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 ?
6001	34575^3182+3182^34575	121106	Hans Havermann	02/2021
6002	5*10^121100-37	121101	Robert Price	11/2021
6003	F(579521)/516247738177	121101	Serge Batalov	07/2024
6004	25592^27467-27467^25592	121078	Frank Doornink	02/2024
6005	29954^10935+10935^29954	120979	Hans Havermann	02/2021
6006	33585^3992+3992^33585	120946	Hans Havermann	02/2021
6007	40296^1003+1003^40296	120941	Hans Havermann	02/2021
6008	2^401725-113251	120932	Enzo Doria	07/2014
6009	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
6010	2^401652+73711	120910	Enzo Doria	04/2016
6011	(2^401632+3)/79	120902	Lelio R Paula	04/2014
6012	40450^973+973^40450	120870	Hans Havermann	01/2021
6013	(8*10^120851-11)/3	120852	Robert Price	07/2023
6014	10^120841+88417	120842	Patrick De Geest	04/2020
6015	10^120841-123456789	120841	Robert Price	02/2020
6016	10^120841-176853	120841	Patrick De Geest	04/2020
6017	2^401406-2791331	120836	Enzo Doria	03/2016
6018	(28^83497+1)/29	120832	Robert Price	07/2013
6019	(22*10^120828+161)/3	120829	Robert Price	05/2019
6020	2^401369+1867367	120825	Enzo Doria	03/2016
6021	(5*10^120821+43)/3	120822	Robert Price	12/2021
6022	26990^27263-27263^26990	120808	Frank Doornink	03/2024
6023	(10^120782+29)/3	120782	Serge Batalov	12/2014
6024	2^401215-1657	120778	Yves Minet	07/2014
6025	2^401159+53	120761	Lelio R Paula	10/2013
6026	27782^22179+22179^27782	120739	Hans Havermann	01/2021
6027	242^50649-50649^242	120738	Norman Luhn	09/2024
6028	32974^4585+4585^32974	120730	Hans Havermann	02/2021
6029	2^401031-113047	120723	Enzo Doria	07/2014
6030	30598^8813+8813^30598	120713	Hans Havermann	02/2021
6031	(71*10^120703-287)/9	120704	Robert Price	09/2019
6032	25671^27370-27370^25671	120687	Frank Doornink	02/2024
6033	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
6034	34793^2940+2940^34793	120675	Hans Havermann	02/2021
6035	26028^27329-27329^26028	120670	Frank Doornink	03/2024
6036	(2^400846+538)/2	120667	Stefano Morozzi	09/2020
6037	(166*10^120654+11)/3	120656	Robert Price	03/2021
6038	34066^3481+3481^34066	120652	Hans Havermann	02/2021
6039	8*10^120637-27	120638	Robert Price	10/2021
6040	(2^400709+3546)/2	120626	Stefano Morozzi	09/2020
6041	(2^400700+3126)/2	120623	Stefano Morozzi	09/2020
6042	(2^400693+2634)/2	120621	Stefano Morozzi	09/2020
6043	9*10^120617-61	120618	Robert Price	06/2021
6044	(29*10^120590-71)/3	120591	Robert Price	07/2021
6045	2^400571-15	120584	Lelio R Paula	10/2013
6046	(10^120574+359)/9	120574	Serge Batalov	12/2014
6047	(8*10^120552-17)/9	120552	Serge Batalov	11/2022
6048	27431^24810+24810^27431	120550	Hans Havermann	02/2021
6049	2^400424-216413	120540	Enzo Doria	04/2013
6050	29090^13911+13911^29090	120531	Hans Havermann	02/2021
6051	(2^400346+1722)/2	120516	Stefano Morozzi	09/2020
6052	27899^20868+20868^27899	120510	Hans Havermann	02/2021
6053	33740^3729+3729^33740	120506	Hans Havermann	02/2021
6054	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
6055	1069^39770-39770^1069	120463	Norbert Schneider	05/2025
6057	2^400166+1874899	120462	Enzo Doria	06/2016
6056	(2^400165+1602)/2	120462	Stefano Morozzi	09/2020
6058	2739^35038-35038^2739	120447	Norbert Schneider	05/2025
6059	37078^1771+1771^37078	120438	Hans Havermann	02/2021
6060	(2^400084+1638)/2	120437	Stefano Morozzi	09/2020
6061	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
6062	2^399999+54173	120412	Norman Luhn	08/2023
6063	(2^399974+2790)/2	120404	Stefano Morozzi	02/2021
6064	2^399966+73759	120402	Enzo Doria	04/2016
6065	(2^399961+2306)/2	120400	Stefano Morozzi	02/2021
6066	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
6067	2^399918-95	120388	Lelio R Paula	04/2013
6068	2^399918+214009	120388	Enzo Doria	10/2023
6069	(28*10^120381-67)/3	120382	Robert Price	10/2020
6070	(49*10^120380-139)/9	120381	Robert Price	03/2019
6071	(2^399874+2194)/2	120374	Stefano Morozzi	09/2020
6072	2^399792-1849259	120350	Enzo Doria	08/2015
6073	9*10^120342-7	120343	Robert Price	09/2015
6074	(2^399751+786)/2	120337	Stefano Morozzi	09/2020
6075	(331*10^120332-7)/9	120334	Robert Price	04/2022
6076	(13*10^120306-37)/3	120307	Robert Price	01/2019
6077	(23*10^120299+37)/3	120300	Robert Price	02/2022
6078	25935^27254-27254^25935	120297	Frank Doornink	03/2024
6079	(2^399604+3070)/2	120293	Stefano Morozzi	09/2020
6080	(2^399549+1062)/2	120276	Stefano Morozzi	09/2020
6081	2^399526-1861721	120270	Enzo Doria	11/2015
6082	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
6083	32016^5687+5687^32016	120217	Hans Havermann	01/2021
6084	(205*10^120212-1)/3	120214	Robert Price	11/2021
6085	2^399322-2798111	120208	Enzo Doria	04/2016
6086	30438^8867+8867^30438	120163	Hans Havermann	02/2021
6087	3^251841-5*2^251841	120159	Jon Grantham	08/2023
6089	72^64693-71^64693	120157	Robert Price	03/2014
6088	(17*10^120156-161)/9	120157	Robert Price	02/2021
6090	2^399111-28489	120145	Enzo Doria	08/2015
6091	2958^34607-34607^2958	120121	Norbert Schneider	04/2025
6092	(2^399014+1318)/2	120115	Stefano Morozzi	02/2021
6093	30254^9333+9333^30254	120110	Hans Havermann	02/2021
6094	2^398972+6561	120103	Henri Lifchitz	10/2024
6095	30882^7745+7745^30882	120101	Hans Havermann	02/2021
6097	2^398877+105	120074	Donovan Johnson	01/2006
6096	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
6098	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
6099	U(686581)/4280145953	120067	Serge Batalov	07/2024
6100	16651^28442-28442^16651	120067	Norbert Schneider	07/2025
6101	12284^29359-29359^12284	120059	Norbert Schneider	06/2025
6102	3207^34240-34240^3207	120049	Norbert Schneider	04/2025
6103	2^398710+57	120024	Lelio R Paula	04/2013
6104	(2^398698+1138)/2	120020	Stefano Morozzi	09/2020
6105	2^398691-115057	120018	Enzo Doria	06/2015
6106	12134^29385-29385^12134	120009	Norbert Schneider	06/2025
6107	6089^31710-31710^6089	120008	Norbert Schneider	05/2025
6108	L(574219)	120005	Renaud Lifchitz	03/2004
6109	2^398571+60413	119982	Yves Minet	03/2011
6110	28623^15538+15538^28623	119971	Hans Havermann	02/2021
6111	p(24179)#/2-64	119949	Robert Price	04/2017
6112	2^398448+1872001	119945	Enzo Doria	05/2016
6113	(10^119946*19-91)/6093	119944	Alfred Reich	10/2023
6114	(19*10^119946-91)/9/677	119944	Alfred Reich	11/2023
6115	(191*10^119941-17)/3	119943	Robert Price	11/2021
6116	634^42803+42803^634	119938	Norbert Schneider	07/2019
6117	31083^7220+7220^31083	119935	Hans Havermann	01/2021
6118	(68*10^119931-11)/3	119933	Robert Price	01/2020
6119	8*10^119930-3	119931	Ray Chandler	04/2011
6120	(2^398398+774)/2	119930	Stefano Morozzi	09/2020
6121	(10^119880+179)/9	119880	Serge Batalov	12/2014
6122	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
6123	(10^119836+77)/3	119836	Robert Price	01/2018
6124	26681^27074-27074^26681	119835	Frank Doornink	03/2024
6125	28179^17870+17870^28179	119821	Hans Havermann	02/2021
6126	2^398029+1872527	119819	Enzo Doria	05/2016
6127	33142^4119+4119^33142	119802	Hans Havermann	01/2021
6128	2^397897-113541	119779	Enzo Doria	08/2014
6129	28636^15171+15171^28636	119728	Hans Havermann	02/2021
6130	87^61730-61730^87	119727	Norman Luhn	09/2024
6131	(10556^29929-1)/(10556^173-1)	119724	Ryan Propper	11/2023
6132	(2^397696+1042)/2	119719	Stefano Morozzi	09/2020
6134	(19*10^119716+101)/3	119717	Robert Price	09/2019
6133	29563^11208+11208^29563	119717	Hans Havermann	02/2021
6135	458^44991-44991^458	119715	Norman Luhn	09/2024
6136	2^397655-933075	119707	Paul Bourdelais	06/2021
6137	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
6138	28243^17308+17308^28243	119701	Hans Havermann	02/2021
6139	77*10^119688+3	119690	Robert Price	06/2020
6140	586*25^85601+3717	119668	Eric Chen	10/2023
6141	(2^397504+1698)/2	119661	Stefano Morozzi	09/2020
6142	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
6143	2^397426+73849	119638	Enzo Doria	04/2016
6144	8*10^119509+29	119510	Robert Price	11/2021
6145	2^396933-112723	119489	Enzo Doria	06/2014
6146	11^114738-150	119488	Enzo Doria	10/2012
6147	(4*10^119474+149)/9	119474	Robert Price	04/2018
6148	26964^26964-13^13	119472	Henri Lifchitz	08/2024
6149	2^396790-21	119446	Lelio R Paula	04/2013
6150	32061^5300+5300^32061	119405	Hans Havermann	01/2021
6151	(2^396633-7)/5	119398	Lelio R Paula	04/2014
6152	27382^22913+22913^27382	119388	Hans Havermann	03/2021
6153	(2^396577+2522)/2	119382	Stefano Morozzi	09/2020
6154	(2^396492+2230)/2	119356	Stefano Morozzi	01/2021
6155	(47*10^119354+259)/9	119355	Robert Price	03/2022
6157	105^59050+104	119352	Norbert Schneider	11/2016
6156	126^56824-125	119352	Norbert Schneider	12/2018
6158	2^396469+111546435	119350	Paul Bourdelais	10/2021
6159	139^55690-138	119345	Norbert Schneider	04/2019
6160	790^41179+41179^790	119322	Norbert Schneider	04/2019
6161	2^396374+73729	119321	Enzo Doria	04/2016
6163	88*10^119295+3	119297	Robert Price	05/2020
6162	21*29^81575+129664	119297	Eric Chen	06/2025
6164	2^396258-459491	119286	Enzo Doria	05/2015
6165	(2^396248+3126)/2	119283	Stefano Morozzi	09/2020
6166	2^396128-396128-1	119247	Karsten Bonath	06/2018
6167	(893*10^119228+7)/9	119230	Robert Price	06/2021
6168	(31*10^119229+257)/9	119230	Robert Price	12/2021
6169	(28*10^119206-67)/3	119207	Robert Price	10/2020
6170	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
6171	11^114458+6	119196	Paul Bourdelais	02/2021
6172	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
6173	(2^395902+202)/2	119179	Stefano Morozzi	09/2020
6174	(2^395825+582)/2	119155	Stefano Morozzi	09/2020
6175	(2^395733+1130)/2	119128	Stefano Morozzi	09/2020
6176	(23^119099)%(10^119099)	119099	Henri Lifchitz	05/2025
6177	29548^10725+10725^29548	119091	Hans Havermann	02/2021
6178	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
6179	(30^80599+1)/31	119054	Robert Price	07/2013
6180	(232*10^119047+17)/3	119049	Robert Price	04/2021
6181	(43*10^119024-403)/9	119025	Robert Price	01/2019
6182	(4*10^119021+47)/3	119022	Robert Price	01/2022
6183	fibonacci(569433)+3	119005	Jon Grantham	08/2023
6184	26603^26888-26888^26603	118978	Norbert Schneider	07/2021
6185	912^40193-40193^912	118972	Norman Luhn	09/2024
6186	681^41992-41992^681	118970	Norman Luhn	09/2024
6187	6*10^118964+43	118965	Robert Price	07/2020
6188	(8*10^118960+49)/3	118961	Robert Price	05/2020
6189	31253^6402+6402^31253	118959	Hans Havermann	02/2021
6190	(194*10^118925-17)/3	118927	Robert Price	09/2020
6191	2^395062-109121	118926	Enzo Doria	04/2014
6192	2^395055-4627	118924	Yves Minet	05/2019
6193	(2^395054+702)/2	118923	Stefano Morozzi	09/2020
6194	2^395018-224141	118913	Harrison Mesh	06/2022
6195	(2^395011+2526)/2	118910	Stefano Morozzi	09/2020
6196	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
6197	25771^26948-26948^25771	118872	Frank Doornink	02/2024
6198	374^46201-46201^374	118870	Norman Luhn	09/2024
6199	(2^394858+1018)/2	118864	Stefano Morozzi	09/2020
6200	(77*10^118862-149)/9	118863	Robert Price	03/2022
6201	(16*10^118852+77)/3	118853	Robert Price	03/2019
6202	fibonacci(568658)-2	118843	Jon Grantham	08/2023
6203	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
6204	10^118772+163599	118773	Patrick De Geest	02/2021
6206	10^118772-40000000001	118772	Robert Price	09/2020
6205	10^118772-207603	118772	Patrick De Geest	02/2021
6207	26842^26577+26577^26842	118763	Hans Havermann	02/2021
6208	(2^394513+2034)/2	118760	Stefano Morozzi	09/2020
6209	(2^394473+2774)/2	118748	Stefano Morozzi	02/2021
6210	27949^17710+17710^27949	118734	Hans Havermann	02/2021
6211	2^394266+71389	118686	Enzo Doria	04/2016
6212	(10^118681-3^118681)/7	118681	Jon Grantham	08/2023
6213	2^394215-51261	118671	Tony Prest / Never Odd Or Even	04/2018
6214	(2^394215-48793)/5/5	118670	Tony Prest / Never Odd Or Even	04/2018
6215	(2^394215-17063)/3/3/5	118669	Tony Prest / Never Odd Or Even	04/2018
6216	(2^394215-24393)/5/5/5/5/5	118668	Tony Prest / Never Odd Or Even	04/2018
6217	(2^394215-35885)/3/71/173	118666	Tony Prest / Never Odd Or Even	04/2018
6218	(2^394215-47925)/353/2269	118665	Tony Prest / Never Odd Or Even	04/2018
6219	29201^11568+11568^29201	118652	Hans Havermann	02/2021
6220	(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673	118650	Tony Prest / Never Odd Or Even	04/2018
6221	(2^394131+2214)/2	118645	Stefano Morozzi	09/2020
6222	(17*10^118635+13)/3	118636	Robert Price	01/2019
6223	5^169727+2	118635	Lelio R Paula	08/2013
6224	2^394034-3	118617	M. Frind & P. Underwood	09/2002
6225	(7*10^118607+179)/3	118608	Robert Price	09/2018
6226	3^248572-6242	118599	Enzo Doria	05/2014
6227	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
6228	(49*10^118576-319)/9	118577	Robert Price	10/2021
6229	7^140303-6	118570	Robert Price	11/2014
6230	(2^393864+2686)/2	118565	Stefano Morozzi	09/2020
6231	(2^393862+3150)/2	118564	Stefano Morozzi	09/2020
6232	(2^393849+3762)/2	118561	Stefano Morozzi	01/2021
6233	(529*10^118554-7)/9	118556	Robert Price	08/2021
6234	26712^26777-26777^26712	118534	Norbert Schneider	07/2021
6235	(2^393661+2666)/2	118504	Stefano Morozzi	09/2020
6236	(2^393650+1614)/2	118501	Stefano Morozzi	09/2020
6237	27655^19264+19264^27655	118495	Hans Havermann	02/2021
6238	10^118485+469413	118486	Patrick De Geest	05/2021
6239	10^118485-50001	118485	Robert Price	08/2020
6240	(2^393528+1030)/2	118464	Stefano Morozzi	09/2020
6241	2^393427+75683	118434	Enzo Doria	04/2016
6242	2^393376-114749	118418	Enzo Doria	04/2015
6243	(65*10^118417+493)/9	118418	Robert Price	08/2021
6244	30960^6671+6671^30960	118397	Hans Havermann	02/2021
6245	(2^393234+2010)/2	118375	Stefano Morozzi	09/2020
6246	(2^393205+3030)/2	118367	Stefano Morozzi	09/2020
6247	(2^393191+2174)/2	118362	Stefano Morozzi	09/2020
6248	2^393180+73	118359	Lelio R Paula	04/2013
6249	3*2^393125+5	118343	Jon Grantham	07/2023
6250	27546^19771+19771^27546	118339	Hans Havermann	02/2021

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PRP Records

Probable Primes Top 10000

(301737 PRPs in the top)