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 ?
9251	2^346058+57933	104174	Stefano Morozzi	11/2024
9257	2^346055-19537	104173	Enzo Doria	05/2013
9258	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
9252	2^346052+26655	104173	Stefano Morozzi	11/2024
9253	2^346052+31611	104173	Stefano Morozzi	11/2024
9254	2^346053+67667	104173	Stefano Morozzi	11/2024
9255	2^346054+30507	104173	Stefano Morozzi	11/2024
9256	2^346054+194589	104173	Stefano Morozzi	11/2024
9259	2^346049+59067	104172	Stefano Morozzi	11/2024
9260	2^346050+3129	104172	Stefano Morozzi	11/2024
9261	2^346050+167125	104172	Stefano Morozzi	11/2024
9262	2^346051+52563	104172	Stefano Morozzi	11/2024
9263	2^346051+90941	104172	Stefano Morozzi	11/2024
9264	2^346046+172107	104171	Stefano Morozzi	11/2024
9265	2^346048+63415	104171	Stefano Morozzi	11/2024
9266	2^346041+197885	104169	Stefano Morozzi	11/2024
9270	2^346037-20125	104168	Enzo Doria	06/2013
9267	2^346036+80773	104168	Stefano Morozzi	11/2024
9268	2^346037+116429	104168	Stefano Morozzi	11/2024
9269	2^346038+147549	104168	Stefano Morozzi	11/2024
9271	2^346034+2205	104167	Stefano Morozzi	11/2024
9272	2^346031+56429	104166	Stefano Morozzi	11/2024
9273	2^346031+68439	104166	Stefano Morozzi	11/2024
9274	2^346031+114891	104166	Stefano Morozzi	11/2024
9275	2^346031+190563	104166	Stefano Morozzi	11/2024
9276	2^346026+179305	104165	Stefano Morozzi	11/2024
9277	2^346027+159425	104165	Stefano Morozzi	11/2024
9278	2^346028+12517	104165	Stefano Morozzi	11/2024
9279	2^346022+84705	104164	Stefano Morozzi	11/2024
9280	2^346019+73673	104163	Stefano Morozzi	11/2024
9281	2^346019+78999	104163	Stefano Morozzi	11/2024
9282	2^346019+79955	104163	Stefano Morozzi	11/2024
9283	2^346020+72993	104163	Stefano Morozzi	11/2024
9284	2^346020+188673	104163	Stefano Morozzi	11/2024
9285	2^346021+100311	104163	Stefano Morozzi	11/2024
9289	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
9286	2^346016+84007	104162	Stefano Morozzi	11/2024
9287	2^346017+122397	104162	Stefano Morozzi	11/2024
9288	2^346017+165791	104162	Stefano Morozzi	11/2024
9290	2^346014+27949	104161	Stefano Morozzi	11/2024
9291	2^346014+46743	104161	Stefano Morozzi	11/2024
9292	2^346015+166089	104161	Stefano Morozzi	11/2024
9293	2^346009+107705	104160	Stefano Morozzi	11/2024
9294	2^346012+35043	104160	Stefano Morozzi	11/2024
9295	2^346012+83091	104160	Stefano Morozzi	11/2024
9303	6^133854-17993	104159	Enzo Doria	03/2013
9296	2^346006+77727	104159	Stefano Morozzi	11/2024
9297	2^346008+9007	104159	Stefano Morozzi	11/2024
9298	2^346008+51567	104159	Stefano Morozzi	11/2024
9299	2^346008+107787	104159	Stefano Morozzi	11/2024
9300	2^346008+146191	104159	Stefano Morozzi	11/2024
9301	2^346008+170823	104159	Stefano Morozzi	11/2024
9302	(131^49201-1)/7538466025870	104159	Paul Vanderveen	06/2025
9304	2^346003+191519	104158	Stefano Morozzi	11/2024
9305	2^345990+1874239	104154	Enzo Doria	06/2016
9306	2^345988-20373	104153	Enzo Doria	06/2013
9307	(2^345965+2214)/2	104146	Stefano Morozzi	09/2020
9308	406^39922+405	104138	Alfred Reich	03/2026
9309	(26*10^104132-503)/9	104133	Robert Price	07/2018
9310	3*5^148968+8	104125	Lelio R Paula	11/2014
9311	(7*10^104113+53)/3	104114	Robert Price	05/2018
9312	p(21253)#/2+8	104113	Robert Price	01/2017
9313	33582^1259+1259^33582	104106	Hans Havermann	09/2020
9314	32958^1441+1441^32958	104104	Hans Havermann	09/2020
9315	29127^3748+3748^29127	104095	Hans Havermann	09/2020
9316	322^41507+41507^322	104094	Norbert Schneider	12/2014
9317	6^133768-17423	104092	Enzo Doria	03/2013
9318	2^345786-19557	104092	Enzo Doria	05/2013
9319	171^46606-2	104072	Lelio R Paula	10/2017
9320	(29*10^104071+91)/3	104072	Robert Price	04/2020
9321	norm(Mod(x,x^3-x-1)^852167-1)	104070	Paul Vanderveen	09/2022
9322	2^345704-149	104068	Lelio R Paula	09/2011
9323	25821^10712+10712^25821	104056	Hans Havermann	09/2020
9324	(2^345662+2038)/2	104055	Stefano Morozzi	09/2020
9325	6^133704-17273	104042	Enzo Doria	02/2013
9326	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
9327	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
9328	2^345547+11	104021	Lelio R Paula	09/2011
9329	(19*10^104014-49)/3	104015	Robert Price	05/2019
9330	(2^345519+1794)/2	104012	Stefano Morozzi	01/2021
9331	2^345504+723	104008	Lelio R Paula	09/2011
9332	2^345498-20037	104006	Enzo Doria	06/2013
9334	18^82854-37	104005	Lelio R Paula	01/2017
9333	(2^345497+2070)/2	104005	Stefano Morozzi	09/2020
9335	2^345486-109065	104002	Enzo Doria	04/2014
9336	2^345487-1851507	104002	Enzo Doria	08/2015
9337	2^345476+777	103999	Lelio R Paula	09/2011
9338	(2^345477+1554)/2	103999	Stefano Morozzi	09/2020
9339	4*10^103981-83	103982	Robert Price	10/2018
9340	815^35716+814	103975	Alfred Reich	06/2026
9341	(2^345327+3206)/2	103954	Stefano Morozzi	09/2020
9342	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
9343	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
9344	(19*10^103907+77)/3	103908	Robert Price	05/2019
9345	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
9346	2^345106-112181	103888	Enzo Doria	06/2014
9347	(2^345105+1326)/2	103887	Stefano Morozzi	02/2021
9348	2^345079+99	103880	Lelio R Paula	09/2011
9349	(2^345034+1198)/2	103866	Stefano Morozzi	09/2020
9350	11^99736-1500	103865	Enzo Doria	12/2012
9351	(569^37699-1)/568	103863	Serge Batalov	06/2022
9352	(2^345010+2082)/2	103859	Stefano Morozzi	09/2020
9353	23263^23784-23784^23263	103857	Norbert Schneider	01/2020
9354	3*10^103844+31	103845	Robert Price	06/2021
9355	444*33^68368+19	103821	Eric Chen	05/2023
9356	23927^21814+21814^23927	103813	Hans Havermann	09/2020
9357	2^344842-20157	103808	Enzo Doria	06/2013
9358	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
9359	2^344802-20765	103796	Enzo Doria	06/2013
9360	2^344794-3821	103794	Yves Minet	05/2011
9361	2^344782-109103	103790	Enzo Doria	04/2014
9362	3^217521-112292	103784	Enzo Doria	06/2014
9363	2^344759-3505	103783	Lelio R Paula	11/2016
9364	2^344735-147	103776	Lelio R Paula	09/2011
9365	L(496533)-p(496533)	103770	Robert Price	02/2018
9366	2*10^103749-69	103750	Robert Price	03/2018
9367	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
9368	2^344607-108891	103738	Enzo Doria	03/2014
9370	(2^344608+3798)/2	103738	Stefano Morozzi	02/2021
9369	(1097^34123-1)/1096	103738	Serge Batalov	06/2022
9371	2^344560+22411	103723	Enzo Doria	09/2023
9372	(148*10^103718-1)/3	103720	Robert Price	03/2020
9373	2^344541-19561	103718	Enzo Doria	05/2013
9374	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
9375	(8896^26263-1)/8895	103714	Serge Batalov	06/2022
9376	(2^344503+1758)/2	103706	Stefano Morozzi	09/2020
9377	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
9378	2^344444-455	103688	Yves Minet	03/2012
9379	(4*10^103678-43)/3	103679	Robert Price	01/2022
9380	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
9381	(2^344367+2738)/2	103665	Stefano Morozzi	01/2021
9383	2^344317-109933	103650	Enzo Doria	04/2014
9382	26055^9508+9508^26055	103650	Hans Havermann	09/2020
9384	2^344309-1852033	103648	Enzo Doria	08/2015
9385	25729^10672+10672^25729	103643	Hans Havermann	09/2020
9386	(2^344289+1166)/2	103642	Stefano Morozzi	09/2020
9387	3*10^103637+61	103638	Robert Price	09/2020
9388	(2^344246+1614)/2	103629	Stefano Morozzi	09/2020
9389	2^344213-21253	103619	Enzo Doria	06/2013
9390	2^344196-465	103614	Lelio R Paula	11/2016
9391	2^344187-20001	103611	Enzo Doria	06/2013
9392	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
9393	(237^43627-1)/236	103601	Serge Batalov	06/2022
9394	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
9395	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
9396	(9^108553-2^108553)/7	103586	Jon Grantham	07/2023
9397	2^344085-20365	103580	Enzo Doria	06/2013
9398	5^148169+54	103566	Lelio R Paula	11/2016
9399	2^344017-108795	103560	Enzo Doria	03/2014
9400	(2^343974+2670)/2	103547	Stefano Morozzi	09/2020
9401	2^343971-5077	103546	Lelio R Paula	09/2011
9402	(7*10^103531+71)/3	103532	Robert Price	05/2018
9403	2^343899+141	103524	Lelio R Paula	08/2011
9404	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
9405	6^133029-67	103517	Lelio R Paula	11/2016
9406	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
9407	66*10^103507+7	103509	Robert Price	07/2020
9408	26297^8614+8614^26297	103485	Hans Havermann	09/2020
9409	(2^343764+2658)/2	103483	Stefano Morozzi	09/2020
9410	26499^8036+8036^26499	103480	Hans Havermann	09/2020
9411	(103^51413-1)/4478483706	103477	Paul Vanderveen	06/2025
9412	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
9413	5^148014-24	103458	Lelio R Paula	11/2016
9414	25^74007-24	103458	Anonymous	09/2024
9415	28316^4503+4503^28316	103453	Hans Havermann	09/2020
9416	(22*10^103450+53)/3	103451	Robert Price	07/2019
9417	2^343604+9931	103436	Yves Minet	01/2011
9418	2^343601-21189	103435	Enzo Doria	06/2013
9419	(10^103423+173)/3	103423	Robert Price	05/2021
9420	2^343508-115229	103407	Enzo Doria	06/2015
9421	(8766^26227-1)/8765	103404	Serge Batalov	06/2022
9422	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
9423	3^216685-113056	103386	Enzo Doria	07/2014
9424	24829^14580+14580^24829	103382	Hans Havermann	08/2020
9425	91355!4+1024	103381	Robert Price	09/2019
9426	774^35787+773	103380	Alfred Reich	06/2026
9427	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
9428	11^99262-20	103371	Lelio R Paula	12/2016
9429	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
9430	(2^343363+3570)/2	103363	Stefano Morozzi	09/2020
9431	2^343356-2791889	103361	Enzo Doria	03/2016
9432	(25*10^103360-241)/9	103361	Robert Price	05/2018
9433	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
9434	(371*33^68040-19)/32	103321	Eric Chen	05/2023
9435	24826^14511+14511^24826	103319	Hans Havermann	09/2020
9436	2^343182-171	103309	Lelio R Paula	08/2011
9437	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
9438	(16487^24649-1)/(16487^157-1)	103287	Ryan Propper	11/2023
9439	(10680^25639-1)/10679	103285	Serge Batalov	06/2022
9440	(7427^26683-1)/7426	103282	Serge Batalov	06/2022
9441	2^343079-1835611	103278	Enzo Doria	05/2015
9442	2^343063-1147	103273	Yves Minet	06/2013
9443	24741^14930+14930^24741	103271	Hans Havermann	09/2020
9444	(16*10^103255-73)/3	103256	Robert Price	07/2020
9445	(219^44119-1)/218	103256	Serge Batalov	06/2022
9446	9*6^132689+7	103254	Lelio R Paula	11/2014
9447	2^342979-18085	103247	Enzo Doria	05/2013
9448	(16*10^103244-31)/3	103245	Robert Price	03/2019
9449	2^342966-16995	103244	Lelio R Paula	11/2016
9450	23797^21774+21774^23797	103230	Hans Havermann	09/2020
9451	25388^11637+11637^25388	103224	Hans Havermann	09/2020
9452	(2^342876+2086)/2	103216	Stefano Morozzi	09/2020
9453	(16*10^103214-31)/3	103215	Robert Price	03/2019
9455	(37*10^103211+611)/9	103212	Robert Price	11/2018
9454	(238*10^103210-1)/3	103212	Robert Price	04/2020
9456	5^147650+16	103203	Lelio R Paula	11/2016
9457	gcd(Phi(852060,10),(10^42603+1)^3(10^42603+1-10^21302)+(10^85206+10^42603)(10^21302+1)+10^127809)	103201	Serge Batalov	04/2015
9458	Phi(852060L,10)	103201	Anonymous	03/2025
9459	2^342817+2707067	103199	Enzo Doria	03/2016
9460	43^63177-42	103198	Theodore Burton	02/2007
9461	2^342805-21025	103195	Enzo Doria	06/2013
9462	24129^18890+18890^24129	103182	Hans Havermann	09/2020
9463	(622*10^103171-1)/9	103173	Robert Price	11/2021
9464	2^342714+12285	103168	Lelio R Paula	11/2016
9465	(2*10^103161-17)/3	103161	Serge Batalov	11/2022
9466	18^82178-4481	103156	Enzo Doria	03/2013
9467	2^342665-17349	103153	Enzo Doria	05/2013
9468	30408^2467+2467^30408	103150	Hans Havermann	09/2020
9469	(5^147571-3^147571)/2	103148	Kellen Shenton	05/2022
9470	(2^342615+3090)/2	103138	Stefano Morozzi	09/2020
9471	2^342612+175	103137	Lelio R Paula	08/2011
9472	5*2^342585-3	103130	Lelio R Paula	09/2014
9473	(16*10^103127+77)/3	103128	Robert Price	03/2019
9474	(2^342527+3774)/2	103111	Stefano Morozzi	02/2021
9475	2^342503-19209	103104	Enzo Doria	05/2013
9476	(2^342484+2586)/2	103098	Stefano Morozzi	09/2020
9477	2^342476+51	103096	Lelio R Paula	08/2011
9478	2^342460-18885	103091	Enzo Doria	05/2013
9479	(2^342442+862)/2	103086	Stefano Morozzi	02/2021
9480	(194*10^103074-17)/3	103076	Robert Price	09/2020
9481	7^121968+82	103075	Lelio R Paula	10/2016
9482	2^342392-108863	103071	Enzo Doria	03/2014
9483	(2^342389+806)/2	103070	Stefano Morozzi	01/2021
9484	3^216014+28	103065	Lelio R Paula	11/2016
9485	2^342353-108879	103059	Enzo Doria	03/2014
9486	10^103055+276081	103056	Patrick De Geest	12/2016
9487	10^103055-53	103055	Lelio R Paula	11/2016
9488	763^35750+762	103051	Alfred Reich	06/2026
9489	(58*10^103046+419)/9	103047	Robert Price	05/2019
9490	7^121933+4	103046	Lelio R Paula	11/2014
9491	(71*10^103028-143)/9	103029	Robert Price	10/2021
9492	reverse(2^342243)-1	103026	Anonymous	07/2026
9493	(2^342235+3618)/2	103023	Stefano Morozzi	09/2020
9494	19^80560-68	103017	Lelio R Paula	10/2016
9495	2^342209+76607	103016	Enzo Doria	05/2016
9497	328^40945+40945^328	103013	Norbert Schneider	12/2014
9496	12^95454-91	103013	Lelio R Paula	10/2016
9498	25833^9716+9716^25833	103009	Hans Havermann	01/2019
9499	(893*10^103004+7)/9	103006	Robert Price	06/2021
9500	(1475^32503-1)/1474	102993	Serge Batalov	06/2022

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