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 ?
5751	Phi(274823,-3)	127907	Henri Lifchitz	12/2025
5752	(62*10^127903+91)/9	127904	Robert Price	07/2021
5753	2^424864-29489	127897	Enzo Doria	08/2015
5754	30438^15893+15893^30438	127877	Hans Havermann	02/2021
5755	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
5756	28929^26258+26258^28929	127845	Hans Havermann	03/2021
5757	30563^15220+15220^30563	127828	Hans Havermann	03/2021
5758	2^424632-2786639	127827	Enzo Doria	03/2016
5759	10^127821-700001	127821	Robert Price	08/2021
5760	2^424577-113755	127811	Enzo Doria	09/2014
5761	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
5762	(56*10^127752+691)/9	127753	Robert Price	05/2019
5763	11^122629-720	127705	Enzo Doria	11/2012
5764	22*10^127645+3	127647	Robert Price	01/2020
5765	28715^27844+27844^28715	127631	Hans Havermann	03/2021
5766	(56*10^127612+187)/9	127613	Robert Price	10/2021
5767	(5*36^81995+821)/7	127609	Eric Chen	01/2021
5768	4*10^127562-39	127563	Robert Price	09/2020
5769	32595^8186+8186^32595	127547	Hans Havermann	03/2021
5770	2^423696-21429	127546	Enzo Doria	07/2013
5771	2^423664-1864559	127536	Enzo Doria	03/2016
5772	37889^2322+2322^37889	127530	Hans Havermann	03/2021
5773	37668^2429+2429^37668	127523	Hans Havermann	03/2021
5774	3^267267-4	127519	Henri Lifchitz	10/2014
5775	fibonacci(610144)-2	127513	Jon Grantham	08/2023
5776	26253^28852-28852^26253	127503	Frank Doornink	03/2024
5777	(103*10^127491+17)/3	127493	Robert Price	08/2020
5778	29376^21869+21869^29376	127487	Hans Havermann	03/2021
5779	31186^12241+12241^31186	127483	Hans Havermann	02/2021
5780	(19^99689+5^99689)/24	127477	Robert Price	09/2013
5781	27069^28754-28754^27069	127452	Frank Doornink	01/2024
5782	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
5783	30594^14645+14645^30594	127446	Hans Havermann	03/2021
5784	2^423328-21537	127435	Enzo Doria	07/2013
5785	(67*10^127413-7)/3	127415	Robert Price	01/2020
5786	(5*34^83193+700233)/11	127408	Eric Chen	08/2023
5787	(2*10^127407+73)/3	127407	Robert Price	09/2020
5788	(2^423165-7)/25	127384	Lelio R Paula	05/2015
5789	(7726^32768+1)/13917994151414876602369	127379	Kellen Shenton	04/2021
5790	(4*10^127349+17)/3	127350	Tyler Busby	01/2023
5791	29512^20647+20647^29512	127341	Hans Havermann	03/2021
5792	2^422987-3001935	127332	Paul Bourdelais	07/2023
5793	(112*10^127324+17)/3	127326	Robert Price	03/2020
5795	29565^20252+20252^29565	127321	Hans Havermann	03/2021
5794	232^232^232+1831^1831	127321	Henri Lifchitz	03/2025
5796	fibonacci(609165)-3	127308	Jon Grantham	08/2023
5798	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
5797	(5^182099-3^182099)/2	127282	Kellen Shenton	05/2022
5799	(16*10^127259+197)/3	127260	Robert Price	04/2019
5800	(26*10^127240+61)/3	127241	Robert Price	10/2019
5801	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
5802	2^422515-114997	127190	Enzo Doria	06/2015
5803	5*10^127179-3	127180	Robert Price	07/2015
5804	31678^10343+10343^31678	127176	Hans Havermann	03/2021
5805	(44*10^127169-233)/9	127170	Robert Price	01/2019
5806	34947^4352+4352^34947	127162	Hans Havermann	03/2021
5807	6*10^127158+19	127159	Robert Price	11/2021
5808	30469^14902+14902^30469	127155	Hans Havermann	03/2021
5809	5*10^127153+77	127154	Robert Price	12/2018
5810	29941^17620+17620^29941	127130	Hans Havermann	02/2021
5811	31607^10516+10516^31607	127119	Hans Havermann	03/2021
5812	(19*10^127118-97)/3	127119	Robert Price	10/2021
5813	(29*10^127111+691)/9	127112	Robert Price	08/2021
5814	736^44335+44335^736	127104	Norbert Schneider	07/2019
5815	33040^7023+7023^33040	127090	Hans Havermann	03/2021
5816	(4*10^127081+167)/9	127081	Robert Price	03/2022
5817	29748^18661+18661^29748	127052	Hans Havermann	03/2021
5818	27905^28578-28578^27905	127049	Frank Doornink	03/2024
5819	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
5820	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
5821	(14*10^127014-137)/3	127015	Robert Price	04/2021
5822	31436^10965+10965^31436	127002	Hans Havermann	03/2021
5823	28905^24758+24758^28905	127001	Hans Havermann	03/2021
5824	2^421860-113285	126993	Enzo Doria	07/2014
5825	(10^127030+7)/81234833/9230384921/6092460488946445358851	126991	Alfred Reich	07/2021
5826	(2^421827-7)/11	126982	Lelio R Paula	05/2015
5827	26268^28729-28729^26268	126966	Frank Doornink	03/2024
5828	11^121910-840	126957	Enzo Doria	12/2012
5829	(56*10^126935+187)/9	126936	Robert Price	10/2021
5830	28915^24538+24538^28915	126933	Hans Havermann	03/2021
5831	(29*10^126928-77)/3	126929	Robert Price	02/2020
5832	(259*10^126919-1)/3	126921	Robert Price	12/2020
5833	10^126919+204567	126920	Patrick De Geest	05/2021
5834	(2^421617+100280245065)	126920	Paul Bourdelais	05/2022
5835	10^126919-100001	126919	Robert Price	07/2020
5836	28340^28503+28503^28340	126907	Norbert Schneider	02/2021
5837	2^421534-3001935	126895	Paul Bourdelais	07/2023
5838	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
5839	(5*10^126871-119)/3	126872	Robert Price	03/2018
5840	Phi(47471,561)	126871	Henri Lifchitz	12/2025
5841	331^50339-10004	126846	Enzo Doria	07/2012
5842	2^421363-2790757	126843	Enzo Doria	03/2016
5843	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
5844	37938^2203+2203^37938	126828	Hans Havermann	03/2021
5845	(13*10^126819+77)/9	126820	Robert Price	07/2022
5846	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
5848	(14*10^126784-83)/3	126785	Robert Price	12/2018
5847	2^421169-3001935	126785	Paul Bourdelais	07/2023
5849	2^421161-286183	126783	Enzo Doria	06/2015
5850	26733^28628-28628^26733	126738	Frank Doornink	03/2024
5851	(106*10^126726+17)/3	126728	Robert Price	04/2021
5852	30718^13347+13347^30718	126724	Hans Havermann	03/2021
5853	2^420939-113935	126716	Enzo Doria	10/2014
5854	11*23^93048+356	126708	Eric Chen	08/2023
5855	177^56363-2	126703	Lelio R Paula	10/2017
5856	2^420741-113659	126656	Enzo Doria	08/2014
5857	2^420694-21	126642	Lelio R Paula	05/2017
5858	(13*10^126638+437)/9	126639	Robert Price	04/2018
5859	(167*10^126637-17)/3	126639	Robert Price	03/2020
5860	4*10^126625+87	126626	Robert Price	08/2018
5861	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
5862	7*10^126600-99	126601	Robert Price	06/2019
5863	U(655247)/250330563881/206066063082749	126596	Serge Batalov	07/2024
5864	2^420424-59189	126561	Enzo Doria	10/2015
5865	28717^25534+25534^28717	126560	Hans Havermann	03/2021
5866	(86*10^126542+103)/9	126543	Robert Price	12/2021
5867	(19*10^126517-7)/3	126518	Robert Price	12/2023
5868	2026^38261-2025^38261	126516	Henri Lifchitz	12/2025
5869	28922^23655+23655^28922	126503	Hans Havermann	03/2021
5870	2^420126+71893	126471	Enzo Doria	04/2016
5871	25982^28643-28643^25982	126450	Frank Doornink	03/2024
5872	(43*10^126441+47)/9	126442	Robert Price	12/2018
5873	8*10^126408+71	126409	Robert Price	05/2022
5874	2^419866+1877059	126393	Enzo Doria	07/2016
5875	29315^20484+20484^29315	126390	Hans Havermann	03/2021
5876	29433^19676+19676^29433	126384	Hans Havermann	03/2021
5877	F(604711)	126377	Henri Lifchitz	02/2005
5878	2^419757+72707	126360	Enzo Doria	04/2016
5879	2^419720-21569	126349	Enzo Doria	07/2013
5880	2^419637+29	126324	Henri Lifchitz	02/2006
5881	31004^11865+11865^31004	126319	Hans Havermann	03/2021
5882	2^419612+1876741	126316	Enzo Doria	07/2016
5883	2^419520+2793271	126289	Enzo Doria	03/2016
5884	(2^419447-5)/369	126264	Lelio R Paula	05/2014
5885	2^419328-1859939	126231	Enzo Doria	03/2016
5886	2^419282-1851507	126217	Enzo Doria	08/2015
5887	(133*10^126212+17)/3	126214	Robert Price	11/2021
5888	2^419251+1866143	126208	Enzo Doria	03/2016
5889	11^121185+2	126202	Robert Price	05/2014
5890	28203^28352+28352^28203	126175	Norbert Schneider	01/2021
5891	Phi(267889,3)	126161	Henri Lifchitz	12/2025
5892	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
5893	2^418851+23	126087	Robert Price	09/2015
5894	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
5895	2^418829+167	126081	Lelio R Paula	01/2012
5896	31037^11530+11530^31037	126067	Hans Havermann	03/2021
5897	4*10^126064-69	126065	Robert Price	01/2022
5898	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
5899	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
5900	(35*10^126048-323)/9	126049	Robert Price	10/2021
5901	33016^6551+6551^33016	126000	Hans Havermann	03/2021
5902	2^418548-111546435	125996	Paul Bourdelais	10/2021
5903	25134^28625-28625^25134	125958	Frank Doornink	12/2023
5904	34736^4227+4227^34736	125954	Hans Havermann	03/2021
5905	(23*35^81566-144013)/34	125944	Eric Chen	05/2025
5906	26197^28502-28502^26197	125930	Frank Doornink	03/2024
5907	2^418319-109501	125927	Enzo Doria	04/2014
5908	2^418316-112373	125926	Enzo Doria	06/2014
5909	40398^1309+1309^40398	125919	Hans Havermann	03/2021
5910	(8*10^125894-29)/3	125895	Robert Price	07/2018
5911	(26*10^125886-413)/9	125887	Robert Price	05/2018
5912	10^(262938+1)-710^62938-1	125877	Robert Price	07/2023
5913	55*10^125847+9	125849	Robert Price	03/2022
5914	4*10^125832+57	125833	Robert Price	05/2022
5915	2^417968+1869811	125821	Enzo Doria	06/2016
5916	2^417902+63	125802	Lelio R Paula	09/2015
5917	(10^125792-91)/9	125792	Serge Batalov	12/2014
5918	30438^13573+13573^30438	125791	Hans Havermann	03/2021
5919	32867^6714+6714^32867	125782	Hans Havermann	03/2021
5920	31155^10892+10892^31155	125777	Hans Havermann	03/2021
5921	(35*10^125754-593)/9	125755	Robert Price	07/2018
5922	30455^13464+13464^30455	125754	Hans Havermann	03/2021
5923	(32*10^125751-77)/9	125752	Robert Price	06/2018
5924	2^417704+77011	125742	Enzo Doria	05/2016
5925	29755^16816+16816^29755	125737	Hans Havermann	03/2021
5926	(22*10^125734+203)/9	125735	Robert Price	10/2021
5927	29918^15915+15915^29918	125710	Hans Havermann	03/2021
5928	(10^125706+149)/3	125706	Serge Batalov	12/2014
5929	28531^25368+25368^28531	125659	Hans Havermann	03/2021
5930	2^417419-115309	125656	Enzo Doria	07/2015
5931	(46*10^125642+593)/9	125643	Robert Price	04/2022
5932	2^417315+213953	125625	Enzo Doria	10/2023
5933	2^417300+77281	125620	Enzo Doria	05/2016
5934	30638^12537+12537^30638	125561	Hans Havermann	03/2021
5935	2^417095-1657	125559	Yves Minet	07/2014
5936	30162^14525+14525^30162	125538	Hans Havermann	03/2021
5937	(56*10^125535+583)/9	125536	Robert Price	08/2021
5938	(23*10^125517-179)/3	125518	Robert Price	06/2022
5939	9*10^125516+29	125517	Robert Price	03/2022
5940	404*35^81280+23	125505	Eric Chen	05/2025
5941	(88*10^125492-637)/9	125493	Robert Price	11/2020
5942	28958^21525+21525^28958	125474	Hans Havermann	02/2021
5945	2^416773-25	125462	Lelio R Paula	09/2015
5943	(10^125482+7)/162685667/1639829194459	125462	Alfred Reich	07/2021
5944	26078^28409-28409^26078	125462	Frank Doornink	03/2024
5946	33889^5032+5032^33889	125449	Hans Havermann	03/2021
5947	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
5948	(2861^36481+1)/(2861^191+1)	125438	Martin Hopf	12/2023
5949	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
5950	(289511#+1896)/(23^3797801939911849)	125434	Makoto Morimoto	06/2019
5951	2^416641-2*416641+1	125422	Robert Price	05/2018
5952	33392^5697+5697^33392	125409	Hans Havermann	03/2021
5953	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
5954	2^416530+1870429	125389	Enzo Doria	05/2016
5955	(56*10^125385+691)/9	125386	Robert Price	05/2019
5956	27953^28198+28198^27953	125381	Norbert Schneider	01/2021
5957	31074^10837+10837^31074	125381	Hans Havermann	03/2021
5958	33745^5194+5194^33745	125380	Hans Havermann	03/2021
5959	2^416490+1875109	125376	Enzo Doria	09/2016
5960	28360^26331+26331^28360	125365	Hans Havermann	03/2021
5961	2^416416-114929	125354	Enzo Doria	05/2015
5962	25805^28412-28412^25805	125346	Frank Doornink	03/2024
5963	(77*10^125330-293)/9	125331	Robert Price	09/2019
5964	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
5965	2^416134+1865899	125269	Enzo Doria	03/2016
5966	153^57337-152	125264	Norbert Schneider	12/2018
5967	(599*10^125224+13)/9	125226	Robert Price	02/2022
5968	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
5969	30054^14657+14657^30054	125207	Hans Havermann	03/2021
5970	(23^91943-1)/22	125201	Robert Price	01/2012
5971	2^415884-933075	125194	Paul Bourdelais	06/2021
5972	43125^27010-106	125185	Enzo Doria	08/2012
5973	(38*10^125166+349)/9	125167	Robert Price	10/2018
5974	10^125166-5001	125166	Robert Price	12/2021
5975	2^415765-112603	125158	Enzo Doria	06/2014
5976	8*10^125088-13	125089	Robert Price	08/2019
5977	(25*10^125076-13)/3	125077	Robert Price	09/2019
5978	(11*10^125054+73)/3	125055	Robert Price	08/2021
5979	(101^62383-1)/17542099700	125026	Paul Vanderveen	06/2025
5980	(29*10^125021-113)/3	125022	Robert Price	10/2019
5981	2^415290-113591	125015	Enzo Doria	08/2014
5982	2^415276-460919	125011	Enzo Doria	06/2015
5983	2^415259+77243	125006	Enzo Doria	05/2016
5984	(67*10^124990+77)/9	124991	Robert Price	10/2021
5985	2^415144-3683	124971	Yves Minet	10/2011
5986	2^415092+111546435	124956	Paul Bourdelais	10/2021
5987	31936^8173+8173^31936	124946	Hans Havermann	03/2021
5988	27458^28145-28145^27458	124927	Frank Doornink	03/2024
5989	5^178715-4	124917	Tyler NeSmith	07/2021
5990	29767^15700+15700^29767	124900	Hans Havermann	03/2021
5991	(310^50131-1)/309	124892	Tom Wu	07/2024
5992	2^414874+79	124890	Lelio R Paula	01/2015
5993	25292^28361-28361^25292	124874	Frank Doornink	01/2024
5994	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
5995	2^414618+79459	124813	Enzo Doria	06/2016
5996	(61*10^124809-1)/3	124811	Robert Price	01/2020
5997	(235*29^85334+129)/28	124794	Eric Chen	06/2025
5998	(29*10^124765-71)/3	124766	Robert Price	07/2021
5999	2^414432-1846709	124757	Enzo Doria	07/2015
6000	2*10^124751-51	124752	Robert Price	04/2018

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Probable Primes Top 10000

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