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 ?
5751	91^65772-2	128851	Lelio R Paula	05/2017
5752	2^428022+43	128848	Lelio R Paula	05/2017
5753	2^427999-459397	128841	Enzo Doria	05/2015
5754	2^427993+76847	128839	Enzo Doria	05/2016
5755	31059^14060+14060^31059	128833	Hans Havermann	03/2021
5756	10^128805+152871	128806	Patrick De Geest	05/2021
5757	10^128805-10001	128805	Robert Price	02/2021
5758	2^427824-1851507	128788	Enzo Doria	08/2015
5759	2^427807-21469	128783	Enzo Doria	07/2013
5760	29082^26783+26783^29082	128772	Hans Havermann	04/2021
5761	40055^1638+1638^40055	128750	Hans Havermann	04/2021
5762	(923^43411-1)/922	128720	Tom Wu	07/2024
5763	11^123594-240	128710	Enzo Doria	09/2012
5764	2^427504-21503	128692	Enzo Doria	07/2013
5765	37727^2574+2574^37727	128673	Hans Havermann	04/2021
5766	29686^21591+21591^29686	128668	Hans Havermann	04/2021
5767	10^128668-70000000001	128668	Robert Price	08/2021
5768	10^128668-350729	128668	Alfred Reich	08/2024
5769	Phi(57476,13#)	128668	Henri Lifchitz	12/2025
5770	2^427420+91	128667	Lelio R Paula	05/2017
5771	8*10^128651-37	128652	Robert Price	03/2022
5772	(68*10^128645-257)/9	128646	Robert Price	07/2019
5773	Phi(236553,7)	128631	Henri Lifchitz	12/2025
5774	2^427269-113635	128621	Enzo Doria	08/2014
5775	136^60270+135	128589	Alfred Reich	03/2026
5776	2^427130+1877569	128579	Enzo Doria	08/2016
5777	2^427068+20011	128561	Enzo Doria	06/2023
5778	2^427016-115349	128545	Enzo Doria	07/2015
5779	2^427001+1334025	128541	Henri Lifchitz	11/2024
5780	(4*10^128510+137)/3	128511	Robert Price	03/2018
5781	2^426889-112879	128507	Enzo Doria	06/2014
5782	2^426804+1869931	128481	Enzo Doria	05/2016
5783	2^426750+77635	128465	Enzo Doria	05/2016
5784	27708^28913-28913^27708	128450	Frank Doornink	03/2024
5785	36988^2969+2969^36988	128445	Hans Havermann	03/2021
5786	36664^3185+3185^36664	128439	Hans Havermann	03/2021
5787	32618^8649+8649^32618	128416	Hans Havermann	04/2021
5788	28883^27874+27874^28883	128391	Hans Havermann	04/2021
5789	2^426425-91	128367	Lelio R Paula	05/2017
5790	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
5791	2^426352+74971	128345	Enzo Doria	04/2016
5792	(199*10^128343-7)/3	128345	Robert Price	05/2020
5793	4*10^128343-21	128344	Robert Price	09/2018
5794	(65*10^128338+493)/9	128339	Robert Price	08/2021
5795	35632^3997+3997^35632	128337	Hans Havermann	04/2021
5796	2^426300-1863689	128330	Enzo Doria	03/2016
5797	2^426293+1881017	128327	Enzo Doria	11/2016
5798	(88*10^128324-637)/9	128325	Robert Price	11/2020
5799	Phi(161347,7)	128320	Henri Lifchitz	12/2025
5800	Phi(135199,-9)	128312	Henri Lifchitz	12/2025
5801	(491*10^128285+31)/9	128287	Robert Price	04/2022
5802	39103^1908+1908^39103	128281	Hans Havermann	04/2021
5803	2^426043+35	128252	Robert Price	11/2015
5804	(4*10^128244-19)/3	128245	Robert Price	03/2018
5805	26220^29021-29021^26220	128234	Frank Doornink	03/2024
5806	35489^4102+4102^35489	128222	Hans Havermann	04/2021
5807	34721^4926+4926^34721	128208	Hans Havermann	04/2021
5808	(305*10^128198+1)/9	128200	Robert Price	02/2020
5809	2^425808-459959	128181	Enzo Doria	06/2015
5810	30632^15291+15291^30632	128178	Hans Havermann	04/2021
5811	U(623603)	128177	Serge Batalov	07/2024
5812	35981^3648+3648^35981	128167	Hans Havermann	04/2021
5813	2^425627-113605	128127	Enzo Doria	08/2014
5814	(4*10^128109+119)/3	128110	Robert Price	12/2021
5815	(22*10^128094+53)/3	128095	Robert Price	07/2019
5816	(86*10^128086-221)/9	128087	Robert Price	09/2019
5817	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
5818	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
5819	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
5820	Phi(149401,10)/30037901719561	128003	Makoto Kamada	07/2022
5821	2^425205+4911	128000	Marek Hubal	02/2017
5822	29241^23836+23836^29241	127995	Hans Havermann	04/2021
5823	2^425118-113663	127974	Enzo Doria	08/2014
5824	(86*10^127967-329)/9	127968	Robert Price	01/2020
5825	2^425061+1869761	127957	Enzo Doria	05/2016
5826	746^44541+44541^746	127955	Norbert Schneider	07/2019
5827	30236^17043+17043^30236	127946	Hans Havermann	03/2021
5828	2^424938+212419	127920	Enzo Doria	08/2023
5829	2^424918-21141	127914	Enzo Doria	07/2013
5830	Phi(274823,-3)	127907	Henri Lifchitz	12/2025
5831	(62*10^127903+91)/9	127904	Robert Price	07/2021
5832	2^424864-29489	127897	Enzo Doria	08/2015
5833	30438^15893+15893^30438	127877	Hans Havermann	02/2021
5834	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
5835	28929^26258+26258^28929	127845	Hans Havermann	03/2021
5836	30563^15220+15220^30563	127828	Hans Havermann	03/2021
5837	2^424632-2786639	127827	Enzo Doria	03/2016
5838	10^127821-700001	127821	Robert Price	08/2021
5839	2^424577-113755	127811	Enzo Doria	09/2014
5840	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
5841	(56*10^127752+691)/9	127753	Robert Price	05/2019
5842	11^122629-720	127705	Enzo Doria	11/2012
5843	22*10^127645+3	127647	Robert Price	01/2020
5844	28715^27844+27844^28715	127631	Hans Havermann	03/2021
5845	(56*10^127612+187)/9	127613	Robert Price	10/2021
5846	(5*36^81995+821)/7	127609	Eric Chen	01/2021
5847	4*10^127562-39	127563	Robert Price	09/2020
5848	32595^8186+8186^32595	127547	Hans Havermann	03/2021
5849	2^423696-21429	127546	Enzo Doria	07/2013
5850	2^423664-1864559	127536	Enzo Doria	03/2016
5851	37889^2322+2322^37889	127530	Hans Havermann	03/2021
5852	37668^2429+2429^37668	127523	Hans Havermann	03/2021
5853	3^267267-4	127519	Henri Lifchitz	10/2014
5854	fibonacci(610144)-2	127513	Jon Grantham	08/2023
5855	26253^28852-28852^26253	127503	Frank Doornink	03/2024
5856	(103*10^127491+17)/3	127493	Robert Price	08/2020
5857	29376^21869+21869^29376	127487	Hans Havermann	03/2021
5858	31186^12241+12241^31186	127483	Hans Havermann	02/2021
5859	(19^99689+5^99689)/24	127477	Robert Price	09/2013
5860	7239^33023-7238^33023	127459	Norbert Schneider	02/2026
5861	27069^28754-28754^27069	127452	Frank Doornink	01/2024
5862	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
5863	30594^14645+14645^30594	127446	Hans Havermann	03/2021
5864	2^423328-21537	127435	Enzo Doria	07/2013
5865	(67*10^127413-7)/3	127415	Robert Price	01/2020
5866	(5*34^83193+700233)/11	127408	Eric Chen	08/2023
5867	(2*10^127407+73)/3	127407	Robert Price	09/2020
5868	(2^423165-7)/25	127384	Lelio R Paula	05/2015
5869	(7726^32768+1)/13917994151414876602369	127379	Kellen Shenton	04/2021
5870	(4*10^127349+17)/3	127350	Tyler Busby	01/2023
5871	29512^20647+20647^29512	127341	Hans Havermann	03/2021
5872	2^422987-3001935	127332	Paul Bourdelais	07/2023
5873	(112*10^127324+17)/3	127326	Robert Price	03/2020
5875	29565^20252+20252^29565	127321	Hans Havermann	03/2021
5874	232^232^232+1831^1831	127321	Henri Lifchitz	03/2025
5876	fibonacci(609165)-3	127308	Jon Grantham	08/2023
5878	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
5877	(5^182099-3^182099)/2	127282	Kellen Shenton	05/2022
5879	(16*10^127259+197)/3	127260	Robert Price	04/2019
5880	(26*10^127240+61)/3	127241	Robert Price	10/2019
5881	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
5882	2^422515-114997	127190	Enzo Doria	06/2015
5883	5*10^127179-3	127180	Robert Price	07/2015
5884	31678^10343+10343^31678	127176	Hans Havermann	03/2021
5885	(44*10^127169-233)/9	127170	Robert Price	01/2019
5886	34947^4352+4352^34947	127162	Hans Havermann	03/2021
5887	6*10^127158+19	127159	Robert Price	11/2021
5888	30469^14902+14902^30469	127155	Hans Havermann	03/2021
5889	5*10^127153+77	127154	Robert Price	12/2018
5890	29941^17620+17620^29941	127130	Hans Havermann	02/2021
5891	31607^10516+10516^31607	127119	Hans Havermann	03/2021
5892	(19*10^127118-97)/3	127119	Robert Price	10/2021
5893	(29*10^127111+691)/9	127112	Robert Price	08/2021
5894	736^44335+44335^736	127104	Norbert Schneider	07/2019
5895	33040^7023+7023^33040	127090	Hans Havermann	03/2021
5896	(4*10^127081+167)/9	127081	Robert Price	03/2022
5897	29748^18661+18661^29748	127052	Hans Havermann	03/2021
5898	27905^28578-28578^27905	127049	Frank Doornink	03/2024
5899	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
5900	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
5901	(14*10^127014-137)/3	127015	Robert Price	04/2021
5902	31436^10965+10965^31436	127002	Hans Havermann	03/2021
5903	28905^24758+24758^28905	127001	Hans Havermann	03/2021
5904	2^421860-113285	126993	Enzo Doria	07/2014
5905	(10^127030+7)/81234833/9230384921/6092460488946445358851	126991	Alfred Reich	07/2021
5906	(2^421827-7)/11	126982	Lelio R Paula	05/2015
5907	26268^28729-28729^26268	126966	Frank Doornink	03/2024
5908	11^121910-840	126957	Enzo Doria	12/2012
5909	(56*10^126935+187)/9	126936	Robert Price	10/2021
5910	28915^24538+24538^28915	126933	Hans Havermann	03/2021
5911	(29*10^126928-77)/3	126929	Robert Price	02/2020
5912	(259*10^126919-1)/3	126921	Robert Price	12/2020
5913	10^126919+204567	126920	Patrick De Geest	05/2021
5914	(2^421617+100280245065)	126920	Paul Bourdelais	05/2022
5915	10^126919-100001	126919	Robert Price	07/2020
5916	28340^28503+28503^28340	126907	Norbert Schneider	02/2021
5917	2^421534-3001935	126895	Paul Bourdelais	07/2023
5918	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
5919	(5*10^126871-119)/3	126872	Robert Price	03/2018
5920	Phi(47471,561)	126871	Henri Lifchitz	12/2025
5921	331^50339-10004	126846	Enzo Doria	07/2012
5922	2^421363-2790757	126843	Enzo Doria	03/2016
5923	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
5924	37938^2203+2203^37938	126828	Hans Havermann	03/2021
5925	(13*10^126819+77)/9	126820	Robert Price	07/2022
5926	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
5928	(14*10^126784-83)/3	126785	Robert Price	12/2018
5927	2^421169-3001935	126785	Paul Bourdelais	07/2023
5929	2^421161-286183	126783	Enzo Doria	06/2015
5930	26733^28628-28628^26733	126738	Frank Doornink	03/2024
5931	(106*10^126726+17)/3	126728	Robert Price	04/2021
5932	30718^13347+13347^30718	126724	Hans Havermann	03/2021
5933	2^420939-113935	126716	Enzo Doria	10/2014
5934	11*23^93048+356	126708	Eric Chen	08/2023
5935	177^56363-2	126703	Lelio R Paula	10/2017
5936	2^420741-113659	126656	Enzo Doria	08/2014
5937	2^420694-21	126642	Lelio R Paula	05/2017
5938	(13*10^126638+437)/9	126639	Robert Price	04/2018
5939	(167*10^126637-17)/3	126639	Robert Price	03/2020
5940	4*10^126625+87	126626	Robert Price	08/2018
5941	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
5942	7*10^126600-99	126601	Robert Price	06/2019
5943	U(655247)/250330563881/206066063082749	126596	Serge Batalov	07/2024
5944	2^420424-59189	126561	Enzo Doria	10/2015
5945	28717^25534+25534^28717	126560	Hans Havermann	03/2021
5946	(86*10^126542+103)/9	126543	Robert Price	12/2021
5947	(19*10^126517-7)/3	126518	Robert Price	12/2023
5948	2026^38261-2025^38261	126516	Henri Lifchitz	12/2025
5949	28922^23655+23655^28922	126503	Hans Havermann	03/2021
5950	2^420126+71893	126471	Enzo Doria	04/2016
5951	25982^28643-28643^25982	126450	Frank Doornink	03/2024
5952	(43*10^126441+47)/9	126442	Robert Price	12/2018
5953	8*10^126408+71	126409	Robert Price	05/2022
5954	2^419866+1877059	126393	Enzo Doria	07/2016
5955	29315^20484+20484^29315	126390	Hans Havermann	03/2021
5956	29433^19676+19676^29433	126384	Hans Havermann	03/2021
5957	F(604711)	126377	Henri Lifchitz	02/2005
5958	2^419757+72707	126360	Enzo Doria	04/2016
5959	2^419720-21569	126349	Enzo Doria	07/2013
5960	2^419637+29	126324	Henri Lifchitz	02/2006
5961	31004^11865+11865^31004	126319	Hans Havermann	03/2021
5962	2^419612+1876741	126316	Enzo Doria	07/2016
5963	2^419520+2793271	126289	Enzo Doria	03/2016
5964	(2^419447-5)/369	126264	Lelio R Paula	05/2014
5965	2^419328-1859939	126231	Enzo Doria	03/2016
5966	2^419282-1851507	126217	Enzo Doria	08/2015
5967	(133*10^126212+17)/3	126214	Robert Price	11/2021
5968	2^419251+1866143	126208	Enzo Doria	03/2016
5969	11^121185+2	126202	Robert Price	05/2014
5970	28203^28352+28352^28203	126175	Norbert Schneider	01/2021
5971	Phi(267889,3)	126161	Henri Lifchitz	12/2025
5972	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
5973	2^418851+23	126087	Robert Price	09/2015
5974	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
5975	2^418829+167	126081	Lelio R Paula	01/2012
5976	31037^11530+11530^31037	126067	Hans Havermann	03/2021
5977	4*10^126064-69	126065	Robert Price	01/2022
5978	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
5979	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
5980	(35*10^126048-323)/9	126049	Robert Price	10/2021
5981	33016^6551+6551^33016	126000	Hans Havermann	03/2021
5982	2^418548-111546435	125996	Paul Bourdelais	10/2021
5983	25134^28625-28625^25134	125958	Frank Doornink	12/2023
5984	34736^4227+4227^34736	125954	Hans Havermann	03/2021
5985	(23*35^81566-144013)/34	125944	Eric Chen	05/2025
5986	26197^28502-28502^26197	125930	Frank Doornink	03/2024
5987	2^418319-109501	125927	Enzo Doria	04/2014
5988	2^418316-112373	125926	Enzo Doria	06/2014
5989	40398^1309+1309^40398	125919	Hans Havermann	03/2021
5990	997^41985+996	125901	Alfred Reich	03/2026
5991	(8*10^125894-29)/3	125895	Robert Price	07/2018
5992	(26*10^125886-413)/9	125887	Robert Price	05/2018
5993	10^(262938+1)-710^62938-1	125877	Robert Price	07/2023
5994	55*10^125847+9	125849	Robert Price	03/2022
5995	4*10^125832+57	125833	Robert Price	05/2022
5996	2^417968+1869811	125821	Enzo Doria	06/2016
5997	2^417902+63	125802	Lelio R Paula	09/2015
5998	(10^125792-91)/9	125792	Serge Batalov	12/2014
5999	30438^13573+13573^30438	125791	Hans Havermann	03/2021
6000	32867^6714+6714^32867	125782	Hans Havermann	03/2021

Find by discoverer :

PRP Records

Probable Primes Top 10000

(302940 PRPs in the top)