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 ?
6501	(2^372181+2250)/2	112038	Stefano Morozzi	01/2021
6502	F(536233)/825798821/1102495049/5641839306317	112036	Serge Batalov	07/2024
6503	(2^372161+2574)/2	112032	Stefano Morozzi	09/2020
6504	8*10^112018-49	112019	Robert Price	08/2019
6506	2^372108+74221	112016	Enzo Doria	04/2016
6505	(2^372109+2046)/2	112016	Stefano Morozzi	09/2020
6507	8*10^112011-73	112012	Robert Price	01/2022
6508	(184*10^112007-1)/3	112009	Robert Price	02/2020
6509	5*10^112003+81	112004	Robert Price	03/2019
6510	215^48018+48018^215	112000	Norbert Schneider	10/2018
6511	25549^24148+24148^25549	111979	Hans Havermann	02/2021
6512	2^371970-459491	111975	Enzo Doria	05/2015
6513	41^69427-40^69427	111971	Robert Price	07/2012
6514	(2^371782+358)/2	111918	Stefano Morozzi	01/2021
6515	15*25^80056+446	111915	Eric Chen	10/2023
6516	(34*10^111902-547)/9	111903	Robert Price	03/2021
6517	(10^111902+71)/9	111902	Serge Batalov	07/2015
6518	(2^371625+1610)/2	111870	Stefano Morozzi	09/2020
6519	29080^7027+7027^29080	111865	Hans Havermann	01/2021
6520	31307^3730+3730^31307	111820	Hans Havermann	02/2021
6521	2^371440-112865	111815	Enzo Doria	06/2014
6522	2^371426-459161	111811	Enzo Doria	05/2015
6523	25768^21771+21771^25768	111779	Hans Havermann	02/2021
6524	28022^9747+9747^28022	111777	Hans Havermann	02/2021
6525	(94*10^111770+11)/3	111772	Robert Price	04/2020
6526	2^371276-461267	111766	Enzo Doria	07/2015
6527	6*10^111760+43	111761	Robert Price	07/2020
6528	98079!4-1024	111747	Robert Price	11/2019
6529	(2^371186+3162)/2	111738	Stefano Morozzi	09/2020
6530	10^(255862+1)-410^55862-1	111725	Robert Price	07/2023
6531	2^371098-113261	111712	Enzo Doria	07/2014
6532	(7*10^111706-61)/9	111706	Erik Branger	01/2011
6533	2^371044+1869391	111696	Enzo Doria	05/2016
6534	26310^17581+17581^26310	111688	Hans Havermann	01/2021
6535	88^57416+87	111645	Norbert Schneider	11/2015
6536	2^370829-109693	111631	Enzo Doria	04/2014
6537	15^94906-2	111619	Lelio R Paula	11/2013
6538	25835^20904+20904^25835	111614	Hans Havermann	02/2021
6539	(2^370726+1198)/2	111600	Stefano Morozzi	09/2020
6540	27758^10479+10479^27758	111597	Hans Havermann	02/2021
6541	2^370695-4627	111591	Yves Minet	05/2019
6542	7*10^111579-87	111580	Robert Price	06/2020
6543	2^370643-37	111575	Yves Minet	01/2012
6544	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
6545	2^370610-3911	111565	Yves Minet	04/2017
6546	(154*10^111549+17)/9	111551	Robert Price	06/2022
6547	26200^18097+18097^26200	111550	Hans Havermann	01/2021
6548	286^45405+45405^286	111532	Norbert Schneider	04/2015
6549	4*5^159563-9	111531	Lelio R Paula	11/2014
6550	5*10^111528-21	111529	Robert Price	12/2021
6551	(4^185225+23)/3	111517	Robert Price	10/2018
6552	2^370393-2797093	111500	Enzo Doria	03/2016
6553	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
6554	(2^370371+554)/2	111493	Stefano Morozzi	09/2020
6555	6^143273-5	111489	Paul Bourdelais	01/2021
6556	2^370292-2791979	111469	Enzo Doria	03/2016
6557	(14*10^111443-11)/3	111444	Robert Price	08/2022
6558	2^370177-461551	111435	Enzo Doria	07/2015
6559	(2^370169+1706)/2	111432	Stefano Morozzi	09/2020
6560	109^54683-108	111413	Norbert Schneider	02/2017
6562	(83*10^111406-173)/9	111407	Robert Price	04/2021
6561	959^37362-37362^959	111407	Henri Lifchitz	10/2024
6563	(2^370043+1010)/2	111394	Stefano Morozzi	09/2020
6564	32961^2396+2396^32961	111392	Hans Havermann	10/2020
6565	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
6566	(19*10^111385+11)/3	111386	Robert Price	07/2023
6567	(23*10^111380-29)/3	111381	Robert Price	03/2022
6568	2^369974+733	111374	Lelio R Paula	05/2013
6569	121^53470+120	111367	Norbert Schneider	10/2018
6570	2^369915-286267	111356	Enzo Doria	07/2015
6571	(62*10^111347-629)/9	111348	Robert Price	07/2021
6572	2^369855-1615	111338	Lelio R Paula	05/2017
6573	7*10^111325+3	111326	Robert Price	08/2015
6574	51^65176+2	111293	Lelio R Paula	08/2013
6575	2^369643-1865767	111274	Enzo Doria	03/2016
6576	2^369603+885	111262	Lelio R Paula	05/2017
6577	25555^22564+22564^25555	111252	Hans Havermann	10/2020
6578	F(532391)/89441689/1425422598617	111243	Serge Batalov	07/2024
6579	L(532277)	111240	Renaud Lifchitz	03/2004
6580	105^55033-2	111233	Lelio R Paula	10/2017
6581	(35*10^111232-737)/9	111233	Robert Price	07/2018
6582	26970^13307+13307^26970	111227	Hans Havermann	10/2020
6583	25419^23716+23716^25419	111210	Hans Havermann	10/2020
6584	(26^78593-3^78593)/23	111206	Robert Price	02/2025
6585	9*10^111201-29	111202	Robert Price	09/2019
6586	2^369392+29835	111199	Lelio R Paula	05/2017
6587	3^233059+16	111198	Robert Price	03/2020
6588	2^369354-3413	111187	Yves Minet	12/2016
6589	2^369296-27	111170	Lelio R Paula	02/2013
6590	(2468^40960+1)/(2468^8192+1)	111161	Martin Hopf	08/2024
6591	2^369239-109837	111153	Enzo Doria	05/2014
6592	2^369224-291839	111148	Enzo Doria	07/2015
6593	2^369216+2798881	111146	Enzo Doria	04/2016
6594	26842^13817+13817^26842	111137	Hans Havermann	11/2020
6595	(5*10^111119-191)/3	111120	Robert Price	05/2021
6596	(29*10^111112-23)/3	111113	Robert Price	03/2022
6597	10^111111+163849	111112	Patrick De Geest	03/2017
6598	10^111111-312911	111111	Patrick De Geest	03/2017
6599	2^369092-216923	111108	Enzo Doria	05/2014
6600	2^369081-55	111105	Lelio R Paula	02/2013
6601	(2^369047+3618)/2	111094	Stefano Morozzi	09/2020
6602	88^57124-87	111077	Norbert Schneider	11/2015
6603	2^368980+753	111075	Lelio R Paula	05/2013
6604	2^368946-3623	111064	Yves Minet	03/2017
6605	2^368929+29835	111059	Lelio R Paula	05/2017
6606	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
6607	111^54298+110	111057	Norbert Schneider	04/2017
6608	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
6609	(29*10^111020-41)/3	111021	Tyler Busby	03/2024
6610	35799^1262+1262^35799	111015	Hans Havermann	10/2020
6611	(298*10^111004+11)/3	111006	Robert Price	11/2020
6612	27648^10349+10349^27648	111004	Hans Havermann	11/2020
6613	28899^6932+6932^28899	110997	Hans Havermann	11/2020
6614	(749^38809+1)/(749^197+1)	110990	Martin Hopf	11/2023
6615	2^368641-460303	110972	Enzo Doria	06/2015
6616	2^368619-109087	110966	Enzo Doria	04/2014
6617	(74*10^110961+313)/9	110962	Robert Price	06/2019
6618	25258^24711+24711^25258	110956	Hans Havermann	11/2020
6619	(2^368539+1290)/2	110941	Stefano Morozzi	01/2021
6620	3*2^368489+7	110927	Lelio R Paula	09/2014
6621	(14*10^110922+61)/3	110923	Robert Price	12/2018
6622	97411!4-2	110913	Robert Price	07/2017
6623	(301*10^110903+23)/9	110905	Robert Price	06/2021
6624	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
6625	25830^19619+19619^25830	110880	Hans Havermann	10/2020
6626	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
6627	26022^18191+18191^26022	110850	Hans Havermann	10/2020
6628	(2^368211+2250)/2	110843	Stefano Morozzi	01/2021
6629	(37*10^110813+251)/9	110814	Robert Price	09/2021
6630	2^368050-64875	110795	Lelio R Paula	05/2017
6631	2^368048+25	110794	Lelio R Paula	02/2013
6632	(2^368017+2262)/2	110784	Stefano Morozzi	02/2021
6633	69^60239-2	110771	Lelio R Paula	10/2013
6634	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
6635	2^367924-69	110757	Lelio R Paula	02/2013
6636	(23*10^110738+61)/3	110739	Robert Price	01/2022
6637	(2^367779+3750)/2	110713	Stefano Morozzi	01/2021
6638	2^367709-109723	110692	Enzo Doria	04/2014
6639	2^367687+213413	110685	Enzo Doria	09/2023
6640	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
6641	(2^367626+3514)/2	110667	Stefano Morozzi	09/2020
6642	(1288676*34^72242-455)/33	110642	Eric Chen	03/2023
6643	379*10^110616+9	110619	Jason Yuen	01/2025
6644	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
6645	140^51515-139	110558	Norbert Schneider	04/2019
6646	2^367215+1879223	110543	Enzo Doria	09/2016
6647	25782^19375+19375^25782	110534	Hans Havermann	10/2020
6648	26117^17058+17058^26117	110526	Hans Havermann	10/2020
6649	2^367141+41	110521	Lelio R Paula	02/2013
6650	2^367126+29835	110516	Lelio R Paula	05/2017
6651	(10^110503-1)/9+2(10^59183-1)/910^25660	110503	Makoto Morimoto	09/2020
6652	(10^110503-1)/9+2(10^65511-1)/910^22496	110503	Makoto Morimoto	09/2020
6653	(10^110503-1)/9+210^108327+210^2175	110503	Makoto Morimoto	09/2020
6654	(10^110503-1)/9+210^66251+210^44251	110503	Makoto Morimoto	09/2020
6655	(10^110503-1)/9+3(10^28813-1)/910^40845	110503	Makoto Morimoto	09/2020
6656	(10^110503-1)/9+3(10^82573-1)/910^13965	110503	Makoto Morimoto	09/2020
6657	(10^110503-1)/9+4(10^43305-1)/910^33599	110503	Makoto Morimoto	09/2020
6658	(10^110503-1)/9+510^70327+510^40175	110503	Makoto Morimoto	09/2020
6659	(10^110503-1)/9+510^99423+510^11079	110503	Makoto Morimoto	09/2020
6660	(10^110503-1)/9+7(10^23617-1)/910^43443	110503	Makoto Morimoto	09/2020
6661	(10^110503-1)/9+8(10^30251-1)/910^40126	110503	Makoto Morimoto	09/2020
6662	3(10^110503-1)/9+110^106036+1*10^4466	110503	Makoto Morimoto	09/2020
6663	3(10^110503-1)/9+110^58962+1*10^51540	110503	Makoto Morimoto	09/2020
6664	3(10^110503-1)/9+110^78213+1*10^32289	110503	Makoto Morimoto	09/2020
6665	3(10^110503-1)/9+210^76898+2*10^33604	110503	Makoto Morimoto	09/2020
6666	3(10^110503-1)/9-110^100802-1*10^9700	110503	Makoto Morimoto	09/2020
6667	3(10^110503-1)/9-110^76355-1*10^34147	110503	Makoto Morimoto	09/2020
6668	3(10^110503-1)/9-210^105704-2*10^4798	110503	Makoto Morimoto	09/2020
6669	7(10^110503-1)/9+1(10^27685-1)/9*10^41409	110503	Makoto Morimoto	09/2020
6670	7(10^110503-1)/9+1(10^91035-1)/9*10^9734	110503	Makoto Morimoto	09/2020
6671	7(10^110503-1)/9-1(10^23717-1)/9*10^43393	110503	Makoto Morimoto	09/2020
6672	7(10^110503-1)/9-110^57906-1*10^52596	110503	Makoto Morimoto	09/2020
6673	7(10^110503-1)/9-110^72287-1*10^38215	110503	Makoto Morimoto	09/2020
6674	7(10^110503-1)/9-2(10^53823-1)/9*10^28340	110503	Makoto Morimoto	09/2020
6675	7(10^110503-1)/9-2(10^88659-1)/9*10^10922	110503	Makoto Morimoto	09/2020
6676	7(10^110503-1)/9-3(10^79921-1)/9*10^15291	110503	Makoto Morimoto	09/2020
6677	7(10^110503-1)/9-310^60024-3*10^50478	110503	Makoto Morimoto	09/2020
6678	7(10^110503-1)/9-4(10^103091-1)/9*10^3706	110503	Makoto Morimoto	09/2020
6679	7(10^110503-1)/9-410^103658-4*10^6844	110503	Makoto Morimoto	09/2020
6680	7(10^110503-1)/9-410^78188-4*10^32314	110503	Makoto Morimoto	09/2020
6681	7(10^110503-1)/9-5(10^35035-1)/9*10^37734	110503	Makoto Morimoto	09/2020
6682	7(10^110503-1)/9-6(10^67347-1)/9*10^21578	110503	Makoto Morimoto	09/2020
6683	7(10^110503-1)/9-610^60391-6*10^50111	110503	Makoto Morimoto	09/2020
6684	(10^110503-1)-4(10^96247-1)/910^7128	110503	Makoto Morimoto	09/2020
6685	(10^110503-1)-410^74037-410^36465	110503	Makoto Morimoto	09/2020
6686	(10^110503-1)-410^77787-410^32715	110503	Makoto Morimoto	09/2020
6687	(10^110503-1)-410^91179-410^19323	110503	Makoto Morimoto	09/2020
6688	(10^110503-1)-5(10^99143-1)/910^5680	110503	Makoto Morimoto	09/2020
6689	(10^110503-1)-7(10^85075-1)/910^12714	110503	Makoto Morimoto	09/2020
6690	(10^110503-1)-710^100712-710^9790	110503	Makoto Morimoto	09/2020
6691	(10^110503-1)-710^76427-710^34075	110503	Makoto Morimoto	09/2020
6692	(10^110503-1)-710^90451-710^20051	110503	Makoto Morimoto	09/2020
6693	(10^110503-1)-810^106252-810^4250	110503	Makoto Morimoto	09/2020
6694	(11*10^110496+49)/3	110497	Robert Price	07/2018
6695	25447^21958+21958^25447	110481	Hans Havermann	11/2020
6696	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
6697	7*10^110468-23	110469	Robert Price	07/2019
6698	5*3^231464-2^231464	110438	Jon Grantham	08/2023
6699	2^366853+5711	110434	Lelio R Paula	05/2017
6700	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
6701	2^366816+315	110423	Lelio R Paula	05/2017
6702	2^366775-2787037	110411	Enzo Doria	03/2016
6703	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
6704	2^366751+2797553	110404	Enzo Doria	03/2016
6705	25276^23331+23331^25276	110404	Hans Havermann	10/2020
6706	2^366748+255	110403	Lelio R Paula	05/2017
6707	2^366738-2985	110400	Yves Minet	09/2014
6708	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
6709	(2^366722+1314)/2	110395	Stefano Morozzi	02/2021
6710	2^366716+1871791	110393	Enzo Doria	05/2016
6711	(239*23^81066-349)/22	110391	Eric Chen	08/2023
6712	2^366695+1334025	110387	Henri Lifchitz	10/2024
6713	2^366649+1871687	110373	Enzo Doria	05/2016
6714	2^366629-351205	110367	Enzo Doria	06/2015
6715	(31*10^110363+257)/9	110364	Robert Price	12/2021
6716	(17*19^86292-215)/18	110347	Eric Chen	01/2023
6718	2^366558+1874479	110345	Enzo Doria	06/2016
6717	25132^24581+24581^25132	110345	Hans Havermann	10/2020
6719	(2^366539+770)/2	110339	Stefano Morozzi	09/2020
6720	26368^15285+15285^26368	110331	Hans Havermann	10/2020
6721	(23*10^110290+19)/3	110291	Robert Price	07/2019
6722	18^87853-4409	110280	Enzo Doria	03/2013
6723	28490^7419+7419^28490	110267	Hans Havermann	11/2020
6724	2^366218-23	110243	Lelio R Paula	02/2013
6725	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
6726	2^366178-343991	110231	Enzo Doria	07/2015
6727	12^102123-11	110210	Riley Fisher	09/2023
6728	25777^18798+18798^25777	110174	Hans Havermann	10/2020
6729	2^365944+1871341	110161	Enzo Doria	05/2016
6730	2^365838-461267	110129	Enzo Doria	07/2015
6731	30152^4491+4491^30152	110126	Hans Havermann	11/2020
6732	2^365802+23359	110118	Enzo Doria	10/2023
6733	10^110111+464019	110112	Patrick De Geest	05/2021
6734	10^110111-40001	110111	Robert Price	01/2021
6735	2^365763-6555	110106	Lelio R Paula	04/2017
6736	(2^365689+2^182845+1)/5	110083		11/2006
6737	2^365666-459161	110077	Enzo Doria	05/2015
6738	3*10^110076-7	110077	Robert Price	08/2015
6739	13^98785-72	110041	Lelio R Paula	03/2017
6741	(25^78707+1)/26	110027	Robert Price	06/2013
6740	(7*10^110027-277)/9	110027	Robert Price	02/2022
6742	(16*10^110014-73)/3	110015	Robert Price	07/2020
6743	(7*10^110006-151)/9	110006	Robert Price	02/2018
6744	6^141361-7	110001	Lelio R Paula	11/2014
6745	10^110000+8029681	110001	Hayden Chesnut	11/2024
6746	10^110000+2044477	110001	Hayden Chesnut	11/2024
6747	10^110000+76407	110001	Hayden Chesnut	11/2024
6748	10^110000+167311	110001	Hayden Chesnut	11/2024
6749	20^84536+81	109984	Lelio R Paula	03/2017
6750	5*2^365347-9	109982	Lelio R Paula	09/2014

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301157 PRPs in the top)