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 ?
11001	2^337101-20241	101478	Enzo Doria	06/2013
11002	2^337035-20001	101458	Enzo Doria	06/2013
11003	(7*10^101456+89)/3	101457	Robert Price	08/2020
11004	2^337017-16995	101453	Lelio R Paula	09/2016
11005	(347^40448+1)/(347^512+1)	101451	Martin Hopf	12/2023
11006	(8677^25759-1)/8676	101445	Serge Batalov	06/2022
11007	2^336979-115315	101441	Enzo Doria	06/2015
11008	2^336970-20885	101439	Enzo Doria	06/2013
11009	2^336958+79	101435	Lelio R Paula	10/2009
11010	(1589^31687-1)/1588	101431	Serge Batalov	06/2022
11011	2^336942+169	101430	Lelio R Paula	10/2009
11012	(193929^19321-1)/(193929^139-1)	101428	Ryan Propper	11/2023
11013	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
11014	4*10^101415-89	101416	Robert Price	11/2018
11015	(14*10^101410-89)/3	101411	Robert Price	05/2020
11016	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
11017	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
11018	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
11019	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
11020	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
11021	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
11022	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
11023	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
11024	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
11025	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
11026	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
11027	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
11028	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
11029	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
11030	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
11031	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
11032	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
11033	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
11034	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
11035	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
11036	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
11037	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
11038	24097^16150+16150^24097	101405	Hans Havermann	12/2018
11039	2^336842+94065	101400	Lelio R Paula	09/2016
11040	(7*10^101395-1)/3	101396	Robert Price	08/2022
11041	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
11042	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
11043	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
11044	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
11045	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
11046	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
11047	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
11048	10^101369+203811	101370	Patrick De Geest	11/2016
11049	10^101369-99	101369	Lelio R Paula	09/2016
11050	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
11051	2^336701-113563	101358	Enzo Doria	08/2014
11052	89717!4-512	101351	Robert Price	11/2019
11053	2^336644-109023	101340	Enzo Doria	04/2014
11054	2^336601-21081	101327	Enzo Doria	06/2013
11055	(4*34^66153+227)/33	101312	Eric Chen	03/2023
11056	20^77869+63	101310	Lelio R Paula	09/2016
11057	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
11059	6^130179-137	101299	Lelio R Paula	10/2016
11058	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
11060	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
11061	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
11062	2^336369-19753	101258	Enzo Doria	05/2013
11063	23842^17653+17653^23842	101253	Hans Havermann	11/2018
11064	2^336350-344291	101252	Enzo Doria	07/2015
11065	(17*10^101251-161)/9	101252	Robert Price	02/2021
11066	(56*10^101222-47)/9	101223	Robert Price	02/2019
11067	2^336243-108777	101220	Enzo Doria	03/2014
11068	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
11069	23535^19954+19954^23535	101202	Hans Havermann	11/2018
11070	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
11071	U(618755)/22275181/747456041	101194	Serge Batalov	07/2024
11072	2^336150-20393	101192	Enzo Doria	06/2013
11073	23996^16473+16473^23996	101186	Hans Havermann	11/2018
11074	L(484301)/52304509/5481318719/94549115629	101185	Serge Batalov	07/2024
11075	2^336112-1865249	101180	Enzo Doria	03/2016
11076	2^336103-109015	101178	Enzo Doria	04/2014
11077	(2^336095+2078)/2	101175	Stefano Morozzi	09/2020
11078	2^336060+22201	101165	Enzo Doria	09/2023
11079	13^90809-96	101157	Lelio R Paula	10/2016
11080	26199^7258+7258^26199	101150	Hans Havermann	11/2018
11081	19^79098-30	101147	Lelio R Paula	10/2016
11082	19^79095+88	101144	Lelio R Paula	10/2016
11083	(30826*34^66040-59)/11	101143	Eric Chen	03/2023
11084	12401^24702-24702^12401	101117	Norbert Schneider	07/2022
11085	15^85976+32	101116	Lelio R Paula	10/2016
11086	2^335872-2776215	101108	Tony Prest / Never Odd Or Even	01/2019
11087	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
11088	(4^167933+17)/3	101106	Robert Price	02/2017
11090	2^335858+153	101104	Lelio R Paula	10/2009
11089	(2^335872-2776871)/5/5/479	101104	Tony Prest / Never Odd Or Even	01/2019
11091	(2^335872-2758787)/23/31/20809	101101	Tony Prest / Never Odd Or Even	01/2019
11092	(2^335839+2114)/2	101098	Stefano Morozzi	09/2020
11093	(2^335872-2795083)/3/3/113/283/148367	101097	Tony Prest / Never Odd Or Even	01/2019
11095	6^129918-35	101096	Lelio R Paula	10/2016
11094	(2*10^101096-107)/3	101096	Robert Price	11/2020
11096	3^211885-70	101095	Lelio R Paula	09/2016
11097	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
11098	(2^335872-2794771)/3/5/5/61/232312440293	101093	Tony Prest / Never Odd Or Even	01/2019
11099	2^335818-20033	101092	Enzo Doria	06/2013
11100	2^335813-110083	101090	Enzo Doria	04/2014
11101	2^335804+2155	101088	Lelio R Paula	09/2016
11102	(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021	101087	Tony Prest / Never Odd Or Even	01/2019
11103	2^335784-16145	101082	Enzo Doria	04/2013
11104	11^97051+62	101069	Lelio R Paula	10/2016
11105	3*10^101065+11	101066	Robert Price	07/2018
11106	27820^4293+4293^27820	101064	Hans Havermann	10/2018
11107	(2^335714+3750)/2	101060	Stefano Morozzi	01/2021
11108	(2^335690+1038)/2	101053	Stefano Morozzi	09/2020
11109	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
11110	2^335658-94395	101044	Lelio R Paula	09/2016
11111	24514^13215+13215^24514	101024	Hans Havermann	11/2018
11112	2^335586+169	101022	Lelio R Paula	10/2009
11113	(56^57787-1)/55	101021	Paul Bourdelais	08/2017
11114	(2^335562+1258)/2	101014	Stefano Morozzi	09/2020
11115	2^335541+4849845	101008	Paul Bourdelais	04/2022
11116	(38*10^100999+169)/9	101000	Robert Price	11/2021
11117	(19*10^100997+737)/9	100998	Robert Price	07/2018
11118	(41^62633-1)/312679033600185641560	100993	Paul Vanderveen	05/2025
11119	47599!2+1024	100991	Robert Price	02/2015
11120	2^335468-18629	100986	Enzo Doria	05/2013
11121	2^335454-20961	100982	Enzo Doria	06/2013
11122	(2^335454+3258)/2	100982	Stefano Morozzi	02/2021
11123	10^100978+61	100979	Lelio R Paula	09/2016
11124	10^100978-156437	100978	Patrick De Geest	11/2016
11125	(2^335422+3114)/2	100972	Stefano Morozzi	09/2020
11126	(35*10^100970-89)/9	100971	Robert Price	02/2022
11127	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
11128	2^335403-1859167	100967	Enzo Doria	03/2016
11129	23599^18976+18976^23599	100962	Hans Havermann	10/2018
11130	6*10^100958+43	100959	Robert Price	07/2020
11131	9*2^335364-5	100956	Lelio R Paula	08/2014
11132	(7998^25867-1)/7997	100955	Serge Batalov	06/2022
11133	2^335349+72287	100951	Enzo Doria	04/2016
11134	2^335329+16095	100945	Lelio R Paula	09/2016
11135	232823#+233663	100937	Makoto Morimoto	10/2017
11136	(232823#+10141)/(10141*1674461)	100927	Makoto Morimoto	06/2019
11137	2^335237-20893	100917	Enzo Doria	06/2013
11138	2^335222-19337	100912	Enzo Doria	05/2013
11139	2^335222-109985	100912	Enzo Doria	04/2014
11140	2^335182-17237	100900	Enzo Doria	05/2013
11141	(2^335107+1634)/2	100877	Stefano Morozzi	09/2020
11142	2^335043-16737	100858	Enzo Doria	05/2013
11143	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
11144	2^335038-20633	100857	Enzo Doria	06/2013
11145	2^335031+1873373	100855	Enzo Doria	06/2016
11146	23489^19650+19650^23489	100847	Hans Havermann	10/2018
11147	3^211354-8816	100842	Enzo Doria	05/2014
11148	2^334984-112757	100841	Enzo Doria	06/2014
11149	(746*10^100827+1)/9	100829	Robert Price	03/2020
11150	29451^2648+2648^29451	100809	Hans Havermann	09/2018
11151	25583^8716+8716^25583	100806	Hans Havermann	08/2018
11153	2^334857+48527	100803	Lelio R Paula	08/2011
11152	12^93406+29	100803	Lelio R Paula	10/2016
11154	28780^3179+3179^28780	100796	Hans Havermann	09/2018
11155	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
11156	(328^40063-1)/327	100791	Serge Batalov	06/2022
11157	2^334809-13	100788	Lelio R Paula	04/2011
11158	Phi(506001,2)	100786	Henri Lifchitz	12/2025
11159	(3552^28387-1)/3551	100784	Serge Batalov	06/2022
11160	(82*10^100780-1)/9	100781	Robert Price	12/2014
11161	31395^1622+1622^31395	100780	Hans Havermann	09/2018
11162	(2^334779+47)/5	100778	Lelio R Paula	12/2013
11163	2^334751+2049	100771	Lelio R Paula	09/2016
11164	13^90443-98	100749	Lelio R Paula	10/2016
11165	(2^334674+3190)/2	100747	Stefano Morozzi	09/2020
11166	(2^334651+1050)/2	100740	Stefano Morozzi	09/2020
11167	(7*10^100737+71)/3	100738	Robert Price	05/2018
11168	(24737*2^334628+1)/3	100737	Lelio R Paula	07/2014
11169	15^85639-28	100720	Lelio R Paula	10/2016
11170	27068^5259+5259^27068	100718	Hans Havermann	08/2018
11171	2^334562+577294575	100711	Lelio R Paula	09/2016
11172	4*3^211077-5	100710	Lelio R Paula	08/2014
11173	2^334524+145	100702	Lelio R Paula	07/2009
11174	(2^334451+714)/2	100680	Stefano Morozzi	09/2020
11175	27648^4375+4375^27648	100666	Hans Havermann	09/2018
11176	(1017*2^334391-1)/3535	100662	Lelio R Paula	05/2015
11177	(2^334309+3122)/2	100637	Stefano Morozzi	09/2020
11178	2^334294-113111	100633	Enzo Doria	07/2014
11179	25581^8582+8582^25581	100626	Hans Havermann	08/2018
11181	6^129308-17723	100622	Enzo Doria	03/2013
11180	(19*10^100627+287)/9/292157	100622	Alfred Reich	11/2022
11182	6^129305+95	100619	Lelio R Paula	10/2016
11183	2^334244-1167	100618	Lelio R Paula	09/2016
11184	(2^334233+3066)/2	100614	Stefano Morozzi	09/2020
11185	(76*10^100611+77)/9	100612	Robert Price	10/2019
11186	7*10^100606-93	100607	Robert Price	08/2020
11187	(26*10^100566+49)/3	100567	Robert Price	08/2019
11188	(582^36373-1)/581	100566	Tom Wu	08/2025
11189	(21*2^334050+1)/935	100558	Lelio R Paula	12/2013
11190	24885^10984+10984^24885	100555	Hans Havermann	07/2018
11191	(1351^32119-1)/1350	100551	Serge Batalov	06/2022
11192	(78557*2^334018+1)/4326021	100548	Lelio R Paula	07/2014
11193	(35*10^100542+1)/9	100543	Serge Batalov	11/2010
11194	23578^18367+18367^23578	100538	Hans Havermann	07/2018
11195	13^90251+24	100535	Lelio R Paula	10/2016
11196	2^333963+789	100533	Lelio R Paula	08/2011
11197	2^333919-1840087	100520	Enzo Doria	06/2015
11198	(2^333916+1698)/2	100519	Stefano Morozzi	09/2020
11199	2^333911+72623	100518	Enzo Doria	04/2016
11200	24605^12168+12168^24605	100517	Hans Havermann	08/2018
11201	66*10^100502+7	100504	Robert Price	07/2020
11202	18^80064-67	100503	Lelio R Paula	10/2016
11203	(13*10^100487+137)/3	100488	Robert Price	06/2021
11204	23034^23034-12085^12085	100483	Serge Batalov	04/2024
11205	5^143742-48	100472	Lelio R Paula	10/2016
11206	24095^14784+14784^24095	100472	Hans Havermann	08/2018
11207	2^333757-112123	100471	Enzo Doria	06/2014
11208	(7953^25759-1)/7952	100470	Serge Batalov	06/2022
11209	23030^23030-7401^7401	100464	Serge Batalov	04/2024
11210	7*10^100457-57	100458	Robert Price	06/2020
11211	27358^4693+4693^27358	100444	Hans Havermann	07/2018
11212	8*10^100439-51	100440	Robert Price	08/2019
11213	2^333603-108861	100425	Enzo Doria	03/2014
11214	9*7^118818-2	100414	Lelio R Paula	11/2014
11215	2^333546-17097	100408	Enzo Doria	05/2013
11216	(19*10^100403+287)/9/3	100403	Alfred Reich	11/2022
11217	17^81597+72	100401	Lelio R Paula	10/2016
11218	(3613^28219-1)/3612	100396	Serge Batalov	06/2022
11219	p(20559)#/2+8	100384	Robert Price	01/2017
11220	11^96390-24	100380	Lelio R Paula	10/2016
11221	23011^23011+18846^18846	100373	Serge Batalov	04/2024
11222	(2^333385+2730)/2	100359	Stefano Morozzi	09/2020
11223	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
11224	23565^18136+18136^23565	100353	Hans Havermann	07/2018
11225	2^333354+763	100350	Lelio R Paula	08/2011
11226	(1608961*2^333333+1)/3	100349	Alex_soldier	09/2022
11227	(424517*2^333333+1)/5	100349	Alex_soldier	09/2022
11228	(887087*2^333333+1)/5	100349	Alex_soldier	09/2022
11229	(1159703*2^333333+1)/7	100349	Alex_soldier	09/2022
11230	(25*10^100343-67)/3	100344	Robert Price	06/2019
11231	V(486482)/9729641	100343	Serge Batalov	07/2024
11232	2^333289-109483	100330	Enzo Doria	04/2014
11233	(194^43853-1)/193	100325	Anonymous	06/2024
11234	2^333240-2790209	100316	Enzo Doria	03/2016
11235	23601^17798+17798^23601	100314	Hans Havermann	05/2018
11237	(2^333227-2^166614+1)/5	100311		11/2006
11236	2^333225+719	100311	Lelio R Paula	08/2011
11238	Phi(1332908L,2)	100311	Anonymous	03/2025
11239	2^333221-2785333	100310	Enzo Doria	10/2015
11240	76^53332-75	100308	Norbert Schneider	02/2015
11241	(29*10^100302+583)/9	100303	Robert Price	06/2021
11242	6^128892-17573	100298	Enzo Doria	03/2013
11243	(47*10^100283-119)/9	100284	Robert Price	05/2019
11244	2^333105-113215	100275	Enzo Doria	07/2014
11245	(31*2^333102+1)/2375	100272	Lelio R Paula	11/2013
11246	4*10^100257-83	100258	Robert Price	10/2018
11247	17^81476-74	100253	Lelio R Paula	10/2016
11248	23392^19207+19207^23392	100199	Hans Havermann	06/2018
11249	(2^332830+750)/2	100192	Stefano Morozzi	09/2020
11250	(206*10^100189-17)/9	100191	Robert Price	01/2020

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Probable Primes Top 10000

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