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	(8*10^102541+49)/3	102542	Robert Price	05/2020
5002	(536*10^102533-23)/9	102535	Robert Price	02/2020
5003	2^340547-108897	102515	Enzo Doria	03/2014
5004	(2^340536+778)/2	102512	Stefano Morozzi	09/2020
5005	25592^10119+10119^25592	102500	Hans Havermann	02/2019
5006	7^121268+82	102484	Lelio R Paula	10/2016
5007	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
5008	2^340434-5955	102481	Lelio R Paula	11/2016
5009	(7*10^102480-19)/3	102481	Robert Price	10/2020
5010	(2^340381+47)/7	102465	Lelio R Paula	12/2013
5011	111^50095+110	102461	Norbert Schneider	04/2017
5012	2^340291-20301	102438	Enzo Doria	06/2013
5013	12^94915+89	102431	Lelio R Paula	10/2016
5014	24466^15349+15349^24466	102417	Hans Havermann	03/2019
5015	2^340208-20373	102413	Enzo Doria	06/2013
5016	6^131598-17273	102404	Enzo Doria	02/2013
5017	(2^340132+1182)/2	102390	Stefano Morozzi	09/2020
5018	(2^340133+1166)/2	102390	Stefano Morozzi	09/2020
5019	2^340115-21181	102385	Enzo Doria	06/2013
5020	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
5021	(2^340064+3630)/2	102370	Stefano Morozzi	09/2020
5022	89^52511-88^52511	102365	Robert Price	06/2015
5023	3^214539-112756	102362	Enzo Doria	07/2014
5024	23159^23450-23450^23159	102353	Norbert Schneider	12/2019
5025	2^340000-19877	102351	Enzo Doria	06/2013
5026	2^339990-114845	102348	Enzo Doria	05/2015
5027	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
5028	20^78661-99	102341	Lelio R Paula	09/2016
5029	2^339951-19585	102336	Enzo Doria	05/2013
5030	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
5031	(236282#+121441)/(121441*25499429)	102332	Makoto Morimoto	08/2020
5032	5*10^102323-91	102324	Robert Price	03/2021
5034	2^339889+29327	102317	Yves Minet	06/2010
5033	(167*10^102315-17)/3	102317	Robert Price	03/2020
5035	26348^7641+7641^26348	102314	Hans Havermann	03/2019
5036	Phi(239414,10)/6333218543	102303	Makoto Kamada	08/2019
5037	2^339834-109493	102301	Enzo Doria	04/2014
5038	(16*10^102299-19)/3	102300	Robert Price	02/2019
5039	(11^98221-5^98221)/6	102286	Robert Price	01/2013
5040	3^214365+1820	102279	Lelio R Paula	10/2016
5041	31978^1579+1579^31978	102278	Hans Havermann	03/2019
5042	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
5043	2^339694-16995	102259	Lelio R Paula	09/2016
5044	(56*10^102255+691)/9	102256	Robert Price	05/2019
5045	122^49008+121	102249	Norbert Schneider	10/2018
5046	(2^339652+3178)/2	102246	Stefano Morozzi	09/2020
5047	7^120985-38	102245	Lelio R Paula	10/2016
5048	10^102244+122961	102245	Patrick De Geest	12/2016
5049	10^102244-27	102244	Lelio R Paula	09/2016
5050	7^120982-62	102242	Lelio R Paula	10/2016
5051	(2^339640+2670)/2	102242	Stefano Morozzi	09/2020
5052	4*6^131382-5	102236	Lelio R Paula	11/2014
5053	(2^339607+3290)/2	102232	Stefano Morozzi	02/2021
5054	2^339586-1091	102226	Yves Minet	11/2012
5055	11^98161-3072000	102225	Enzo Doria	12/2012
5056	9*7^120961-4	102225	Lelio R Paula	11/2014
5057	5*3^214250+2	102224	Serge Batalov	10/2010
5058	12^94713-59	102213	Lelio R Paula	10/2016
5059	12^94705+89	102204	Lelio R Paula	10/2016
5060	2^339407-177	102172	Lelio R Paula	08/2011
5061	4*10^102163-57	102164	Robert Price	10/2018
5062	2^339355+65	102157	Lelio R Paula	07/2011
5063	(28*10^102142-31)/3	102143	Robert Price	12/2019
5064	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
5065	(2^339268+1758)/2	102130	Stefano Morozzi	09/2020
5066	s(178551)	102122	Robert Price	05/2020
5067	(2^339175+2790)/2	102102	Stefano Morozzi	02/2021
5070	2^339168+21	102100	Lelio R Paula	07/2011
5068	2^339167-108807	102100	Enzo Doria	03/2014
5069	(2^339169+42)/2	102100	Stefano Morozzi	09/2020
5071	2^339156+163	102097	Lelio R Paula	08/2011
5072	(2^339149+746)/2	102094	Stefano Morozzi	09/2020
5073	(25*10^102076-67)/3	102077	Robert Price	06/2019
5074	2^339081-4543	102074	Yves Minet	03/2019
5075	2*10^102062+77	102063	Robert Price	08/2020
5076	24327^15668+15668^24327	102053	Hans Havermann	02/2019
5077	25080^11711+11711^25080	102041	Hans Havermann	02/2019
5078	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
5079	2^338891-18885	102017	Enzo Doria	05/2013
5080	8*10^102000+51	102001	Robert Price	08/2019
5081	(2^338832+642)/2	101999	Stefano Morozzi	09/2020
5082	2^338829-113239	101998	Enzo Doria	07/2014
5083	2^338828-113297	101998	Enzo Doria	07/2014
5084	2^338796+93	101988	Donovan Johnson	06/2008
5085	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
5086	25295^10744+10744^25295	101969	Hans Havermann	01/2019
5087	25712^9243+9243^25712	101969	Hans Havermann	01/2019
5088	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
5089	2^338682-19865	101954	Enzo Doria	06/2013
5090	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
5091	(2^338666+3154)/2	101949	Stefano Morozzi	09/2020
5092	28594^3673+3673^28594	101939	Hans Havermann	02/2019
5093	(2^338587+2306)/2	101925	Stefano Morozzi	02/2021
5094	2^338568+37	101920	Lelio R Paula	07/2011
5095	2^338559-1858777	101917	Enzo Doria	04/2016
5096	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
5097	24502^14419+14419^24502	101903	Hans Havermann	01/2019
5098	2^338497-17041	101898	Enzo Doria	05/2013
5099	2^338475+54615	101892	Lelio R Paula	10/2016
5100	2^338426-19797	101877	Enzo Doria	06/2013
5101	2^338368-20369	101859	Enzo Doria	06/2013
5102	2^338366+74179	101859	Enzo Doria	04/2016
5103	27088^5755+5755^27088	101853	Hans Havermann	01/2019
5104	2^338280-19745	101833	Enzo Doria	06/2013
5105	(2^338242+2782)/2	101821	Stefano Morozzi	02/2021
5106	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
5107	6^130841+103	101815	Lelio R Paula	10/2016
5108	2^338122-20117	101785	Enzo Doria	06/2013
5109	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
5110	35^65917-7092	101781	Enzo Doria	03/2013
5111	2^338010-19833	101752	Enzo Doria	06/2013
5112	3^213215-76	101730	Lelio R Paula	09/2016
5113	23907^17998+17998^23907	101730	Hans Havermann	01/2019
5114	10^101728+154953	101729	Patrick De Geest	02/2020
5117	2^337930+63	101728	Lelio R Paula	07/2011
5115	10^101728-987654321	101728	Robert Price	12/2019
5116	10^101728-60741	101728	Patrick De Geest	02/2020
5118	2^337920+1869661	101725	Enzo Doria	05/2016
5119	24116^16509+16509^24116	101715	Hans Havermann	01/2019
5120	(2^337875+3174)/2	101711	Stefano Morozzi	09/2020
5121	2^337859-19645	101706	Enzo Doria	05/2013
5122	2^337754+1869169	101675	Enzo Doria	05/2016
5123	3*10^101657-37	101658	Robert Price	07/2018
5124	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
5125	11^97605-24	101646	Lelio R Paula	10/2016
5126	(2^337624+3606)/2	101635	Stefano Morozzi	09/2020
5127	8^112539-112539	101633	Robert Price	01/2014
5128	(2^337575+1818)/2	101620	Stefano Morozzi	02/2021
5129	25694^9003+9003^25694	101605	Hans Havermann	12/2018
5130	2^337515-19869	101603	Enzo Doria	06/2013
5131	2^337473+719	101590	Lelio R Paula	08/2011
5132	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
5134	2^337452-108815	101584	Enzo Doria	03/2014
5133	2^337453+1185	101584	Lelio R Paula	09/2016
5135	2^337410-113561	101571	Enzo Doria	08/2014
5136	2^337387+855	101564	Lelio R Paula	09/2016
5137	2^337367-17295	101558	Lelio R Paula	09/2016
5138	2^337342-109035	101551	Enzo Doria	04/2014
5139	23703^19238+19238^23703	101548	Hans Havermann	12/2018
5140	(26*10^101537-167)/3	101538	Robert Price	10/2019
5141	2^337267-19	101528	Lelio R Paula	07/2011
5142	(2^337259+1766)/2	101525	Stefano Morozzi	09/2020
5143	(2^337257+2306)/2	101525	Stefano Morozzi	02/2021
5144	(2^337195+2646)/2	101506	Stefano Morozzi	09/2020
5145	2^337183-19989	101503	Enzo Doria	06/2013
5146	2^337149+72425	101492	Enzo Doria	04/2016
5147	24041^16642+16642^24041	101483	Hans Havermann	12/2018
5148	33982^969+969^33982	101482	Hans Havermann	12/2018
5149	2^337101-20241	101478	Enzo Doria	06/2013
5150	2^337035-20001	101458	Enzo Doria	06/2013
5151	(7*10^101456+89)/3	101457	Robert Price	08/2020
5152	2^337017-16995	101453	Lelio R Paula	09/2016
5153	2^336979-115315	101441	Enzo Doria	06/2015
5154	2^336970-20885	101439	Enzo Doria	06/2013
5155	2^336958+79	101435	Lelio R Paula	10/2009
5156	2^336942+169	101430	Lelio R Paula	10/2009
5157	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
5158	4*10^101415-89	101416	Robert Price	11/2018
5159	(14*10^101410-89)/3	101411	Robert Price	05/2020
5160	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
5161	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
5162	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
5163	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
5164	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
5165	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
5166	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
5167	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
5168	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
5169	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
5170	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
5171	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
5172	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
5173	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
5174	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
5175	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
5176	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
5177	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
5178	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
5179	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
5180	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
5181	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
5182	24097^16150+16150^24097	101405	Hans Havermann	12/2018
5183	2^336842+94065	101400	Lelio R Paula	09/2016
5184	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
5185	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
5186	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
5187	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
5188	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
5189	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
5190	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
5191	10^101369+203811	101370	Patrick De Geest	11/2016
5192	10^101369-99	101369	Lelio R Paula	09/2016
5193	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
5194	2^336701-113563	101358	Enzo Doria	08/2014
5195	89717!4-512	101351	Robert Price	11/2019
5196	2^336644-109023	101340	Enzo Doria	04/2014
5197	2^336601-21081	101327	Enzo Doria	06/2013
5198	20^77869+63	101310	Lelio R Paula	09/2016
5199	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
5200	6^130179-137	101299	Lelio R Paula	10/2016
5201	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
5202	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
5203	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
5204	2^336369-19753	101258	Enzo Doria	05/2013
5205	23842^17653+17653^23842	101253	Hans Havermann	11/2018
5207	2^336350-344291	101252	Enzo Doria	07/2015
5206	(17*10^101251-161)/9	101252	Robert Price	02/2021
5208	(56*10^101222-47)/9	101223	Robert Price	02/2019
5209	2^336243-108777	101220	Enzo Doria	03/2014
5210	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
5211	23535^19954+19954^23535	101202	Hans Havermann	11/2018
5212	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
5213	2^336150-20393	101192	Enzo Doria	06/2013
5214	23996^16473+16473^23996	101186	Hans Havermann	11/2018
5215	2^336112-1865249	101180	Enzo Doria	03/2016
5216	2^336103-109015	101178	Enzo Doria	04/2014
5217	(2^336095+2078)/2	101175	Stefano Morozzi	09/2020
5218	13^90809-96	101157	Lelio R Paula	10/2016
5219	26199^7258+7258^26199	101150	Hans Havermann	11/2018
5220	19^79098-30	101147	Lelio R Paula	10/2016
5221	19^79095+88	101144	Lelio R Paula	10/2016
5222	15^85976+32	101116	Lelio R Paula	10/2016
5223	2^335872-2776215	101108	Tony Prest / Never Odd Or Even	01/2019
5224	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
5225	(4^167933+17)/3	101106	Robert Price	02/2017
5227	2^335858+153	101104	Lelio R Paula	10/2009
5226	(2^335872-2776871)/5/5/479	101104	Tony Prest / Never Odd Or Even	01/2019
5228	(2^335872-2758787)/23/31/20809	101101	Tony Prest / Never Odd Or Even	01/2019
5229	(2^335839+2114)/2	101098	Stefano Morozzi	09/2020
5230	(2^335872-2795083)/3/3/113/283/148367	101097	Tony Prest / Never Odd Or Even	01/2019
5231	6^129918-35	101096	Lelio R Paula	10/2016
5232	(2*10^101096-107)/3	101096	Robert Price	11/2020
5233	3^211885-70	101095	Lelio R Paula	09/2016
5235	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
5234	(2^335872-2794771)/3/5/5/61/232312440293	101093	Tony Prest / Never Odd Or Even	01/2019
5236	2^335818-20033	101092	Enzo Doria	06/2013
5237	2^335813-110083	101090	Enzo Doria	04/2014
5238	2^335804+2155	101088	Lelio R Paula	09/2016
5239	(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021	101087	Tony Prest / Never Odd Or Even	01/2019
5240	2^335784-16145	101082	Enzo Doria	04/2013
5241	11^97051+62	101069	Lelio R Paula	10/2016
5242	3*10^101065+11	101066	Robert Price	07/2018
5243	27820^4293+4293^27820	101064	Hans Havermann	10/2018
5244	(2^335714+3750)/2	101060	Stefano Morozzi	01/2021
5245	(2^335690+1038)/2	101053	Stefano Morozzi	09/2020
5246	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
5247	2^335658-94395	101044	Lelio R Paula	09/2016
5248	24514^13215+13215^24514	101024	Hans Havermann	11/2018
5249	2^335586+169	101022	Lelio R Paula	10/2009
5250	(56^57787-1)/55	101021	Paul Bourdelais	08/2017

Find by discoverer :

PRP Records

Probable Primes Top 10000

(280932 PRPs in the top)