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	2^368929+29835	111059	Lelio R Paula	05/2017
7252	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
7253	111^54298+110	111057	Norbert Schneider	04/2017
7254	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
7255	(29*10^111020-41)/3	111021	Tyler Busby	03/2024
7256	35799^1262+1262^35799	111015	Hans Havermann	10/2020
7257	(298*10^111004+11)/3	111006	Robert Price	11/2020
7258	27648^10349+10349^27648	111004	Hans Havermann	11/2020
7259	28899^6932+6932^28899	110997	Hans Havermann	11/2020
7260	(749^38809+1)/(749^197+1)	110990	Martin Hopf	11/2023
7261	2^368641-460303	110972	Enzo Doria	06/2015
7262	2^368619-109087	110966	Enzo Doria	04/2014
7263	(74*10^110961+313)/9	110962	Robert Price	06/2019
7264	25258^24711+24711^25258	110956	Hans Havermann	11/2020
7265	(2^368539+1290)/2	110941	Stefano Morozzi	01/2021
7266	3*2^368489+7	110927	Lelio R Paula	09/2014
7267	(14*10^110922+61)/3	110923	Robert Price	12/2018
7268	97411!4-2	110913	Robert Price	07/2017
7269	(301*10^110903+23)/9	110905	Robert Price	06/2021
7270	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
7271	25830^19619+19619^25830	110880	Hans Havermann	10/2020
7272	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
7273	26022^18191+18191^26022	110850	Hans Havermann	10/2020
7274	(2^368211+2250)/2	110843	Stefano Morozzi	01/2021
7275	(37*10^110813+251)/9	110814	Robert Price	09/2021
7276	2^368050-64875	110795	Lelio R Paula	05/2017
7277	2^368048+25	110794	Lelio R Paula	02/2013
7278	(2^368017+2262)/2	110784	Stefano Morozzi	02/2021
7279	69^60239-2	110771	Lelio R Paula	10/2013
7280	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
7281	2^367924-69	110757	Lelio R Paula	02/2013
7282	(23*10^110738+61)/3	110739	Robert Price	01/2022
7283	(2^367779+3750)/2	110713	Stefano Morozzi	01/2021
7284	2^367709-109723	110692	Enzo Doria	04/2014
7285	2^367687+213413	110685	Enzo Doria	09/2023
7286	Phi(44407,-561)	110674	Henri Lifchitz	12/2025
7287	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
7288	(2^367626+3514)/2	110667	Stefano Morozzi	09/2020
7289	(1288676*34^72242-455)/33	110642	Eric Chen	03/2023
7290	379*10^110616+9	110619	Jason Yuen	01/2025
7291	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
7292	140^51515-139	110558	Norbert Schneider	04/2019
7293	2^367215+1879223	110543	Enzo Doria	09/2016
7294	25782^19375+19375^25782	110534	Hans Havermann	10/2020
7295	26117^17058+17058^26117	110526	Hans Havermann	10/2020
7296	2^367141+41	110521	Lelio R Paula	02/2013
7297	2^367126+29835	110516	Lelio R Paula	05/2017
7298	(10^110503-1)/9+2(10^59183-1)/910^25660	110503	Makoto Morimoto	09/2020
7299	(10^110503-1)/9+2(10^65511-1)/910^22496	110503	Makoto Morimoto	09/2020
7300	(10^110503-1)/9+210^108327+210^2175	110503	Makoto Morimoto	09/2020
7301	(10^110503-1)/9+210^66251+210^44251	110503	Makoto Morimoto	09/2020
7302	(10^110503-1)/9+3(10^28813-1)/910^40845	110503	Makoto Morimoto	09/2020
7303	(10^110503-1)/9+3(10^82573-1)/910^13965	110503	Makoto Morimoto	09/2020
7304	(10^110503-1)/9+4(10^43305-1)/910^33599	110503	Makoto Morimoto	09/2020
7305	(10^110503-1)/9+510^70327+510^40175	110503	Makoto Morimoto	09/2020
7306	(10^110503-1)/9+510^99423+510^11079	110503	Makoto Morimoto	09/2020
7307	(10^110503-1)/9+7(10^23617-1)/910^43443	110503	Makoto Morimoto	09/2020
7308	(10^110503-1)/9+8(10^30251-1)/910^40126	110503	Makoto Morimoto	09/2020
7309	3(10^110503-1)/9+110^106036+1*10^4466	110503	Makoto Morimoto	09/2020
7310	3(10^110503-1)/9+110^58962+1*10^51540	110503	Makoto Morimoto	09/2020
7311	3(10^110503-1)/9+110^78213+1*10^32289	110503	Makoto Morimoto	09/2020
7312	3(10^110503-1)/9+210^76898+2*10^33604	110503	Makoto Morimoto	09/2020
7313	3(10^110503-1)/9-110^100802-1*10^9700	110503	Makoto Morimoto	09/2020
7314	3(10^110503-1)/9-110^76355-1*10^34147	110503	Makoto Morimoto	09/2020
7315	3(10^110503-1)/9-210^105704-2*10^4798	110503	Makoto Morimoto	09/2020
7316	7(10^110503-1)/9+1(10^27685-1)/9*10^41409	110503	Makoto Morimoto	09/2020
7317	7(10^110503-1)/9+1(10^91035-1)/9*10^9734	110503	Makoto Morimoto	09/2020
7318	7(10^110503-1)/9-1(10^23717-1)/9*10^43393	110503	Makoto Morimoto	09/2020
7319	7(10^110503-1)/9-110^57906-1*10^52596	110503	Makoto Morimoto	09/2020
7320	7(10^110503-1)/9-110^72287-1*10^38215	110503	Makoto Morimoto	09/2020
7321	7(10^110503-1)/9-2(10^53823-1)/9*10^28340	110503	Makoto Morimoto	09/2020
7322	7(10^110503-1)/9-2(10^88659-1)/9*10^10922	110503	Makoto Morimoto	09/2020
7323	7(10^110503-1)/9-3(10^79921-1)/9*10^15291	110503	Makoto Morimoto	09/2020
7324	7(10^110503-1)/9-310^60024-3*10^50478	110503	Makoto Morimoto	09/2020
7325	7(10^110503-1)/9-4(10^103091-1)/9*10^3706	110503	Makoto Morimoto	09/2020
7326	7(10^110503-1)/9-410^103658-4*10^6844	110503	Makoto Morimoto	09/2020
7327	7(10^110503-1)/9-410^78188-4*10^32314	110503	Makoto Morimoto	09/2020
7328	7(10^110503-1)/9-5(10^35035-1)/9*10^37734	110503	Makoto Morimoto	09/2020
7329	7(10^110503-1)/9-6(10^67347-1)/9*10^21578	110503	Makoto Morimoto	09/2020
7330	7(10^110503-1)/9-610^60391-6*10^50111	110503	Makoto Morimoto	09/2020
7331	(10^110503-1)-4(10^96247-1)/910^7128	110503	Makoto Morimoto	09/2020
7332	(10^110503-1)-410^74037-410^36465	110503	Makoto Morimoto	09/2020
7333	(10^110503-1)-410^77787-410^32715	110503	Makoto Morimoto	09/2020
7334	(10^110503-1)-410^91179-410^19323	110503	Makoto Morimoto	09/2020
7335	(10^110503-1)-5(10^99143-1)/910^5680	110503	Makoto Morimoto	09/2020
7336	(10^110503-1)-7(10^85075-1)/910^12714	110503	Makoto Morimoto	09/2020
7337	(10^110503-1)-710^100712-710^9790	110503	Makoto Morimoto	09/2020
7338	(10^110503-1)-710^76427-710^34075	110503	Makoto Morimoto	09/2020
7339	(10^110503-1)-710^90451-710^20051	110503	Makoto Morimoto	09/2020
7340	(10^110503-1)-810^106252-810^4250	110503	Makoto Morimoto	09/2020
7341	(11*10^110496+49)/3	110497	Robert Price	07/2018
7342	25447^21958+21958^25447	110481	Hans Havermann	11/2020
7343	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
7344	7*10^110468-23	110469	Robert Price	07/2019
7345	5*3^231464-2^231464	110438	Jon Grantham	08/2023
7346	2^366853+5711	110434	Lelio R Paula	05/2017
7347	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
7348	(4^231439)%(3^231439)	110425	Henri Lifchitz	06/2025
7349	2^366816+315	110423	Lelio R Paula	05/2017
7350	(11^2667520)/(10^2667520)	110416	Henri Lifchitz	06/2025
7351	2^366775-2787037	110411	Enzo Doria	03/2016
7352	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
7353	2^366751+2797553	110404	Enzo Doria	03/2016
7354	25276^23331+23331^25276	110404	Hans Havermann	10/2020
7355	2^366748+255	110403	Lelio R Paula	05/2017
7356	2^366738-2985	110400	Yves Minet	09/2014
7357	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
7358	(2^366722+1314)/2	110395	Stefano Morozzi	02/2021
7359	2^366716+1871791	110393	Enzo Doria	05/2016
7360	(239*23^81066-349)/22	110391	Eric Chen	08/2023
7361	2^366695+1334025	110387	Henri Lifchitz	10/2024
7362	(5^528189)%F(528189)	110385	Henri Lifchitz	06/2025
7363	2^366649+1871687	110373	Enzo Doria	05/2016
7364	2^366629-351205	110367	Enzo Doria	06/2015
7365	(31*10^110363+257)/9	110364	Robert Price	12/2021
7366	(5^183291)%(4^183291)	110353	Henri Lifchitz	06/2025
7367	(17*19^86292-215)/18	110347	Eric Chen	01/2023
7369	2^366558+1874479	110345	Enzo Doria	06/2016
7368	25132^24581+24581^25132	110345	Hans Havermann	10/2020
7370	(2^366539+770)/2	110339	Stefano Morozzi	09/2020
7371	26368^15285+15285^26368	110331	Hans Havermann	10/2020
7372	(23*10^110290+19)/3	110291	Robert Price	07/2019
7373	18^87853-4409	110280	Enzo Doria	03/2013
7374	28490^7419+7419^28490	110267	Hans Havermann	11/2020
7375	2^366218-23	110243	Lelio R Paula	02/2013
7376	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
7377	2^366178-343991	110231	Enzo Doria	07/2015
7378	12^102123-11	110210	Riley Fisher	09/2023
7379	(725*35^71368+16649)/34	110199	Eric Chen	05/2025
7380	25777^18798+18798^25777	110174	Hans Havermann	10/2020
7381	2^365944+1871341	110161	Enzo Doria	05/2016
7382	2^365838-461267	110129	Enzo Doria	07/2015
7383	30152^4491+4491^30152	110126	Hans Havermann	11/2020
7384	2^365802+23359	110118	Enzo Doria	10/2023
7385	10^110111+464019	110112	Patrick De Geest	05/2021
7386	10^110111-40001	110111	Robert Price	01/2021
7387	2^365763-6555	110106	Lelio R Paula	04/2017
7388	(2^365689+2^182845+1)/5	110083		11/2006
7389	(83^57367-1)/3536509644718	110080	Paul Vanderveen	05/2025
7390	2^365666-459161	110077	Enzo Doria	05/2015
7391	3*10^110076-7	110077	Robert Price	08/2015
7392	(102936^21961-1)/102935	110076	Anonymous	09/2025
7393	13^98785-72	110041	Lelio R Paula	03/2017
7395	(25^78707+1)/26	110027	Robert Price	06/2013
7394	(7*10^110027-277)/9	110027	Robert Price	02/2022
7396	(16*10^110014-73)/3	110015	Robert Price	07/2020
7397	Phi(8869,17!)	110007	Henri Lifchitz	12/2025
7398	(7*10^110006-151)/9	110006	Robert Price	02/2018
7399	6^141361-7	110001	Lelio R Paula	11/2014
7400	10^110000+8029681	110001	Hayden Chesnut	11/2024
7401	10^110000+2044477	110001	Hayden Chesnut	11/2024
7402	10^110000+76407	110001	Hayden Chesnut	11/2024
7403	10^110000+167311	110001	Hayden Chesnut	11/2024
7404	20^84536+81	109984	Lelio R Paula	03/2017
7405	5*2^365347-9	109982	Lelio R Paula	09/2014
7406	9*6^141303+7	109957	Lelio R Paula	11/2014
7407	27635^9522+9522^27635	109953	Hans Havermann	11/2020
7408	78^58099+77	109929	Norbert Schneider	02/2015
7409	2*10^109928-7	109929	Robert Price	10/2015
7410	30580^3933+3933^30580	109927	Hans Havermann	11/2020
7411	26380^14689+14689^26380	109926	Hans Havermann	11/2020
7412	(2^365161+1130)/2	109925	Stefano Morozzi	09/2020
7413	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
7414	29^75157-30	109910	Anonymous	09/2024
7415	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
7416	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
7417	(2^365069+3774)/2	109897	Stefano Morozzi	02/2021
7418	29652^5083+5083^29652	109894	Mark Rodenkirch	10/2020
7419	(2^365049+722)/2	109891	Stefano Morozzi	09/2020
7420	(35*10^109888-89)/9	109889	Robert Price	02/2022
7421	18^87533-11	109878	Lelio R Paula	04/2017
7422	2^364982-5	109871	Henri Lifchitz	04/2006
7423	3*10^109861+59	109862	Robert Price	08/2018
7424	5*10^109860-69	109861	Robert Price	02/2021
7425	2^364936-1867979	109857	Enzo Doria	04/2016
7426	27013^11652+11652^27013	109846	Hans Havermann	10/2020
7427	2^364867-112087	109836	Enzo Doria	06/2014
7428	4^182415-85061	109825	Mike Oakes	06/2011
7429	(2^364809+1034)/2	109819	Stefano Morozzi	09/2020
7430	24972^24972-8323^8323	109814	Henri Lifchitz	10/2024
7431	(53*10^109809-287)/9	109810	Robert Price	02/2022
7432	(52*10^109807-133)/9	109808	Robert Price	09/2021
7433	25708^18675+18675^25708	109806	Hans Havermann	10/2020
7434	(17^89227+16^89227)/33	109788	Robert Price	08/2013
7435	2^364687-187	109782	Lelio R Paula	01/2012
7436	2^364644+67	109769	Lelio R Paula	01/2012
7437	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
7438	(2^364616+5)/9	109760	Lelio R Paula	01/2014
7439	(55*10^109759+89)/9	109760	Robert Price	03/2019
7440	(14*32^72921+4171)/31	109757	Eric Chen	04/2023
7441	12^101694+73	109747	Lelio R Paula	03/2017
7442	13^98518-66	109744	Lelio R Paula	03/2017
7443	(35^71069+2^71069)/37	109734	Robert Price	01/2025
7444	(8*10^109721-269)/9	109721	Robert Price	09/2021
7445	2^364478-113261	109719	Enzo Doria	07/2014
7446	(2^364513+1)/(3*44290516579)	109719	Gord Palameta	08/2018
7447	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
7448	27814^8777+8777^27814	109681	Hans Havermann	10/2020
7449	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
7450	3^229824+340	109654	Lelio R Paula	03/2017
7451	(16623*33^72206-8095)/16	109649	Eric Chen	05/2023
7452	(2*10^109645-71)/3	109645	Robert Price	12/2017
7453	V(786978)	109644	Serge Batalov	07/2024
7454	2^364169-112813	109626	Enzo Doria	06/2014
7455	28822^6359+6359^28822	109622	Hans Havermann	11/2020
7456	10^109615+21	109616	Lelio R Paula	03/2017
7457	10^109615-456267	109615	Patrick De Geest	03/2017
7458	522^40331-40331^522	109607	Norman Luhn	09/2024
7459	2^364094-113	109604	Lelio R Paula	01/2012
7460	25251^21898+21898^25251	109600	Hans Havermann	11/2020
7461	(4^182026+11)/3	109591	Robert Price	02/2017
7462	2^364041-6883	109588	Lelio R Paula	09/2011
7463	12^101545+11	109586	Lelio R Paula	03/2017
7464	26536^13475+13475^26536	109582	Hans Havermann	11/2020
7465	2^363842-2787101	109528	Enzo Doria	03/2016
7466	(2^363812+3570)/2	109519	Stefano Morozzi	09/2020
7467	(996^36527+1)/997	109515	Jinyuan Wang	12/2024
7468	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
7469	2^363769+5711	109506	Lelio R Paula	04/2017
7470	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
7471	26^77372+25	109480	Anonymous	09/2024
7472	(2^363670+100280245065)	109476	Paul Bourdelais	05/2022
7473	p(22245)#/2-8	109462	Robert Price	01/2017
7474	2^363556+55	109442	Lelio R Paula	01/2012
7475	(509*10^109414+31)/9	109416	Robert Price	08/2022
7476	(2^363437+1682)/2	109406	Stefano Morozzi	09/2020
7477	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
7478	2^363406+1871569	109397	Enzo Doria	05/2016
7479	(129^51829-1)/128	109388	Anonymous	06/2024
7480	(2^363370+1338)/2	109385	Stefano Morozzi	02/2021
7481	(2^363349+7)/9	109378	Lelio R Paula	01/2014
7482	(13869^26569-1)/(13869^163-1)	109375	Ryan Propper	11/2023
7483	3^229236+100	109374	Lelio R Paula	03/2017
7484	(2^363315+3258)/2	109369	Stefano Morozzi	02/2021
7485	2^363268-58695	109355	Lelio R Paula	04/2017
7486	2^363191-112321	109332	Enzo Doria	06/2014
7487	26231^14718+14718^26231	109327	Hans Havermann	10/2020
7488	25461^19672+19672^25461	109326	Hans Havermann	10/2020
7489	4*10^109316-63	109317	Robert Price	10/2018
7490	2^363120+3	109311	Donovan Johnson	04/2006
7491	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
7492	2^363042-114641	109287	Enzo Doria	04/2015
7493	2^363020-112793	109280	Enzo Doria	06/2014
7494	(8732^27889-1)/(8732^167-1)	109256	Ryan Propper	11/2023
7495	(85*10^109253+203)/9	109254	Robert Price	09/2020
7496	24990^23431+23431^24990	109202	Hans Havermann	10/2020
7497	Phi(369781,-2)	109200	Henri Lifchitz	12/2025
7498	(2^362746+3738)/2	109198	Stefano Morozzi	09/2020
7499	(2^362716+1282)/2	109189	Stefano Morozzi	01/2021
7500	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014

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Probable Primes Top 10000

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