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	2^371440-112865	111815	Enzo Doria	06/2014
7502	2^371426-459161	111811	Enzo Doria	05/2015
7503	25768^21771+21771^25768	111779	Hans Havermann	02/2021
7504	28022^9747+9747^28022	111777	Hans Havermann	02/2021
7505	(94*10^111770+11)/3	111772	Robert Price	04/2020
7506	2^371276-461267	111766	Enzo Doria	07/2015
7507	6*10^111760+43	111761	Robert Price	07/2020
7508	98079!4-1024	111747	Robert Price	11/2019
7509	(2^371186+3162)/2	111738	Stefano Morozzi	09/2020
7510	10^(255862+1)-410^55862-1	111725	Robert Price	07/2023
7511	2^371098-113261	111712	Enzo Doria	07/2014
7512	(7*10^111706-61)/9	111706	Erik Branger	01/2011
7513	2^371044+1869391	111696	Enzo Doria	05/2016
7514	26310^17581+17581^26310	111688	Hans Havermann	01/2021
7515	88^57416+87	111645	Norbert Schneider	11/2015
7516	2^370829-109693	111631	Enzo Doria	04/2014
7517	15^94906-2	111619	Lelio R Paula	11/2013
7518	25835^20904+20904^25835	111614	Hans Havermann	02/2021
7519	(2^370726+1198)/2	111600	Stefano Morozzi	09/2020
7520	27758^10479+10479^27758	111597	Hans Havermann	02/2021
7521	2^370695-4627	111591	Yves Minet	05/2019
7522	7*10^111579-87	111580	Robert Price	06/2020
7524	2^370643-37	111575	Yves Minet	01/2012
7523	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
7525	2^370610-3911	111565	Yves Minet	04/2017
7526	(154*10^111549+17)/9	111551	Robert Price	06/2022
7527	26200^18097+18097^26200	111550	Hans Havermann	01/2021
7528	286^45405+45405^286	111532	Norbert Schneider	04/2015
7529	4*5^159563-9	111531	Lelio R Paula	11/2014
7530	5*10^111528-21	111529	Robert Price	12/2021
7531	(4^185225+23)/3	111517	Robert Price	10/2018
7532	2^370393-2797093	111500	Enzo Doria	03/2016
7533	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
7534	(2^370371+554)/2	111493	Stefano Morozzi	09/2020
7535	6^143273-5	111489	Paul Bourdelais	01/2021
7536	2^370292-2791979	111469	Enzo Doria	03/2016
7537	(14*10^111443-11)/3	111444	Robert Price	08/2022
7538	2^370177-461551	111435	Enzo Doria	07/2015
7539	(2^370169+1706)/2	111432	Stefano Morozzi	09/2020
7540	109^54683-108	111413	Norbert Schneider	02/2017
7541	(83*10^111406-173)/9	111407	Robert Price	04/2021
7542	959^37362-37362^959	111407	Henri Lifchitz	10/2024
7543	(2^370043+1010)/2	111394	Stefano Morozzi	09/2020
7544	32961^2396+2396^32961	111392	Hans Havermann	10/2020
7545	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
7546	(19*10^111385+11)/3	111386	Robert Price	07/2023
7547	(23*10^111380-29)/3	111381	Robert Price	03/2022
7548	2^369974+733	111374	Lelio R Paula	05/2013
7549	121^53470+120	111367	Norbert Schneider	10/2018
7550	2^369915-286267	111356	Enzo Doria	07/2015
7551	(62*10^111347-629)/9	111348	Robert Price	07/2021
7552	2^369855-1615	111338	Lelio R Paula	05/2017
7553	(27^77783+5^77783)/32	111335	Robert Price	07/2026
7554	7*10^111325+3	111326	Robert Price	08/2015
7555	((3127254-28405)F(532650)-(127254-28405)*L(532650))/2	111322	Yaroslav Berezhko	09/2026
7556	51^65176+2	111293	Lelio R Paula	08/2013
7557	Phi(43329,-43329)	111283	Henri Lifchitz	06/2025
7558	2^369643-1865767	111274	Enzo Doria	03/2016
7559	2^369603+885	111262	Lelio R Paula	05/2017
7560	25555^22564+22564^25555	111252	Hans Havermann	10/2020
7561	F(532391)/89441689/1425422598617	111243	Serge Batalov	07/2024
7562	L(532277)	111240	Renaud Lifchitz	03/2004
7564	105^55033-2	111233	Lelio R Paula	10/2017
7563	(35*10^111232-737)/9	111233	Robert Price	07/2018
7565	26970^13307+13307^26970	111227	Hans Havermann	10/2020
7566	25419^23716+23716^25419	111210	Hans Havermann	10/2020
7567	(26^78593-3^78593)/23	111206	Robert Price	02/2025
7568	9*10^111201-29	111202	Robert Price	09/2019
7569	2^369392+29835	111199	Lelio R Paula	05/2017
7570	3^233059+16	111198	Robert Price	03/2020
7571	2^369354-3413	111187	Yves Minet	12/2016
7572	2^369296-27	111170	Lelio R Paula	02/2013
7573	(2468^40960+1)/(2468^8192+1)	111161	Martin Hopf	08/2024
7574	2^369239-109837	111153	Enzo Doria	05/2014
7575	2^369224-291839	111148	Enzo Doria	07/2015
7576	2^369216+2798881	111146	Enzo Doria	04/2016
7577	26842^13817+13817^26842	111137	Hans Havermann	11/2020
7578	(5*10^111119-191)/3	111120	Robert Price	05/2021
7579	(29*10^111112-23)/3	111113	Robert Price	03/2022
7580	10^111111+163849	111112	Patrick De Geest	03/2017
7581	10^111111-312911	111111	Patrick De Geest	03/2017
7582	2^369092-216923	111108	Enzo Doria	05/2014
7583	2^369081-55	111105	Lelio R Paula	02/2013
7584	(2^369047+3618)/2	111094	Stefano Morozzi	09/2020
7585	88^57124-87	111077	Norbert Schneider	11/2015
7586	2^368980+753	111075	Lelio R Paula	05/2013
7587	2^368946-3623	111064	Yves Minet	03/2017
7588	2^368929+29835	111059	Lelio R Paula	05/2017
7589	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
7590	111^54298+110	111057	Norbert Schneider	04/2017
7591	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
7592	(29*10^111020-41)/3	111021	Tyler Busby	03/2024
7593	35799^1262+1262^35799	111015	Hans Havermann	10/2020
7594	(298*10^111004+11)/3	111006	Robert Price	11/2020
7595	27648^10349+10349^27648	111004	Hans Havermann	11/2020
7596	28899^6932+6932^28899	110997	Hans Havermann	11/2020
7597	(749^38809+1)/(749^197+1)	110990	Martin Hopf	11/2023
7598	2^368641-460303	110972	Enzo Doria	06/2015
7599	2^368619-109087	110966	Enzo Doria	04/2014
7600	(74*10^110961+313)/9	110962	Robert Price	06/2019
7601	25258^24711+24711^25258	110956	Hans Havermann	11/2020
7602	2^368550+1125899906842623	110945	Alfred Reich	05/2026
7603	(2^368539+1290)/2	110941	Stefano Morozzi	01/2021
7604	3*2^368489+7	110927	Lelio R Paula	09/2014
7605	(14*10^110922+61)/3	110923	Robert Price	12/2018
7606	97411!4-2	110913	Robert Price	07/2017
7607	(301*10^110903+23)/9	110905	Robert Price	06/2021
7608	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
7609	25830^19619+19619^25830	110880	Hans Havermann	10/2020
7610	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
7611	Phi(119761,10)/85476950837250449	110864	Anonymous	01/2026
7612	26022^18191+18191^26022	110850	Hans Havermann	10/2020
7613	(2^368211+2250)/2	110843	Stefano Morozzi	01/2021
7614	(37*10^110813+251)/9	110814	Robert Price	09/2021
7615	2^368050-64875	110795	Lelio R Paula	05/2017
7616	2^368048+25	110794	Lelio R Paula	02/2013
7617	(2^368017+2262)/2	110784	Stefano Morozzi	02/2021
7618	69^60239-2	110771	Lelio R Paula	10/2013
7619	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
7620	2^367924-69	110757	Lelio R Paula	02/2013
7621	(23*10^110738+61)/3	110739	Robert Price	01/2022
7622	(2^367779+3750)/2	110713	Stefano Morozzi	01/2021
7623	2^367709-109723	110692	Enzo Doria	04/2014
7624	2^367687+213413	110685	Enzo Doria	09/2023
7625	Phi(44407,-561)	110674	Henri Lifchitz	12/2025
7626	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
7627	(2^367626+3514)/2	110667	Stefano Morozzi	09/2020
7628	(1288676*34^72242-455)/33	110642	Eric Chen	03/2023
7629	379*10^110616+9	110619	Jason Yuen	01/2025
7630	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
7631	140^51515-139	110558	Norbert Schneider	04/2019
7632	2^367215+1879223	110543	Enzo Doria	09/2016
7633	25782^19375+19375^25782	110534	Hans Havermann	10/2020
7634	26117^17058+17058^26117	110526	Hans Havermann	10/2020
7635	2^367141+41	110521	Lelio R Paula	02/2013
7636	2^367126+29835	110516	Lelio R Paula	05/2017
7637	(10^110503-1)/9+2(10^59183-1)/910^25660	110503	Makoto Morimoto	09/2020
7638	(10^110503-1)/9+2(10^65511-1)/910^22496	110503	Makoto Morimoto	09/2020
7639	(10^110503-1)/9+210^108327+210^2175	110503	Makoto Morimoto	09/2020
7640	(10^110503-1)/9+210^66251+210^44251	110503	Makoto Morimoto	09/2020
7641	(10^110503-1)/9+3(10^28813-1)/910^40845	110503	Makoto Morimoto	09/2020
7642	(10^110503-1)/9+3(10^82573-1)/910^13965	110503	Makoto Morimoto	09/2020
7643	(10^110503-1)/9+4(10^43305-1)/910^33599	110503	Makoto Morimoto	09/2020
7644	(10^110503-1)/9+510^70327+510^40175	110503	Makoto Morimoto	09/2020
7645	(10^110503-1)/9+510^99423+510^11079	110503	Makoto Morimoto	09/2020
7646	(10^110503-1)/9+7(10^23617-1)/910^43443	110503	Makoto Morimoto	09/2020
7647	(10^110503-1)/9+8(10^30251-1)/910^40126	110503	Makoto Morimoto	09/2020
7648	3(10^110503-1)/9+110^106036+1*10^4466	110503	Makoto Morimoto	09/2020
7649	3(10^110503-1)/9+110^58962+1*10^51540	110503	Makoto Morimoto	09/2020
7650	3(10^110503-1)/9+110^78213+1*10^32289	110503	Makoto Morimoto	09/2020
7651	3(10^110503-1)/9+210^76898+2*10^33604	110503	Makoto Morimoto	09/2020
7652	3(10^110503-1)/9-110^100802-1*10^9700	110503	Makoto Morimoto	09/2020
7653	3(10^110503-1)/9-110^76355-1*10^34147	110503	Makoto Morimoto	09/2020
7654	3(10^110503-1)/9-210^105704-2*10^4798	110503	Makoto Morimoto	09/2020
7655	7(10^110503-1)/9+1(10^27685-1)/9*10^41409	110503	Makoto Morimoto	09/2020
7656	7(10^110503-1)/9+1(10^91035-1)/9*10^9734	110503	Makoto Morimoto	09/2020
7657	7(10^110503-1)/9-1(10^23717-1)/9*10^43393	110503	Makoto Morimoto	09/2020
7658	7(10^110503-1)/9-110^57906-1*10^52596	110503	Makoto Morimoto	09/2020
7659	7(10^110503-1)/9-110^72287-1*10^38215	110503	Makoto Morimoto	09/2020
7660	7(10^110503-1)/9-2(10^53823-1)/9*10^28340	110503	Makoto Morimoto	09/2020
7661	7(10^110503-1)/9-2(10^88659-1)/9*10^10922	110503	Makoto Morimoto	09/2020
7662	7(10^110503-1)/9-3(10^79921-1)/9*10^15291	110503	Makoto Morimoto	09/2020
7663	7(10^110503-1)/9-310^60024-3*10^50478	110503	Makoto Morimoto	09/2020
7664	7(10^110503-1)/9-4(10^103091-1)/9*10^3706	110503	Makoto Morimoto	09/2020
7665	7(10^110503-1)/9-410^103658-4*10^6844	110503	Makoto Morimoto	09/2020
7666	7(10^110503-1)/9-410^78188-4*10^32314	110503	Makoto Morimoto	09/2020
7667	7(10^110503-1)/9-5(10^35035-1)/9*10^37734	110503	Makoto Morimoto	09/2020
7668	7(10^110503-1)/9-6(10^67347-1)/9*10^21578	110503	Makoto Morimoto	09/2020
7669	7(10^110503-1)/9-610^60391-6*10^50111	110503	Makoto Morimoto	09/2020
7670	(10^110503-1)-4(10^96247-1)/910^7128	110503	Makoto Morimoto	09/2020
7671	(10^110503-1)-410^74037-410^36465	110503	Makoto Morimoto	09/2020
7672	(10^110503-1)-410^77787-410^32715	110503	Makoto Morimoto	09/2020
7673	(10^110503-1)-410^91179-410^19323	110503	Makoto Morimoto	09/2020
7674	(10^110503-1)-5(10^99143-1)/910^5680	110503	Makoto Morimoto	09/2020
7675	(10^110503-1)-7(10^85075-1)/910^12714	110503	Makoto Morimoto	09/2020
7676	(10^110503-1)-710^100712-710^9790	110503	Makoto Morimoto	09/2020
7677	(10^110503-1)-710^76427-710^34075	110503	Makoto Morimoto	09/2020
7678	(10^110503-1)-710^90451-710^20051	110503	Makoto Morimoto	09/2020
7679	(10^110503-1)-810^106252-810^4250	110503	Makoto Morimoto	09/2020
7680	(11*10^110496+49)/3	110497	Robert Price	07/2018
7681	25447^21958+21958^25447	110481	Hans Havermann	11/2020
7682	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
7683	7*10^110468-23	110469	Robert Price	07/2019
7684	5*3^231464-2^231464	110438	Jon Grantham	08/2023
7685	2^366853+5711	110434	Lelio R Paula	05/2017
7686	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
7687	(4^231439)%(3^231439)	110425	Henri Lifchitz	06/2025
7688	2^366816+315	110423	Lelio R Paula	05/2017
7689	(11^2667520)/(10^2667520)	110416	Henri Lifchitz	06/2025
7690	2^366775-2787037	110411	Enzo Doria	03/2016
7691	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
7692	2^366751+2797553	110404	Enzo Doria	03/2016
7693	25276^23331+23331^25276	110404	Hans Havermann	10/2020
7694	2^366748+255	110403	Lelio R Paula	05/2017
7695	2^366738-2985	110400	Yves Minet	09/2014
7696	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
7697	(2^366722+1314)/2	110395	Stefano Morozzi	02/2021
7698	2^366716+1871791	110393	Enzo Doria	05/2016
7699	(239*23^81066-349)/22	110391	Eric Chen	08/2023
7700	2^366695+1334025	110387	Henri Lifchitz	10/2024
7701	(5^528189)%F(528189)	110385	Henri Lifchitz	06/2025
7702	2^366649+1871687	110373	Enzo Doria	05/2016
7703	2^366629-351205	110367	Enzo Doria	06/2015
7704	(31*10^110363+257)/9	110364	Robert Price	12/2021
7705	(5^183291)%(4^183291)	110353	Henri Lifchitz	06/2025
7706	(17*19^86292-215)/18	110347	Eric Chen	01/2023
7708	2^366558+1874479	110345	Enzo Doria	06/2016
7707	25132^24581+24581^25132	110345	Hans Havermann	10/2020
7709	(2^366539+770)/2	110339	Stefano Morozzi	09/2020
7710	26368^15285+15285^26368	110331	Hans Havermann	10/2020
7711	(23*10^110290+19)/3	110291	Robert Price	07/2019
7712	18^87853-4409	110280	Enzo Doria	03/2013
7713	28490^7419+7419^28490	110267	Hans Havermann	11/2020
7714	2^366218-23	110243	Lelio R Paula	02/2013
7715	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
7716	2^366178-343991	110231	Enzo Doria	07/2015
7717	12^102123-11	110210	Riley Fisher	09/2023
7718	(725*35^71368+16649)/34	110199	Eric Chen	05/2025
7719	25777^18798+18798^25777	110174	Hans Havermann	10/2020
7720	2^365944+1871341	110161	Enzo Doria	05/2016
7721	2^365838-461267	110129	Enzo Doria	07/2015
7722	30152^4491+4491^30152	110126	Hans Havermann	11/2020
7723	2^365802+23359	110118	Enzo Doria	10/2023
7724	10^110111+464019	110112	Patrick De Geest	05/2021
7725	10^110111-40001	110111	Robert Price	01/2021
7726	2^365763-6555	110106	Lelio R Paula	04/2017
7727	(2^365689+2^182845+1)/5	110083	Jean Penné	11/2006
7728	(83^57367-1)/3536509644718	110080	Paul Vanderveen	05/2025
7729	2^365666-459161	110077	Enzo Doria	05/2015
7730	3*10^110076-7	110077	Robert Price	08/2015
7731	(102936^21961-1)/102935	110076	Anonymous	09/2025
7732	13^98785-72	110041	Lelio R Paula	03/2017
7734	(25^78707+1)/26	110027	Robert Price	06/2013
7733	(7*10^110027-277)/9	110027	Robert Price	02/2022
7735	(16*10^110014-73)/3	110015	Robert Price	07/2020
7736	Phi(8869,17!)	110007	Henri Lifchitz	12/2025
7737	(7*10^110006-151)/9	110006	Robert Price	02/2018
7738	6^141361-7	110001	Lelio R Paula	11/2014
7739	10^110000+8029681	110001	Hayden Chesnut	11/2024
7740	10^110000+2044477	110001	Hayden Chesnut	11/2024
7741	10^110000+76407	110001	Hayden Chesnut	11/2024
7742	10^110000+167311	110001	Hayden Chesnut	11/2024
7743	20^84536+81	109984	Lelio R Paula	03/2017
7744	5*2^365347-9	109982	Lelio R Paula	09/2014
7745	9*6^141303+7	109957	Lelio R Paula	11/2014
7746	27635^9522+9522^27635	109953	Hans Havermann	11/2020
7747	78^58099+77	109929	Norbert Schneider	02/2015
7748	2*10^109928-7	109929	Robert Price	10/2015
7749	30580^3933+3933^30580	109927	Hans Havermann	11/2020
7750	26380^14689+14689^26380	109926	Hans Havermann	11/2020

Find by discoverer :

PRP Records

Probable Primes Top 10000

(303436 PRPs in the top)