5060	(31*10^130414-49)/9	130415	Robert Price	11/2021
5061	26462^29485-29485^26462	130402	Frank Doornink	03/2024
5062	33481^7848+7848^33481	130401	Hans Havermann	03/2021
5063	(17*10^130393+7)/3	130394	Robert Price	06/2023
5064	(22*10^130392+203)/9	130393	Robert Price	10/2021
5065	29773^23950+23950^29773	130386	Hans Havermann	04/2021
5066	2^433023-113497	130353	Enzo Doria	08/2014
5067	31175^15178+15178^31175	130350	Hans Havermann	04/2021
5068	2^433002+1179379	130347	Enzo Doria	06/2016
5069	2^432974+19	130339	Robert Price	08/2015
5070	31903^12168+12168^31903	130331	Hans Havermann	04/2021
5071	2^432917+22217	130322	Enzo Doria	09/2023
5072	29387^27112+27112^29387	130278	Hans Havermann	04/2021
5073	2^432768+213181	130277	Enzo Doria	09/2023
5074	29577^25370+25370^29577	130267	Hans Havermann	04/2021
5075	31738^12685+12685^31738	130231	Hans Havermann	03/2021
5076	44235^878+878^44235	130206	Hans Havermann	04/2021
5077	32160^11171+11171^32160	130187	Hans Havermann	04/2021
5078	29489^25956+25956^29489	130172	Hans Havermann	04/2021
5079	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
5080	33005^8766+8766^33005	130133	Hans Havermann	04/2021
5081	(35*10^130132-611)/9	130133	Robert Price	02/2022
5082	(444^49408+1)/(444^256+1)	130125	Martin Hopf	12/2023
5083	2^432217+41	130111	Lelio R Paula	06/2017
5084	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
5085	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
5086	97^65480-2	130094	Lelio R Paula	05/2017
5087	36007^4102+4102^36007	130094	Hans Havermann	04/2021
5088	4*10^130088-89	130089	Robert Price	11/2018
5089	2^432117-113215	130081	Enzo Doria	07/2014
5090	(4*10^130080+41)/9	130080	Serge Batalov	11/2022
5091	2^431804+72511	129986	Enzo Doria	04/2016
5092	27902^29237-29237^27902	129978	Frank Doornink	03/2024
5093	(2313^38809-1)/(2313^197-1)	129898	Ryan Propper	11/2023
5094	(13*10^129896+137)/3	129897	Robert Price	06/2021
5095	(13*10^129890+71)/3	129891	Robert Price	06/2021
5096	29048^29101-29101^29048	129882	Norbert Schneider	03/2022
5097	37832^2709+2709^37832	129871	Hans Havermann	04/2021
5098	31055^15184+15184^31055	129853	Hans Havermann	04/2021
5100	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
5099	Phi(1632846L,3)	129844	Anonymous	03/2025
5101	31385^13702+13702^31385	129833	Hans Havermann	04/2021
5102	(13*10^129826+41)/9	129827	Tyler Busby	02/2023
5103	28901^29102-29102^28901	129822	Norbert Schneider	03/2022
5104	(47*10^129789-119)/9	129790	Robert Price	05/2019
5105	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
5106	25999^29384-29384^25999	129730	Frank Doornink	03/2024
5107	25771^29408-29408^25771	129723	Frank Doornink	02/2024
5108	(166*10^129712+17)/3	129714	Robert Price	07/2022
5109	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
5110	2^430807+1869563	129686	Enzo Doria	05/2016
5111	2^430721-21429	129660	Enzo Doria	07/2013
5112	(4*10^129618+89)/3	129619	Robert Price	08/2021
5113	(142^60223-1)/141	129616	Anonymous	06/2024
5114	(10^129587-7^129587)/3	129587	Jon Grantham	07/2023
5115	2^430415-276271	129568	Enzo Doria	07/2015
5116	32282^10311+10311^32282	129558	Hans Havermann	04/2021
5117	29486^24741+24741^29486	129545	Hans Havermann	04/2021
5118	(29*10^129543+313)/9	129544	Robert Price	04/2021
5119	37095^3104+3104^37095	129533	Hans Havermann	04/2021
5120	31132^14459+14459^31132	129514	Hans Havermann	04/2021
5121	32582^9435+9435^32582	129506	Hans Havermann	03/2021
5122	30442^17953+17953^30442	129505	Hans Havermann	03/2021
5123	(199*10^129487-7)/3	129489	Robert Price	05/2020
5124	2^430142-2791721	129486	Enzo Doria	03/2016
5125	(7*10^129472-13)/3	129473	Robert Price	07/2018
5126	(8*10^129469+79)/3	129470	Robert Price	10/2020
5127	31678^12213+12213^31678	129463	Hans Havermann	04/2021
5128	10620^32143-10619^32143	129412	Norbert Schneider	08/2023
5129	(772*10^129406-7)/9	129408	Robert Price	06/2022
5130	(535^47431-1)/534	129406	Tom Wu	09/2024
5131	((320425-8193)F(618977)-(20425-8193)*L(618977))/2	129363	Yaroslav Berezhko	03/2025
5132	31100^14439+14439^31100	129362	Hans Havermann	04/2021
5133	33009^8288+8288^33009	129345	Hans Havermann	04/2021
5134	25895^29306-29306^25895	129334	Frank Doornink	03/2024
5135	(44^78697+43^78697)/87	129333	Aurel Gibier	11/2023
5136	29675^22804+22804^29675	129324	Hans Havermann	04/2021
5137	29068^28099+28099^29068	129315	Hans Havermann	04/2021
5138	2^429568-21017	129313	Enzo Doria	07/2013
5139	(10^129295+83)/3	129295	Robert Price	08/2021
5140	(853*10^129274-7)/9	129276	Robert Price	07/2021
5141	30958^14961+14961^30958	129249	Hans Havermann	04/2021
5142	(11*10^129239-179)/3	129240	Robert Price	09/2018
5143	28659^28988+28988^28659	129208	Norbert Schneider	02/2021
5144	29423^24616+24616^29423	129203	Hans Havermann	03/2021
5145	2^429194-112685	129201	Enzo Doria	06/2014
5146	2^429145-2780449	129186	Enzo Doria	04/2016
5147	32500^9427+9427^32500	129168	Hans Havermann	04/2021
5148	33577^7014+7014^33577	129136	Hans Havermann	03/2021
5149	2^428892-113453	129110	Enzo Doria	07/2014
5150	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
5151	2^428727-113959	129060	Enzo Doria	10/2014
5152	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
5153	(10^129051-31)/3	129051	Serge Batalov	12/2014
5154	(134*10^129038+7)/3	129040	Robert Price	02/2020
5155	2^428564+71161	129011	Enzo Doria	04/2016
5156	28781^28930+28930^28781	129002	Norbert Schneider	02/2021
5157	29065^27424+27424^29065	128995	Hans Havermann	04/2021
5158	2^428502-113285	128992	Enzo Doria	07/2014
5159	2^428421-21373	128968	Enzo Doria	06/2013
5160	L(616787)	128901	Henri Lifchitz	09/2008
5161	(765^44701-1)/764	128900	Tom Wu	07/2024
5162	20^99055-3	128874	Paul Bourdelais	12/2020
5163	91^65772-2	128851	Lelio R Paula	05/2017
5164	2^428022+43	128848	Lelio R Paula	05/2017
5165	2^427999-459397	128841	Enzo Doria	05/2015
5166	2^427993+76847	128839	Enzo Doria	05/2016
5167	31059^14060+14060^31059	128833	Hans Havermann	03/2021
5168	10^128805+152871	128806	Patrick De Geest	05/2021
5169	10^128805-10001	128805	Robert Price	02/2021
5170	2^427824-1851507	128788	Enzo Doria	08/2015
5171	2^427807-21469	128783	Enzo Doria	07/2013
5172	29082^26783+26783^29082	128772	Hans Havermann	04/2021
5173	40055^1638+1638^40055	128750	Hans Havermann	04/2021
5174	(923^43411-1)/922	128720	Tom Wu	07/2024
5175	11^123594-240	128710	Enzo Doria	09/2012
5176	2^427504-21503	128692	Enzo Doria	07/2013
5177	37727^2574+2574^37727	128673	Hans Havermann	04/2021
5178	29686^21591+21591^29686	128668	Hans Havermann	04/2021
5179	10^128668-70000000001	128668	Robert Price	08/2021
5180	10^128668-350729	128668	Alfred Reich	08/2024
5181	2^427420+91	128667	Lelio R Paula	05/2017
5182	8*10^128651-37	128652	Robert Price	03/2022
5183	(68*10^128645-257)/9	128646	Robert Price	07/2019
5184	2^427269-113635	128621	Enzo Doria	08/2014
5185	2^427130+1877569	128579	Enzo Doria	08/2016
5186	2^427068+20011	128561	Enzo Doria	06/2023
5187	2^427016-115349	128545	Enzo Doria	07/2015
5188	2^427001+1334025	128541	Henri Lifchitz	11/2024
5189	(4*10^128510+137)/3	128511	Robert Price	03/2018
5190	2^426889-112879	128507	Enzo Doria	06/2014
5191	2^426804+1869931	128481	Enzo Doria	05/2016
5192	2^426750+77635	128465	Enzo Doria	05/2016
5193	27708^28913-28913^27708	128450	Frank Doornink	03/2024
5194	36988^2969+2969^36988	128445	Hans Havermann	03/2021
5195	36664^3185+3185^36664	128439	Hans Havermann	03/2021
5196	32618^8649+8649^32618	128416	Hans Havermann	04/2021
5197	28883^27874+27874^28883	128391	Hans Havermann	04/2021
5198	2^426425-91	128367	Lelio R Paula	05/2017
5199	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
5200	2^426352+74971	128345	Enzo Doria	04/2016
5201	(199*10^128343-7)/3	128345	Robert Price	05/2020
5202	4*10^128343-21	128344	Robert Price	09/2018
5203	(65*10^128338+493)/9	128339	Robert Price	08/2021
5204	35632^3997+3997^35632	128337	Hans Havermann	04/2021
5205	2^426300-1863689	128330	Enzo Doria	03/2016
5206	2^426293+1881017	128327	Enzo Doria	11/2016
5207	(88*10^128324-637)/9	128325	Robert Price	11/2020
5208	(491*10^128285+31)/9	128287	Robert Price	04/2022
5209	39103^1908+1908^39103	128281	Hans Havermann	04/2021
5210	2^426043+35	128252	Robert Price	11/2015
5211	(4*10^128244-19)/3	128245	Robert Price	03/2018
5212	26220^29021-29021^26220	128234	Frank Doornink	03/2024
5213	35489^4102+4102^35489	128222	Hans Havermann	04/2021
5214	34721^4926+4926^34721	128208	Hans Havermann	04/2021
5215	(305*10^128198+1)/9	128200	Robert Price	02/2020
5216	2^425808-459959	128181	Enzo Doria	06/2015
5217	30632^15291+15291^30632	128178	Hans Havermann	04/2021
5218	U(623603)	128177	Serge Batalov	07/2024
5219	35981^3648+3648^35981	128167	Hans Havermann	04/2021
5220	2^425627-113605	128127	Enzo Doria	08/2014
5221	(4*10^128109+119)/3	128110	Robert Price	12/2021
5222	(22*10^128094+53)/3	128095	Robert Price	07/2019
5223	(86*10^128086-221)/9	128087	Robert Price	09/2019
5224	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
5225	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
5226	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
5227	Phi(149401,10)/30037901719561	128003	Makoto Kamada	07/2022
5228	2^425205+4911	128000	Marek Hubal	02/2017
5229	29241^23836+23836^29241	127995	Hans Havermann	04/2021
5230	2^425118-113663	127974	Enzo Doria	08/2014
5231	(86*10^127967-329)/9	127968	Robert Price	01/2020
5232	2^425061+1869761	127957	Enzo Doria	05/2016
5233	746^44541+44541^746	127955	Norbert Schneider	07/2019
5234	30236^17043+17043^30236	127946	Hans Havermann	03/2021
5235	2^424938+212419	127920	Enzo Doria	08/2023
5236	2^424918-21141	127914	Enzo Doria	07/2013
5237	(62*10^127903+91)/9	127904	Robert Price	07/2021
5238	2^424864-29489	127897	Enzo Doria	08/2015
5239	30438^15893+15893^30438	127877	Hans Havermann	02/2021
5240	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
5241	28929^26258+26258^28929	127845	Hans Havermann	03/2021
5242	30563^15220+15220^30563	127828	Hans Havermann	03/2021
5243	2^424632-2786639	127827	Enzo Doria	03/2016
5244	10^127821-700001	127821	Robert Price	08/2021
5245	2^424577-113755	127811	Enzo Doria	09/2014
5246	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
5247	(56*10^127752+691)/9	127753	Robert Price	05/2019
5248	11^122629-720	127705	Enzo Doria	11/2012
5249	22*10^127645+3	127647	Robert Price	01/2020
5250	28715^27844+27844^28715	127631	Hans Havermann	03/2021

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301352 PRPs in the top)