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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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 ?
7501	29^75157-30	109910	Anonymous	09/2024
7502	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
7503	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
7504	(2^365069+3774)/2	109897	Stefano Morozzi	02/2021
7505	29652^5083+5083^29652	109894	Mark Rodenkirch	10/2020
7506	(2^365049+722)/2	109891	Stefano Morozzi	09/2020
7507	(35*10^109888-89)/9	109889	Robert Price	02/2022
7508	18^87533-11	109878	Lelio R Paula	04/2017
7509	2^364982-5	109871	Henri Lifchitz	04/2006
7510	3*10^109861+59	109862	Robert Price	08/2018
7511	5*10^109860-69	109861	Robert Price	02/2021
7512	2^364936-1867979	109857	Enzo Doria	04/2016
7513	27013^11652+11652^27013	109846	Hans Havermann	10/2020
7514	2^364867-112087	109836	Enzo Doria	06/2014
7515	4^182415-85061	109825	Mike Oakes	06/2011
7516	(2^364809+1034)/2	109819	Stefano Morozzi	09/2020
7517	24972^24972-8323^8323	109814	Henri Lifchitz	10/2024
7518	(53*10^109809-287)/9	109810	Robert Price	02/2022
7519	(52*10^109807-133)/9	109808	Robert Price	09/2021
7520	25708^18675+18675^25708	109806	Hans Havermann	10/2020
7521	(17^89227+16^89227)/33	109788	Robert Price	08/2013
7522	2^364687-187	109782	Lelio R Paula	01/2012
7523	2^364644+67	109769	Lelio R Paula	01/2012
7524	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
7525	(2^364616+5)/9	109760	Lelio R Paula	01/2014
7526	(55*10^109759+89)/9	109760	Robert Price	03/2019
7527	(14*32^72921+4171)/31	109757	Eric Chen	04/2023
7528	12^101694+73	109747	Lelio R Paula	03/2017
7529	13^98518-66	109744	Lelio R Paula	03/2017
7530	(35^71069+2^71069)/37	109734	Robert Price	01/2025
7531	(8*10^109721-269)/9	109721	Robert Price	09/2021
7532	2^364478-113261	109719	Enzo Doria	07/2014
7533	(2^364513+1)/(3*44290516579)	109719	Gord Palameta	08/2018
7534	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
7535	27814^8777+8777^27814	109681	Hans Havermann	10/2020
7536	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
7537	3^229824+340	109654	Lelio R Paula	03/2017
7538	(16623*33^72206-8095)/16	109649	Eric Chen	05/2023
7539	(2*10^109645-71)/3	109645	Robert Price	12/2017
7540	V(786978)	109644	Serge Batalov	07/2024
7541	2^364169-112813	109626	Enzo Doria	06/2014
7542	28822^6359+6359^28822	109622	Hans Havermann	11/2020
7543	10^109615+21	109616	Lelio R Paula	03/2017
7544	10^109615-456267	109615	Patrick De Geest	03/2017
7545	522^40331-40331^522	109607	Norman Luhn	09/2024
7546	2^364094-113	109604	Lelio R Paula	01/2012
7547	25251^21898+21898^25251	109600	Hans Havermann	11/2020
7548	(4^182026+11)/3	109591	Robert Price	02/2017
7549	2^364041-6883	109588	Lelio R Paula	09/2011
7550	12^101545+11	109586	Lelio R Paula	03/2017
7551	26536^13475+13475^26536	109582	Hans Havermann	11/2020
7552	2^363842-2787101	109528	Enzo Doria	03/2016
7553	(2^363812+3570)/2	109519	Stefano Morozzi	09/2020
7554	(996^36527+1)/997	109515	Jinyuan Wang	12/2024
7555	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
7556	2^363769+5711	109506	Lelio R Paula	04/2017
7557	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
7558	26^77372+25	109480	Anonymous	09/2024
7559	(2^363670+100280245065)	109476	Paul Bourdelais	05/2022
7560	p(22245)#/2-8	109462	Robert Price	01/2017
7561	2^363556+55	109442	Lelio R Paula	01/2012
7562	(509*10^109414+31)/9	109416	Robert Price	08/2022
7563	(2^363437+1682)/2	109406	Stefano Morozzi	09/2020
7564	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
7565	2^363406+1871569	109397	Enzo Doria	05/2016
7566	(129^51829-1)/128	109388	Anonymous	06/2024
7567	(2^363370+1338)/2	109385	Stefano Morozzi	02/2021
7568	(2^363349+7)/9	109378	Lelio R Paula	01/2014
7569	(13869^26569-1)/(13869^163-1)	109375	Ryan Propper	11/2023
7570	3^229236+100	109374	Lelio R Paula	03/2017
7571	(2^363315+3258)/2	109369	Stefano Morozzi	02/2021
7572	2^363268-58695	109355	Lelio R Paula	04/2017
7573	2^363191-112321	109332	Enzo Doria	06/2014
7574	26231^14718+14718^26231	109327	Hans Havermann	10/2020
7575	25461^19672+19672^25461	109326	Hans Havermann	10/2020
7576	4*10^109316-63	109317	Robert Price	10/2018
7577	2^363120+3	109311	Donovan Johnson	04/2006
7578	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
7579	2^363042-114641	109287	Enzo Doria	04/2015
7580	2^363020-112793	109280	Enzo Doria	06/2014
7581	(8732^27889-1)/(8732^167-1)	109256	Ryan Propper	11/2023
7582	(85*10^109253+203)/9	109254	Robert Price	09/2020
7583	24990^23431+23431^24990	109202	Hans Havermann	10/2020
7584	Phi(369781,-2)	109200	Henri Lifchitz	12/2025
7585	(2^362746+3738)/2	109198	Stefano Morozzi	09/2020
7586	(2^362716+1282)/2	109189	Stefano Morozzi	01/2021
7587	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
7588	25060^22737+22737^25060	109180	Hans Havermann	10/2020
7589	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
7590	5^156181+38	109166	Lelio R Paula	02/2017
7591	(2^362623+3618)/2	109161	Stefano Morozzi	09/2020
7592	25138^21993+21993^25138	109157	Hans Havermann	10/2020
7593	4*10^109142+91	109143	Robert Price	08/2018
7594	3^228750+68	109142	Lelio R Paula	03/2017
7595	(2^362561+786)/2	109142	Stefano Morozzi	09/2020
7596	578*29^74623+7	109132	Eric Chen	06/2025
7597	(23*10^109113+61)/3	109114	Robert Price	01/2022
7598	2*10^109100-49	109101	Robert Price	09/2020
7599	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
7600	65^60167-64^60167	109078	Robert Price	08/2013
7601	Phi(63393,-1105)	109075	Henri Lifchitz	12/2025
7602	7*3^228589-2	109066	Lelio R Paula	09/2014
7603	24874^24243+24243^24874	109063	Hans Havermann	11/2020
7604	(17*10^109059-161)/9	109060	Robert Price	02/2021
7605	29158^5495+5495^29158	109050	Hans Havermann	11/2020
7606	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
7607	2*7^129008+9	109025	Lelio R Paula	11/2014
7608	88*10^109022+7	109024	Robert Price	03/2020
7609	28194^7337+7337^28194	108985	Hans Havermann	10/2020
7610	(5*10^108960+91)/3	108961	Robert Price	04/2018
7611	2^361957+76367	108960	Enzo Doria	05/2016
7612	(11*29^74504-245655)/28	108955	Eric Chen	06/2025
7613	2^361873-1411	108935	Yves Minet	01/2013
7614	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
7615	216^216^216+91^91^91	108917	Henri Lifchitz	03/2025
7616	47^65132-65132^47	108908	Norman Luhn	09/2024
7617	115^52842-114	108892	Norbert Schneider	07/2018
7618	13^97745-24	108883	Lelio R Paula	03/2017
7619	(2^361696+2562)/2	108882	Stefano Morozzi	09/2020
7620	17^88475+8	108864	Lelio R Paula	04/2017
7621	2^361567+51	108843	Lelio R Paula	01/2012
7622	2^361563-109501	108842	Enzo Doria	04/2014
7623	12^100852+83	108838	Lelio R Paula	03/2017
7624	2^361497+767	108822	Lelio R Paula	01/2012
7625	L(520691)/78103651/1057002731/42794551909	108791	Serge Batalov	07/2024
7626	28019^7630+7630^28019	108785	Hans Havermann	10/2020
7627	24723^24758-24758^24723	108765	Norbert Schneider	11/2020
7628	2^361280-112349	108757	Enzo Doria	06/2014
7629	2^361271-5955	108754	Lelio R Paula	04/2017
7630	12^100757+19	108736	Lelio R Paula	03/2017
7631	25368^19333+19333^25368	108735	Hans Havermann	11/2020
7632	(2^361195+3618)/2	108731	Stefano Morozzi	09/2020
7633	2^361153-111546435	108718	Paul Bourdelais	10/2021
7634	14^94849-61	108710	Lelio R Paula	05/2017
7635	27267^9700+9700^27267	108708	Hans Havermann	11/2020
7636	(19^85009-5^85009)/14	108705	Robert Price	07/2013
7637	24832^23853+23853^24832	108704	Hans Havermann	11/2020
7638	27502^8963+8963^27502	108701	Hans Havermann	11/2020
7639	(130^51419-1)/129	108695	Anonymous	06/2024
7640	25807^16278+16278^25807	108689	Hans Havermann	11/2020
7641	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
7642	2^360973+1299	108664	Lelio R Paula	04/2017
7643	24^78728+23	108662	Anonymous	09/2024
7644	2^360959-109101	108660	Enzo Doria	04/2014
7645	6*5^155454+7	108659	Lelio R Paula	11/2014
7646	10^108656+79	108657	Lelio R Paula	02/2017
7647	10^108656-50001	108656	Patrick De Geest	03/2017
7648	2^360918-35	108648	Lelio R Paula	01/2012
7649	4*10^108646-47	108647	Robert Price	10/2021
7650	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
7651	3*10^108624-49	108625	Robert Price	07/2018
7652	(2^360831+666)/2	108621	Stefano Morozzi	09/2020
7653	(134*10^108610+7)/3	108612	Robert Price	02/2020
7654	2*10^108609+29	108610	Robert Price	02/2021
7655	(10^108604+7)/71/191	108600	Alfred Reich	06/2021
7656	(2^360742+3222)/2	108594	Stefano Morozzi	09/2020
7657	2^360706-458903	108584	Enzo Doria	04/2015
7658	31112^3087+3087^31112	108567	Hans Havermann	11/2020
7659	2^360641-113185	108564	Enzo Doria	07/2014
7660	(29*10^108559-71)/3	108560	Robert Price	07/2021
7662	2^360618+75019	108557	Enzo Doria	04/2016
7661	2^360618+2025	108557	Henri Lifchitz	01/2025
7663	2^360607-216367	108554	Harrison Mesh	06/2022
7664	29^74228+556	108551	Eric Chen	06/2025
7665	(14*10^108545-221)/9	108546	Robert Price	04/2018
7666	(44*10^108544-233)/9	108545	Robert Price	01/2019
7667	3*5^155286+2	108541	Lelio R Paula	11/2014
7668	7^128422+4	108530	Lelio R Paula	11/2014
7669	7^128421-80	108529	Lelio R Paula	03/2017
7670	2^360497+53807	108521	Yves Minet	07/2010
7671	2^360468-4559	108512	Yves Minet	03/2019
7672	(2^360451+578)/2	108507	Stefano Morozzi	09/2020
7673	2^360366+1459	108481	Lelio R Paula	09/2011
7674	2^360364-1499	108481	Yves Minet	05/2013
7675	25662^16871+16871^25662	108477	Hans Havermann	10/2020
7676	25009^21748+21748^25009	108475	Hans Havermann	10/2020
7677	14^94642-23	108472	Lelio R Paula	05/2017
7678	(197*10^108446-11)/3	108448	Robert Price	03/2020
7679	(2^360229+1290)/2	108440	Stefano Morozzi	01/2021
7680	4*10^108412+9	108413	Robert Price	05/2015
7681	(259*10^108409-1)/3	108411	Robert Price	12/2020
7682	(2^360122+1194)/2	108408	Stefano Morozzi	09/2020
7683	133^51042-132	108406	Norbert Schneider	02/2019
7684	2^360093-351103	108399	Enzo Doria	06/2015
7685	2^360042+723	108384	Lelio R Paula	01/2012
7686	85^56164-2	108364	Lelio R Paula	10/2013
7687	2^359937-29323	108352	Enzo Doria	07/2015
7688	22^80712-23	108350	Anonymous	09/2024
7689	(2^359922+1762)/2	108348	Stefano Morozzi	09/2020
7690	(2^359903+758)/2	108342	Stefano Morozzi	09/2020
7691	2^359898-19997	108341	Enzo Doria	06/2013
7692	(2^359886+2122)/2	108337	Stefano Morozzi	09/2020
7693	2*5^154948-7	108305	Lelio R Paula	11/2014
7694	10^108303+13	108304	Lelio R Paula	02/2017
7695	10^108303-207959	108303	Patrick De Geest	03/2017
7696	7*10^108300+69	108301	Robert Price	07/2019
7697	198^47155-47155^198	108300	Norman Luhn	09/2024
7698	2^359730+753	108290	Lelio R Paula	12/2011
7699	(8*10^108273+13)/3	108274	Robert Price	06/2018
7700	2^359650-19797	108266	Enzo Doria	06/2013
7701	(47*10^108261+259)/9	108262	Robert Price	03/2022
7702	91^55259-90^55259	108255	Robert Price	07/2015
7703	10^108251+85749	108252	Patrick De Geest	02/2021
7704	10^108251-50000000001	108251	Robert Price	12/2020
7705	10^108251-252081	108251	Patrick De Geest	02/2021
7706	4*10^108238-71	108239	Robert Price	12/2018
7707	3^226845+68	108233	Lelio R Paula	03/2017
7708	31836^2509+2509^31836	108227	Hans Havermann	10/2020
7709	5^154822-12866	108216	Enzo Doria	05/2014
7710	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
7711	2^359454-177	108207	Lelio R Paula	12/2011
7712	(19*10^108184+191)/3	108185	Robert Price	05/2019
7713	6^139022-59	108181	Lelio R Paula	02/2017
7714	(19*10^108176-43)/3	108177	Robert Price	05/2019
7715	2^359352-179	108176	Lelio R Paula	12/2011
7716	2^359338-1858781	108172	Enzo Doria	04/2016
7717	12^100230-97	108167	Lelio R Paula	03/2017
7718	27028^10043+10043^27028	108163	Hans Havermann	11/2020
7719	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
7720	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
7721	26583^11702+11702^26583	108147	Hans Havermann	11/2020
7722	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
7723	6^138956-59	108129	Lelio R Paula	02/2017
7724	2^359184+30285	108126	Lelio R Paula	04/2017
7725	13^97059+10	108119	Lelio R Paula	03/2017
7726	2^359137-81	108112	Lelio R Paula	12/2011
7728	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
7727	2^359110-11655	108103	Lelio R Paula	04/2017
7729	2^359069-933075	108091	Paul Bourdelais	06/2021
7730	26227^13222+13222^26227	108090	Hans Havermann	10/2020
7731	8*6^138875+5	108067	Lelio R Paula	11/2014
7732	2^358987-216919	108066	Enzo Doria	05/2014
7733	(2^358977+2714)/2	108063	Stefano Morozzi	09/2020
7734	39^67918-67918^39	108062	Norbert Schneider	02/2017
7735	24^78283-1*78283^24	108048	Dylan Delgado	12/2019
7736	25282^18767+18767^25282	108040	Hans Havermann	11/2020
7737	(918^36457-1)/917	108014	Tom Wu	08/2025
7738	2^358785-16933	108006	Enzo Doria	05/2013
7739	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
7740	6^138770-77	107985	Lelio R Paula	02/2017
7741	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
7742	10^107976+19	107977	Lelio R Paula	02/2017
7743	10^107976-202103	107976	Patrick De Geest	03/2017
7744	2^358684+75781	107975	Enzo Doria	04/2016
7745	24928^21411+21411^24928	107955	Hans Havermann	10/2020
7746	99^54094+2	107952	Lelio R Paula	06/2013
7747	(2^358583-9)/391	107942	Lelio R Paula	12/2013
7748	(2^358562+838)/2	107938	Stefano Morozzi	02/2021
7749	2^358538+55	107931	Lelio R Paula	12/2011
7750	2^358517-109009	107925	Enzo Doria	03/2014

Find by discoverer :

PRP Records

Probable Primes Top 10000

(302856 PRPs in the top)