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	2^404858+71329	121875	Enzo Doria	04/2016
5752	2^404813-114703	121861	Enzo Doria	04/2015
5753	2^404764+77791	121847	Enzo Doria	05/2016
5754	28830^16841+16841^28830	121847	Hans Havermann	03/2021
5755	(4*10^121825+89)/3	121826	Robert Price	08/2021
5756	317^48694+48694^317	121787	Norbert Schneider	08/2015
5757	2^404536-115259	121778	Enzo Doria	06/2015
5758	2^404501-631	121767	Yves Minet	07/2012
5759	5*10^121764-69	121765	Robert Price	02/2021
5760	28236^20485+20485^28236	121738	Hans Havermann	02/2021
5761	(382*10^121694-31)/9	121696	Robert Price	06/2022
5762	63^67620+2	121672	Lelio R Paula	08/2015
5763	(25*34^79445-28062367)/33	121669	Eric Chen	08/2023
5764	(13*33^80110-121453)/32	121648	Eric Chen	12/2023
5765	(16*10^121633+167)/3	121634	Robert Price	06/2019
5766	29955^11494+11494^29955	121632	Hans Havermann	02/2021
5767	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
5768	31088^8163+8163^31088	121612	Hans Havermann	02/2021
5769	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
5770	(211^52301-1)/210	121560	Anonymous	04/2024
5771	(10^121543-79)/3	121543	Robert Price	01/2018
5772	801^41852-41852^801	121523	Norman Luhn	10/2024
5773	2^403676+76831	121519	Enzo Doria	05/2016
5774	715^42564-42564^715	121491	Norman Luhn	10/2024
5775	(7*10^121487+143)/3	121488	Robert Price	03/2018
5776	27965^22086+22086^27965	121484	Hans Havermann	02/2021
5777	(893*10^121470+7)/9	121472	Robert Price	06/2021
5778	(206*10^121462-11)/3	121464	Robert Price	02/2022
5779	26282^27481-27481^26282	121457	Frank Doornink	03/2024
5780	(77*10^121455+67)/9	121456	Robert Price	12/2021
5781	2^403363-113635	121425	Enzo Doria	08/2014
5782	25531^27552-27552^25531	121424	Frank Doornink	02/2024
5783	(17*10^121418-113)/3	121419	Robert Price	06/2021
5784	2^403336-1861469	121417	Enzo Doria	03/2016
5785	27929^22186+22186^27929	121382	Hans Havermann	02/2021
5786	p(24442)#/2-64	121381	Robert Price	04/2017
5787	11^116555-720	121380	Enzo Doria	11/2012
5788	(873^41263+1)/874	121353	Jinyuan Wang	12/2024
5789	2^403100-461267	121346	Enzo Doria	07/2015
5790	2^403093-112213	121344	Enzo Doria	06/2014
5791	29404^13385+13385^29404	121340	Hans Havermann	02/2021
5792	28106^20745+20745^28106	121332	Hans Havermann	02/2021
5793	(316^48539+1)/317	121330	Eric Chen	10/2017
5794	(23*10^121320-71)/3	121321	Robert Price	07/2020
5795	2^403004+1866361	121317	Enzo Doria	03/2016
5796	2^402953+89	121301	Lelio R Paula	10/2013
5797	2^402944-2788319	121299	Enzo Doria	03/2016
5798	(44*10^121297-719)/9	121298	Robert Price	12/2018
5799	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
5800	2^402828-113183	121264	Enzo Doria	07/2014
5801	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
5802	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
5803	282^49477-49477^282	121231	Norman Luhn	10/2024
5805	2^402715+1874223	121230	Enzo Doria	06/2016
5804	(35*10^121229-593)/9	121230	Robert Price	07/2018
5806	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
5807	291^49190-49190^291	121199	Norman Luhn	10/2024
5808	(10^121243)/(121243^10)	121193	Henri Lifchitz	05/2025
5809	28719^16568+16568^28719	121174	Hans Havermann	02/2021
5810	7*10^121144+9	121145	Robert Price	09/2015
5811	27490^25467+25467^27490	121121	Hans Havermann	02/2021
5812	34575^3182+3182^34575	121106	Hans Havermann	02/2021
5813	5*10^121100-37	121101	Robert Price	11/2021
5814	F(579521)/516247738177	121101	Serge Batalov	07/2024
5815	25592^27467-27467^25592	121078	Frank Doornink	02/2024
5816	29954^10935+10935^29954	120979	Hans Havermann	02/2021
5817	33585^3992+3992^33585	120946	Hans Havermann	02/2021
5818	40296^1003+1003^40296	120941	Hans Havermann	02/2021
5819	2^401725-113251	120932	Enzo Doria	07/2014
5820	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
5821	2^401652+73711	120910	Enzo Doria	04/2016
5822	(2^401632+3)/79	120902	Lelio R Paula	04/2014
5823	40450^973+973^40450	120870	Hans Havermann	01/2021
5824	(8*10^120851-11)/3	120852	Robert Price	07/2023
5825	10^120841+88417	120842	Patrick De Geest	04/2020
5826	10^120841-123456789	120841	Robert Price	02/2020
5827	10^120841-176853	120841	Patrick De Geest	04/2020
5828	2^401406-2791331	120836	Enzo Doria	03/2016
5829	(28^83497+1)/29	120832	Robert Price	07/2013
5830	(22*10^120828+161)/3	120829	Robert Price	05/2019
5831	2^401369+1867367	120825	Enzo Doria	03/2016
5832	(5*10^120821+43)/3	120822	Robert Price	12/2021
5833	26990^27263-27263^26990	120808	Frank Doornink	03/2024
5834	(10^120782+29)/3	120782	Serge Batalov	12/2014
5835	2^401215-1657	120778	Yves Minet	07/2014
5836	2^401159+53	120761	Lelio R Paula	10/2013
5837	27782^22179+22179^27782	120739	Hans Havermann	01/2021
5838	242^50649-50649^242	120738	Norman Luhn	09/2024
5839	32974^4585+4585^32974	120730	Hans Havermann	02/2021
5840	2^401031-113047	120723	Enzo Doria	07/2014
5841	30598^8813+8813^30598	120713	Hans Havermann	02/2021
5842	(71*10^120703-287)/9	120704	Robert Price	09/2019
5843	25671^27370-27370^25671	120687	Frank Doornink	02/2024
5844	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
5845	34793^2940+2940^34793	120675	Hans Havermann	02/2021
5846	26028^27329-27329^26028	120670	Frank Doornink	03/2024
5847	(2^400846+538)/2	120667	Stefano Morozzi	09/2020
5848	(166*10^120654+11)/3	120656	Robert Price	03/2021
5849	34066^3481+3481^34066	120652	Hans Havermann	02/2021
5850	8*10^120637-27	120638	Robert Price	10/2021
5851	(2^400709+3546)/2	120626	Stefano Morozzi	09/2020
5852	(2^400700+3126)/2	120623	Stefano Morozzi	09/2020
5853	(2^400693+2634)/2	120621	Stefano Morozzi	09/2020
5854	9*10^120617-61	120618	Robert Price	06/2021
5855	(29*10^120590-71)/3	120591	Robert Price	07/2021
5856	2^400571-15	120584	Lelio R Paula	10/2013
5857	(10^120574+359)/9	120574	Serge Batalov	12/2014
5858	(8*10^120552-17)/9	120552	Serge Batalov	11/2022
5859	27431^24810+24810^27431	120550	Hans Havermann	02/2021
5860	2^400424-216413	120540	Enzo Doria	04/2013
5861	29090^13911+13911^29090	120531	Hans Havermann	02/2021
5862	(2^400346+1722)/2	120516	Stefano Morozzi	09/2020
5863	27899^20868+20868^27899	120510	Hans Havermann	02/2021
5864	33740^3729+3729^33740	120506	Hans Havermann	02/2021
5865	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
5866	1069^39770-39770^1069	120463	Norbert Schneider	05/2025
5868	2^400166+1874899	120462	Enzo Doria	06/2016
5867	(2^400165+1602)/2	120462	Stefano Morozzi	09/2020
5869	2739^35038-35038^2739	120447	Norbert Schneider	05/2025
5870	37078^1771+1771^37078	120438	Hans Havermann	02/2021
5871	(2^400084+1638)/2	120437	Stefano Morozzi	09/2020
5872	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
5873	2^399999+54173	120412	Norman Luhn	08/2023
5874	(2^399974+2790)/2	120404	Stefano Morozzi	02/2021
5875	2^399966+73759	120402	Enzo Doria	04/2016
5876	(2^399961+2306)/2	120400	Stefano Morozzi	02/2021
5877	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
5879	2^399918-95	120388	Lelio R Paula	04/2013
5878	2^399918+214009	120388	Enzo Doria	10/2023
5880	(28*10^120381-67)/3	120382	Robert Price	10/2020
5881	(49*10^120380-139)/9	120381	Robert Price	03/2019
5882	(2^399874+2194)/2	120374	Stefano Morozzi	09/2020
5883	2^399792-1849259	120350	Enzo Doria	08/2015
5884	9*10^120342-7	120343	Robert Price	09/2015
5885	(2^399751+786)/2	120337	Stefano Morozzi	09/2020
5886	(331*10^120332-7)/9	120334	Robert Price	04/2022
5887	(13*10^120306-37)/3	120307	Robert Price	01/2019
5888	(23*10^120299+37)/3	120300	Robert Price	02/2022
5889	25935^27254-27254^25935	120297	Frank Doornink	03/2024
5890	(2^399604+3070)/2	120293	Stefano Morozzi	09/2020
5891	(2^399549+1062)/2	120276	Stefano Morozzi	09/2020
5892	2^399526-1861721	120270	Enzo Doria	11/2015
5893	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
5894	32016^5687+5687^32016	120217	Hans Havermann	01/2021
5895	(205*10^120212-1)/3	120214	Robert Price	11/2021
5896	2^399322-2798111	120208	Enzo Doria	04/2016
5897	30438^8867+8867^30438	120163	Hans Havermann	02/2021
5898	3^251841-5*2^251841	120159	Jon Grantham	08/2023
5900	72^64693-71^64693	120157	Robert Price	03/2014
5899	(17*10^120156-161)/9	120157	Robert Price	02/2021
5901	2^399111-28489	120145	Enzo Doria	08/2015
5902	2958^34607-34607^2958	120121	Norbert Schneider	04/2025
5903	(2^399014+1318)/2	120115	Stefano Morozzi	02/2021
5904	30254^9333+9333^30254	120110	Hans Havermann	02/2021
5905	2^398972+6561	120103	Henri Lifchitz	10/2024
5906	30882^7745+7745^30882	120101	Hans Havermann	02/2021
5908	2^398877+105	120074	Donovan Johnson	01/2006
5907	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
5909	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
5910	U(686581)/4280145953	120067	Serge Batalov	07/2024
5911	3207^34240-34240^3207	120049	Norbert Schneider	04/2025
5912	2^398710+57	120024	Lelio R Paula	04/2013
5913	(2^398698+1138)/2	120020	Stefano Morozzi	09/2020
5914	2^398691-115057	120018	Enzo Doria	06/2015
5915	6089^31710-31710^6089	120008	Norbert Schneider	05/2025
5916	L(574219)	120005	Renaud Lifchitz	03/2004
5917	2^398571+60413	119982	Yves Minet	03/2011
5918	28623^15538+15538^28623	119971	Hans Havermann	02/2021
5919	p(24179)#/2-64	119949	Robert Price	04/2017
5920	2^398448+1872001	119945	Enzo Doria	05/2016
5921	(10^119946*19-91)/6093	119944	Alfred Reich	10/2023
5922	(19*10^119946-91)/9/677	119944	Alfred Reich	11/2023
5923	(191*10^119941-17)/3	119943	Robert Price	11/2021
5924	634^42803+42803^634	119938	Norbert Schneider	07/2019
5925	31083^7220+7220^31083	119935	Hans Havermann	01/2021
5926	(68*10^119931-11)/3	119933	Robert Price	01/2020
5927	8*10^119930-3	119931	Ray Chandler	04/2011
5928	(2^398398+774)/2	119930	Stefano Morozzi	09/2020
5929	(10^119880+179)/9	119880	Serge Batalov	12/2014
5930	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
5931	(10^119836+77)/3	119836	Robert Price	01/2018
5932	26681^27074-27074^26681	119835	Frank Doornink	03/2024
5933	28179^17870+17870^28179	119821	Hans Havermann	02/2021
5934	2^398029+1872527	119819	Enzo Doria	05/2016
5935	33142^4119+4119^33142	119802	Hans Havermann	01/2021
5936	2^397897-113541	119779	Enzo Doria	08/2014
5937	28636^15171+15171^28636	119728	Hans Havermann	02/2021
5938	87^61730-61730^87	119727	Norman Luhn	09/2024
5939	(10556^29929-1)/(10556^173-1)	119724	Ryan Propper	11/2023
5940	(2^397696+1042)/2	119719	Stefano Morozzi	09/2020
5942	(19*10^119716+101)/3	119717	Robert Price	09/2019
5941	29563^11208+11208^29563	119717	Hans Havermann	02/2021
5943	458^44991-44991^458	119715	Norman Luhn	09/2024
5944	2^397655-933075	119707	Paul Bourdelais	06/2021
5945	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
5946	28243^17308+17308^28243	119701	Hans Havermann	02/2021
5947	77*10^119688+3	119690	Robert Price	06/2020
5948	586*25^85601+3717	119668	Eric Chen	10/2023
5949	(2^397504+1698)/2	119661	Stefano Morozzi	09/2020
5950	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
5951	2^397426+73849	119638	Enzo Doria	04/2016
5952	8*10^119509+29	119510	Robert Price	11/2021
5953	2^396933-112723	119489	Enzo Doria	06/2014
5954	11^114738-150	119488	Enzo Doria	10/2012
5955	(4*10^119474+149)/9	119474	Robert Price	04/2018
5956	26964^26964-13^13	119472	Henri Lifchitz	08/2024
5957	2^396790-21	119446	Lelio R Paula	04/2013
5958	32061^5300+5300^32061	119405	Hans Havermann	01/2021
5959	(2^396633-7)/5	119398	Lelio R Paula	04/2014
5960	27382^22913+22913^27382	119388	Hans Havermann	03/2021
5961	(2^396577+2522)/2	119382	Stefano Morozzi	09/2020
5962	(2^396492+2230)/2	119356	Stefano Morozzi	01/2021
5963	(47*10^119354+259)/9	119355	Robert Price	03/2022
5965	105^59050+104	119352	Norbert Schneider	11/2016
5964	126^56824-125	119352	Norbert Schneider	12/2018
5966	2^396469+111546435	119350	Paul Bourdelais	10/2021
5967	139^55690-138	119345	Norbert Schneider	04/2019
5968	790^41179+41179^790	119322	Norbert Schneider	04/2019
5969	2^396374+73729	119321	Enzo Doria	04/2016
5970	88*10^119295+3	119297	Robert Price	05/2020
5971	2^396258-459491	119286	Enzo Doria	05/2015
5972	(2^396248+3126)/2	119283	Stefano Morozzi	09/2020
5973	2^396128-396128-1	119247	Karsten Bonath	06/2018
5975	(893*10^119228+7)/9	119230	Robert Price	06/2021
5974	(31*10^119229+257)/9	119230	Robert Price	12/2021
5976	(28*10^119206-67)/3	119207	Robert Price	10/2020
5977	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
5978	11^114458+6	119196	Paul Bourdelais	02/2021
5979	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
5980	(2^395902+202)/2	119179	Stefano Morozzi	09/2020
5981	(2^395825+582)/2	119155	Stefano Morozzi	09/2020
5982	(2^395733+1130)/2	119128	Stefano Morozzi	09/2020
5983	(23^119099)%(10^119099)	119099	Henri Lifchitz	05/2025
5984	29548^10725+10725^29548	119091	Hans Havermann	02/2021
5985	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
5986	(30^80599+1)/31	119054	Robert Price	07/2013
5987	(232*10^119047+17)/3	119049	Robert Price	04/2021
5988	(43*10^119024-403)/9	119025	Robert Price	01/2019
5989	(4*10^119021+47)/3	119022	Robert Price	01/2022
5990	fibonacci(569433)+3	119005	Jon Grantham	08/2023
5991	26603^26888-26888^26603	118978	Norbert Schneider	07/2021
5992	912^40193-40193^912	118972	Norman Luhn	09/2024
5993	681^41992-41992^681	118970	Norman Luhn	09/2024
5994	6*10^118964+43	118965	Robert Price	07/2020
5995	(8*10^118960+49)/3	118961	Robert Price	05/2020
5996	31253^6402+6402^31253	118959	Hans Havermann	02/2021
5997	(194*10^118925-17)/3	118927	Robert Price	09/2020
5998	2^395062-109121	118926	Enzo Doria	04/2014
5999	2^395055-4627	118924	Yves Minet	05/2019
6000	(2^395054+702)/2	118923	Stefano Morozzi	09/2020

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Probable Primes Top 10000

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