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 ?
7251	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
7252	(4^231439)%(3^231439)	110425	Henri Lifchitz	06/2025
7253	2^366816+315	110423	Lelio R Paula	05/2017
7254	(11^2667520)/(10^2667520)	110416	Henri Lifchitz	06/2025
7255	2^366775-2787037	110411	Enzo Doria	03/2016
7256	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
7257	2^366751+2797553	110404	Enzo Doria	03/2016
7258	25276^23331+23331^25276	110404	Hans Havermann	10/2020
7259	2^366748+255	110403	Lelio R Paula	05/2017
7260	2^366738-2985	110400	Yves Minet	09/2014
7261	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
7262	(2^366722+1314)/2	110395	Stefano Morozzi	02/2021
7263	2^366716+1871791	110393	Enzo Doria	05/2016
7264	(239*23^81066-349)/22	110391	Eric Chen	08/2023
7265	2^366695+1334025	110387	Henri Lifchitz	10/2024
7266	(5^528189)%F(528189)	110385	Henri Lifchitz	06/2025
7267	2^366649+1871687	110373	Enzo Doria	05/2016
7268	2^366629-351205	110367	Enzo Doria	06/2015
7269	(31*10^110363+257)/9	110364	Robert Price	12/2021
7270	(5^183291)%(4^183291)	110353	Henri Lifchitz	06/2025
7271	(17*19^86292-215)/18	110347	Eric Chen	01/2023
7273	2^366558+1874479	110345	Enzo Doria	06/2016
7272	25132^24581+24581^25132	110345	Hans Havermann	10/2020
7274	(2^366539+770)/2	110339	Stefano Morozzi	09/2020
7275	26368^15285+15285^26368	110331	Hans Havermann	10/2020
7276	(23*10^110290+19)/3	110291	Robert Price	07/2019
7277	18^87853-4409	110280	Enzo Doria	03/2013
7278	28490^7419+7419^28490	110267	Hans Havermann	11/2020
7279	2^366218-23	110243	Lelio R Paula	02/2013
7280	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
7281	2^366178-343991	110231	Enzo Doria	07/2015
7282	12^102123-11	110210	Riley Fisher	09/2023
7283	(725*35^71368+16649)/34	110199	Eric Chen	05/2025
7284	25777^18798+18798^25777	110174	Hans Havermann	10/2020
7285	2^365944+1871341	110161	Enzo Doria	05/2016
7286	2^365838-461267	110129	Enzo Doria	07/2015
7287	30152^4491+4491^30152	110126	Hans Havermann	11/2020
7288	2^365802+23359	110118	Enzo Doria	10/2023
7289	10^110111+464019	110112	Patrick De Geest	05/2021
7290	10^110111-40001	110111	Robert Price	01/2021
7291	2^365763-6555	110106	Lelio R Paula	04/2017
7292	(2^365689+2^182845+1)/5	110083		11/2006
7293	(83^57367-1)/3536509644718	110080	Paul Vanderveen	05/2025
7294	2^365666-459161	110077	Enzo Doria	05/2015
7295	3*10^110076-7	110077	Robert Price	08/2015
7296	(102936^21961-1)/102935	110076	Anonymous	09/2025
7297	13^98785-72	110041	Lelio R Paula	03/2017
7299	(25^78707+1)/26	110027	Robert Price	06/2013
7298	(7*10^110027-277)/9	110027	Robert Price	02/2022
7300	(16*10^110014-73)/3	110015	Robert Price	07/2020
7301	(7*10^110006-151)/9	110006	Robert Price	02/2018
7302	6^141361-7	110001	Lelio R Paula	11/2014
7303	10^110000+8029681	110001	Hayden Chesnut	11/2024
7304	10^110000+2044477	110001	Hayden Chesnut	11/2024
7305	10^110000+76407	110001	Hayden Chesnut	11/2024
7306	10^110000+167311	110001	Hayden Chesnut	11/2024
7307	20^84536+81	109984	Lelio R Paula	03/2017
7308	5*2^365347-9	109982	Lelio R Paula	09/2014
7309	9*6^141303+7	109957	Lelio R Paula	11/2014
7310	27635^9522+9522^27635	109953	Hans Havermann	11/2020
7311	78^58099+77	109929	Norbert Schneider	02/2015
7312	2*10^109928-7	109929	Robert Price	10/2015
7313	30580^3933+3933^30580	109927	Hans Havermann	11/2020
7314	26380^14689+14689^26380	109926	Hans Havermann	11/2020
7315	(2^365161+1130)/2	109925	Stefano Morozzi	09/2020
7316	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
7317	29^75157-30	109910	Anonymous	09/2024
7318	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
7319	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
7320	(2^365069+3774)/2	109897	Stefano Morozzi	02/2021
7321	29652^5083+5083^29652	109894	Mark Rodenkirch	10/2020
7322	(2^365049+722)/2	109891	Stefano Morozzi	09/2020
7323	(35*10^109888-89)/9	109889	Robert Price	02/2022
7324	18^87533-11	109878	Lelio R Paula	04/2017
7325	2^364982-5	109871	Henri Lifchitz	04/2006
7326	3*10^109861+59	109862	Robert Price	08/2018
7327	5*10^109860-69	109861	Robert Price	02/2021
7328	2^364936-1867979	109857	Enzo Doria	04/2016
7329	27013^11652+11652^27013	109846	Hans Havermann	10/2020
7330	2^364867-112087	109836	Enzo Doria	06/2014
7331	4^182415-85061	109825	Mike Oakes	06/2011
7332	(2^364809+1034)/2	109819	Stefano Morozzi	09/2020
7333	24972^24972-8323^8323	109814	Henri Lifchitz	10/2024
7334	(53*10^109809-287)/9	109810	Robert Price	02/2022
7335	(52*10^109807-133)/9	109808	Robert Price	09/2021
7336	25708^18675+18675^25708	109806	Hans Havermann	10/2020
7337	(17^89227+16^89227)/33	109788	Robert Price	08/2013
7338	2^364687-187	109782	Lelio R Paula	01/2012
7339	2^364644+67	109769	Lelio R Paula	01/2012
7340	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
7341	(2^364616+5)/9	109760	Lelio R Paula	01/2014
7342	(55*10^109759+89)/9	109760	Robert Price	03/2019
7343	(14*32^72921+4171)/31	109757	Eric Chen	04/2023
7344	12^101694+73	109747	Lelio R Paula	03/2017
7345	13^98518-66	109744	Lelio R Paula	03/2017
7346	(35^71069+2^71069)/37	109734	Robert Price	01/2025
7347	(8*10^109721-269)/9	109721	Robert Price	09/2021
7348	2^364478-113261	109719	Enzo Doria	07/2014
7349	(2^364513+1)/(3*44290516579)	109719	Gord Palameta	08/2018
7350	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
7351	27814^8777+8777^27814	109681	Hans Havermann	10/2020
7352	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
7353	3^229824+340	109654	Lelio R Paula	03/2017
7354	(16623*33^72206-8095)/16	109649	Eric Chen	05/2023
7355	(2*10^109645-71)/3	109645	Robert Price	12/2017
7356	V(786978)	109644	Serge Batalov	07/2024
7357	2^364169-112813	109626	Enzo Doria	06/2014
7358	28822^6359+6359^28822	109622	Hans Havermann	11/2020
7359	10^109615+21	109616	Lelio R Paula	03/2017
7360	10^109615-456267	109615	Patrick De Geest	03/2017
7361	522^40331-40331^522	109607	Norman Luhn	09/2024
7362	2^364094-113	109604	Lelio R Paula	01/2012
7363	25251^21898+21898^25251	109600	Hans Havermann	11/2020
7364	(4^182026+11)/3	109591	Robert Price	02/2017
7365	2^364041-6883	109588	Lelio R Paula	09/2011
7366	12^101545+11	109586	Lelio R Paula	03/2017
7367	26536^13475+13475^26536	109582	Hans Havermann	11/2020
7368	2^363842-2787101	109528	Enzo Doria	03/2016
7369	(2^363812+3570)/2	109519	Stefano Morozzi	09/2020
7370	(996^36527+1)/997	109515	Jinyuan Wang	12/2024
7371	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
7372	2^363769+5711	109506	Lelio R Paula	04/2017
7373	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
7374	26^77372+25	109480	Anonymous	09/2024
7375	(2^363670+100280245065)	109476	Paul Bourdelais	05/2022
7376	p(22245)#/2-8	109462	Robert Price	01/2017
7377	2^363556+55	109442	Lelio R Paula	01/2012
7378	(509*10^109414+31)/9	109416	Robert Price	08/2022
7379	(2^363437+1682)/2	109406	Stefano Morozzi	09/2020
7380	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
7381	2^363406+1871569	109397	Enzo Doria	05/2016
7382	(129^51829-1)/128	109388	Anonymous	06/2024
7383	(2^363370+1338)/2	109385	Stefano Morozzi	02/2021
7384	(2^363349+7)/9	109378	Lelio R Paula	01/2014
7385	(13869^26569-1)/(13869^163-1)	109375	Ryan Propper	11/2023
7386	3^229236+100	109374	Lelio R Paula	03/2017
7387	(2^363315+3258)/2	109369	Stefano Morozzi	02/2021
7388	2^363268-58695	109355	Lelio R Paula	04/2017
7389	2^363191-112321	109332	Enzo Doria	06/2014
7390	26231^14718+14718^26231	109327	Hans Havermann	10/2020
7391	25461^19672+19672^25461	109326	Hans Havermann	10/2020
7392	4*10^109316-63	109317	Robert Price	10/2018
7393	2^363120+3	109311	Donovan Johnson	04/2006
7394	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
7395	2^363042-114641	109287	Enzo Doria	04/2015
7396	2^363020-112793	109280	Enzo Doria	06/2014
7397	(8732^27889-1)/(8732^167-1)	109256	Ryan Propper	11/2023
7398	(85*10^109253+203)/9	109254	Robert Price	09/2020
7399	24990^23431+23431^24990	109202	Hans Havermann	10/2020
7400	(2^362746+3738)/2	109198	Stefano Morozzi	09/2020
7401	(2^362716+1282)/2	109189	Stefano Morozzi	01/2021
7402	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
7403	25060^22737+22737^25060	109180	Hans Havermann	10/2020
7404	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
7405	5^156181+38	109166	Lelio R Paula	02/2017
7406	(2^362623+3618)/2	109161	Stefano Morozzi	09/2020
7407	25138^21993+21993^25138	109157	Hans Havermann	10/2020
7408	4*10^109142+91	109143	Robert Price	08/2018
7409	3^228750+68	109142	Lelio R Paula	03/2017
7410	(2^362561+786)/2	109142	Stefano Morozzi	09/2020
7411	578*29^74623+7	109132	Eric Chen	06/2025
7412	(23*10^109113+61)/3	109114	Robert Price	01/2022
7413	2*10^109100-49	109101	Robert Price	09/2020
7414	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
7415	65^60167-64^60167	109078	Robert Price	08/2013
7416	7*3^228589-2	109066	Lelio R Paula	09/2014
7417	24874^24243+24243^24874	109063	Hans Havermann	11/2020
7418	(17*10^109059-161)/9	109060	Robert Price	02/2021
7419	29158^5495+5495^29158	109050	Hans Havermann	11/2020
7420	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
7421	2*7^129008+9	109025	Lelio R Paula	11/2014
7422	88*10^109022+7	109024	Robert Price	03/2020
7423	28194^7337+7337^28194	108985	Hans Havermann	10/2020
7424	(5*10^108960+91)/3	108961	Robert Price	04/2018
7425	2^361957+76367	108960	Enzo Doria	05/2016
7426	(11*29^74504-245655)/28	108955	Eric Chen	06/2025
7427	2^361873-1411	108935	Yves Minet	01/2013
7428	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
7429	216^216^216+91^91^91	108917	Henri Lifchitz	03/2025
7430	47^65132-65132^47	108908	Norman Luhn	09/2024
7431	115^52842-114	108892	Norbert Schneider	07/2018
7432	13^97745-24	108883	Lelio R Paula	03/2017
7433	(2^361696+2562)/2	108882	Stefano Morozzi	09/2020
7434	17^88475+8	108864	Lelio R Paula	04/2017
7435	2^361567+51	108843	Lelio R Paula	01/2012
7436	2^361563-109501	108842	Enzo Doria	04/2014
7437	12^100852+83	108838	Lelio R Paula	03/2017
7438	2^361497+767	108822	Lelio R Paula	01/2012
7439	L(520691)/78103651/1057002731/42794551909	108791	Serge Batalov	07/2024
7440	28019^7630+7630^28019	108785	Hans Havermann	10/2020
7441	24723^24758-24758^24723	108765	Norbert Schneider	11/2020
7442	2^361280-112349	108757	Enzo Doria	06/2014
7443	2^361271-5955	108754	Lelio R Paula	04/2017
7444	12^100757+19	108736	Lelio R Paula	03/2017
7445	25368^19333+19333^25368	108735	Hans Havermann	11/2020
7446	(2^361195+3618)/2	108731	Stefano Morozzi	09/2020
7447	2^361153-111546435	108718	Paul Bourdelais	10/2021
7448	14^94849-61	108710	Lelio R Paula	05/2017
7449	27267^9700+9700^27267	108708	Hans Havermann	11/2020
7450	(19^85009-5^85009)/14	108705	Robert Price	07/2013
7451	24832^23853+23853^24832	108704	Hans Havermann	11/2020
7452	27502^8963+8963^27502	108701	Hans Havermann	11/2020
7453	(130^51419-1)/129	108695	Anonymous	06/2024
7454	25807^16278+16278^25807	108689	Hans Havermann	11/2020
7455	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
7456	2^360973+1299	108664	Lelio R Paula	04/2017
7457	24^78728+23	108662	Anonymous	09/2024
7458	2^360959-109101	108660	Enzo Doria	04/2014
7459	6*5^155454+7	108659	Lelio R Paula	11/2014
7460	10^108656+79	108657	Lelio R Paula	02/2017
7461	10^108656-50001	108656	Patrick De Geest	03/2017
7462	2^360918-35	108648	Lelio R Paula	01/2012
7463	4*10^108646-47	108647	Robert Price	10/2021
7464	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
7465	3*10^108624-49	108625	Robert Price	07/2018
7466	(2^360831+666)/2	108621	Stefano Morozzi	09/2020
7467	(134*10^108610+7)/3	108612	Robert Price	02/2020
7468	2*10^108609+29	108610	Robert Price	02/2021
7469	(10^108604+7)/71/191	108600	Alfred Reich	06/2021
7470	(2^360742+3222)/2	108594	Stefano Morozzi	09/2020
7471	2^360706-458903	108584	Enzo Doria	04/2015
7472	31112^3087+3087^31112	108567	Hans Havermann	11/2020
7473	2^360641-113185	108564	Enzo Doria	07/2014
7474	(29*10^108559-71)/3	108560	Robert Price	07/2021
7476	2^360618+75019	108557	Enzo Doria	04/2016
7475	2^360618+2025	108557	Henri Lifchitz	01/2025
7477	2^360607-216367	108554	Harrison Mesh	06/2022
7478	29^74228+556	108551	Eric Chen	06/2025
7479	(14*10^108545-221)/9	108546	Robert Price	04/2018
7480	(44*10^108544-233)/9	108545	Robert Price	01/2019
7481	3*5^155286+2	108541	Lelio R Paula	11/2014
7482	7^128422+4	108530	Lelio R Paula	11/2014
7483	7^128421-80	108529	Lelio R Paula	03/2017
7484	2^360497+53807	108521	Yves Minet	07/2010
7485	2^360468-4559	108512	Yves Minet	03/2019
7486	(2^360451+578)/2	108507	Stefano Morozzi	09/2020
7487	2^360366+1459	108481	Lelio R Paula	09/2011
7488	2^360364-1499	108481	Yves Minet	05/2013
7489	25662^16871+16871^25662	108477	Hans Havermann	10/2020
7490	25009^21748+21748^25009	108475	Hans Havermann	10/2020
7491	14^94642-23	108472	Lelio R Paula	05/2017
7492	(197*10^108446-11)/3	108448	Robert Price	03/2020
7493	(2^360229+1290)/2	108440	Stefano Morozzi	01/2021
7494	4*10^108412+9	108413	Robert Price	05/2015
7495	(259*10^108409-1)/3	108411	Robert Price	12/2020
7496	(2^360122+1194)/2	108408	Stefano Morozzi	09/2020
7497	133^51042-132	108406	Norbert Schneider	02/2019
7498	2^360093-351103	108399	Enzo Doria	06/2015
7499	2^360042+723	108384	Lelio R Paula	01/2012
7500	85^56164-2	108364	Lelio R Paula	10/2013

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