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 ?
3751	32595^8186+8186^32595	127547	Hans Havermann	03/2021
3752	2^423696-21429	127546	Enzo Doria	07/2013
3753	2^423664-1864559	127536	Enzo Doria	03/2016
3754	37889^2322+2322^37889	127530	Hans Havermann	03/2021
3755	37668^2429+2429^37668	127523	Hans Havermann	03/2021
3756	3^267267-4	127519	Henri Lifchitz	10/2014
3757	(103*10^127491+17)/3	127493	Robert Price	08/2020
3758	29376^21869+21869^29376	127487	Hans Havermann	03/2021
3759	31186^12241+12241^31186	127483	Hans Havermann	02/2021
3760	(19^99689+5^99689)/24	127477	Robert Price	09/2013
3761	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
3762	30594^14645+14645^30594	127446	Hans Havermann	03/2021
3763	2^423328-21537	127435	Enzo Doria	07/2013
3764	(67*10^127413-7)/3	127415	Robert Price	01/2020
3765	(2*10^127407+73)/3	127407	Robert Price	09/2020
3766	(2^423165-7)/25	127384	Lelio R Paula	05/2015
3767	(7726^32768+1)/13917994151414876602369	127379	Kellen Shenton	04/2021
3768	(4*10^127349+17)/3	127350	Tyler Busby	01/2023
3769	29512^20647+20647^29512	127341	Hans Havermann	03/2021
3770	(112*10^127324+17)/3	127326	Robert Price	03/2020
3771	29565^20252+20252^29565	127321	Hans Havermann	03/2021
3773	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
3772	(5^182099-3^182099)/2	127282	Kellen Shenton	05/2022
3774	(16*10^127259+197)/3	127260	Robert Price	04/2019
3775	(26*10^127240+61)/3	127241	Robert Price	10/2019
3776	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
3777	2^422515-114997	127190	Enzo Doria	06/2015
3778	5*10^127179-3	127180	Robert Price	07/2015
3779	31678^10343+10343^31678	127176	Hans Havermann	03/2021
3780	(44*10^127169-233)/9	127170	Robert Price	01/2019
3781	34947^4352+4352^34947	127162	Hans Havermann	03/2021
3782	6*10^127158+19	127159	Robert Price	11/2021
3783	30469^14902+14902^30469	127155	Hans Havermann	03/2021
3784	5*10^127153+77	127154	Robert Price	12/2018
3785	29941^17620+17620^29941	127130	Hans Havermann	02/2021
3786	31607^10516+10516^31607	127119	Hans Havermann	03/2021
3787	(19*10^127118-97)/3	127119	Robert Price	10/2021
3788	(29*10^127111+691)/9	127112	Robert Price	08/2021
3789	736^44335+44335^736	127104	Norbert Schneider	07/2019
3790	33040^7023+7023^33040	127090	Hans Havermann	03/2021
3791	(4*10^127081+167)/9	127081	Robert Price	03/2022
3792	29748^18661+18661^29748	127052	Hans Havermann	03/2021
3793	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
3794	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
3795	(14*10^127014-137)/3	127015	Robert Price	04/2021
3796	31436^10965+10965^31436	127002	Hans Havermann	03/2021
3797	28905^24758+24758^28905	127001	Hans Havermann	03/2021
3798	2^421860-113285	126993	Enzo Doria	07/2014
3799	(10^127030+7)/81234833/9230384921/6092460488946445358851	126991	Alfred Reich	07/2021
3800	(2^421827-7)/11	126982	Lelio R Paula	05/2015
3801	11^121910-840	126957	Enzo Doria	12/2012
3802	(56*10^126935+187)/9	126936	Robert Price	10/2021
3803	28915^24538+24538^28915	126933	Hans Havermann	03/2021
3804	(29*10^126928-77)/3	126929	Robert Price	02/2020
3805	(259*10^126919-1)/3	126921	Robert Price	12/2020
3806	10^126919+204567	126920	Patrick De Geest	05/2021
3807	(2^421617+100280245065)	126920	Paul Bourdelais	05/2022
3808	10^126919-100001	126919	Robert Price	07/2020
3809	28340^28503+28503^28340	126907	Norbert Schneider	02/2021
3810	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
3811	(5*10^126871-119)/3	126872	Robert Price	03/2018
3812	331^50339-10004	126846	Enzo Doria	07/2012
3813	2^421363-2790757	126843	Enzo Doria	03/2016
3814	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
3815	37938^2203+2203^37938	126828	Hans Havermann	03/2021
3816	(13*10^126819+77)/9	126820	Robert Price	07/2022
3817	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
3818	(14*10^126784-83)/3	126785	Robert Price	12/2018
3819	2^421161-286183	126783	Enzo Doria	06/2015
3820	(106*10^126726+17)/3	126728	Robert Price	04/2021
3821	30718^13347+13347^30718	126724	Hans Havermann	03/2021
3822	2^420939-113935	126716	Enzo Doria	10/2014
3823	177^56363-2	126703	Lelio R Paula	10/2017
3824	2^420741-113659	126656	Enzo Doria	08/2014
3825	2^420694-21	126642	Lelio R Paula	05/2017
3826	(13*10^126638+437)/9	126639	Robert Price	04/2018
3827	(167*10^126637-17)/3	126639	Robert Price	03/2020
3828	4*10^126625+87	126626	Robert Price	08/2018
3829	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
3830	7*10^126600-99	126601	Robert Price	06/2019
3831	2^420424-59189	126561	Enzo Doria	10/2015
3832	28717^25534+25534^28717	126560	Hans Havermann	03/2021
3833	(86*10^126542+103)/9	126543	Robert Price	12/2021
3834	28922^23655+23655^28922	126503	Hans Havermann	03/2021
3835	2^420126+71893	126471	Enzo Doria	04/2016
3836	(43*10^126441+47)/9	126442	Robert Price	12/2018
3837	8*10^126408+71	126409	Robert Price	05/2022
3838	2^419866+1877059	126393	Enzo Doria	07/2016
3839	29315^20484+20484^29315	126390	Hans Havermann	03/2021
3840	29433^19676+19676^29433	126384	Hans Havermann	03/2021
3841	F(604711)	126377	Henri Lifchitz	02/2005
3842	2^419757+72707	126360	Enzo Doria	04/2016
3843	2^419720-21569	126349	Enzo Doria	07/2013
3844	2^419637+29	126324	Henri Lifchitz	02/2006
3845	31004^11865+11865^31004	126319	Hans Havermann	03/2021
3846	2^419612+1876741	126316	Enzo Doria	07/2016
3847	2^419520+2793271	126289	Enzo Doria	03/2016
3848	(2^419447-5)/369	126264	Lelio R Paula	05/2014
3849	2^419328-1859939	126231	Enzo Doria	03/2016
3850	2^419282-1851507	126217	Enzo Doria	08/2015
3851	(133*10^126212+17)/3	126214	Robert Price	11/2021
3852	2^419251+1866143	126208	Enzo Doria	03/2016
3853	11^121185+2	126202	Robert Price	05/2014
3854	28203^28352+28352^28203	126175	Norbert Schneider	01/2021
3855	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
3856	2^418851+23	126087	Robert Price	09/2015
3857	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
3858	2^418829+167	126081	Lelio R Paula	01/2012
3859	31037^11530+11530^31037	126067	Hans Havermann	03/2021
3860	4*10^126064-69	126065	Robert Price	01/2022
3861	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
3862	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
3863	(35*10^126048-323)/9	126049	Robert Price	10/2021
3864	33016^6551+6551^33016	126000	Hans Havermann	03/2021
3865	2^418548-111546435	125996	Paul Bourdelais	10/2021
3866	34736^4227+4227^34736	125954	Hans Havermann	03/2021
3867	2^418319-109501	125927	Enzo Doria	04/2014
3868	2^418316-112373	125926	Enzo Doria	06/2014
3869	40398^1309+1309^40398	125919	Hans Havermann	03/2021
3870	(8*10^125894-29)/3	125895	Robert Price	07/2018
3871	(26*10^125886-413)/9	125887	Robert Price	05/2018
3872	55*10^125847+9	125849	Robert Price	03/2022
3873	4*10^125832+57	125833	Robert Price	05/2022
3874	2^417968+1869811	125821	Enzo Doria	06/2016
3875	2^417902+63	125802	Lelio R Paula	09/2015
3876	(10^125792-91)/9	125792	Serge Batalov	12/2014
3877	30438^13573+13573^30438	125791	Hans Havermann	03/2021
3878	32867^6714+6714^32867	125782	Hans Havermann	03/2021
3879	31155^10892+10892^31155	125777	Hans Havermann	03/2021
3880	(35*10^125754-593)/9	125755	Robert Price	07/2018
3881	30455^13464+13464^30455	125754	Hans Havermann	03/2021
3882	(32*10^125751-77)/9	125752	Robert Price	06/2018
3883	2^417704+77011	125742	Enzo Doria	05/2016
3884	29755^16816+16816^29755	125737	Hans Havermann	03/2021
3885	(22*10^125734+203)/9	125735	Robert Price	10/2021
3886	29918^15915+15915^29918	125710	Hans Havermann	03/2021
3887	(10^125706+149)/3	125706	Serge Batalov	12/2014
3888	28531^25368+25368^28531	125659	Hans Havermann	03/2021
3889	2^417419-115309	125656	Enzo Doria	07/2015
3890	(46*10^125642+593)/9	125643	Robert Price	04/2022
3891	2^417300+77281	125620	Enzo Doria	05/2016
3892	30638^12537+12537^30638	125561	Hans Havermann	03/2021
3893	2^417095-1657	125559	Yves Minet	07/2014
3894	30162^14525+14525^30162	125538	Hans Havermann	03/2021
3895	(56*10^125535+583)/9	125536	Robert Price	08/2021
3896	(23*10^125517-179)/3	125518	Robert Price	06/2022
3897	9*10^125516+29	125517	Robert Price	03/2022
3898	(88*10^125492-637)/9	125493	Robert Price	11/2020
3899	28958^21525+21525^28958	125474	Hans Havermann	02/2021
3901	2^416773-25	125462	Lelio R Paula	09/2015
3900	(10^125482+7)/162685667/1639829194459	125462	Alfred Reich	07/2021
3902	33889^5032+5032^33889	125449	Hans Havermann	03/2021
3903	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
3904	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
3905	(289511#+1896)/(23^3797801939911849)	125434	Makoto Morimoto	06/2019
3906	2^416641-2*416641+1	125422	Robert Price	05/2018
3907	33392^5697+5697^33392	125409	Hans Havermann	03/2021
3908	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
3909	2^416530+1870429	125389	Enzo Doria	05/2016
3910	(56*10^125385+691)/9	125386	Robert Price	05/2019
3911	27953^28198+28198^27953	125381	Norbert Schneider	01/2021
3912	31074^10837+10837^31074	125381	Hans Havermann	03/2021
3913	33745^5194+5194^33745	125380	Hans Havermann	03/2021
3914	2^416490+1875109	125376	Enzo Doria	09/2016
3915	28360^26331+26331^28360	125365	Hans Havermann	03/2021
3916	2^416416-114929	125354	Enzo Doria	05/2015
3917	(77*10^125330-293)/9	125331	Robert Price	09/2019
3918	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
3919	2^416134+1865899	125269	Enzo Doria	03/2016
3920	153^57337-152	125264	Norbert Schneider	12/2018
3921	(599*10^125224+13)/9	125226	Robert Price	02/2022
3922	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
3923	30054^14657+14657^30054	125207	Hans Havermann	03/2021
3924	(23^91943-1)/22	125201	Robert Price	01/2012
3925	2^415884-933075	125194	Paul Bourdelais	06/2021
3926	43125^27010-106	125185	Enzo Doria	08/2012
3927	(38*10^125166+349)/9	125167	Robert Price	10/2018
3928	10^125166-5001	125166	Robert Price	12/2021
3929	2^415765-112603	125158	Enzo Doria	06/2014
3930	8*10^125088-13	125089	Robert Price	08/2019
3931	(25*10^125076-13)/3	125077	Robert Price	09/2019
3932	(11*10^125054+73)/3	125055	Robert Price	08/2021
3933	(29*10^125021-113)/3	125022	Robert Price	10/2019
3934	2^415290-113591	125015	Enzo Doria	08/2014
3935	2^415276-460919	125011	Enzo Doria	06/2015
3936	2^415259+77243	125006	Enzo Doria	05/2016
3937	(67*10^124990+77)/9	124991	Robert Price	10/2021
3938	2^415144-3683	124971	Yves Minet	10/2011
3939	2^415092+111546435	124956	Paul Bourdelais	10/2021
3940	31936^8173+8173^31936	124946	Hans Havermann	03/2021
3941	5^178715-4	124916	Tyler NeSmith	07/2021
3942	29767^15700+15700^29767	124900	Hans Havermann	03/2021
3943	2^414874+79	124890	Lelio R Paula	01/2015
3944	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
3945	2^414618+79459	124813	Enzo Doria	06/2016
3946	(61*10^124809-1)/3	124811	Robert Price	01/2020
3947	(29*10^124765-71)/3	124766	Robert Price	07/2021
3948	2^414432-1846709	124757	Enzo Doria	07/2015
3949	2*10^124751-51	124752	Robert Price	04/2018
3950	(56*10^124735+367)/9	124736	Robert Price	06/2019
3951	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
3952	(23*10^124690+37)/3	124691	Robert Price	02/2022
3953	56*10^124656-3	124658	Robert Price	03/2020
3954	(7*10^124648+197)/3	124649	Robert Price	07/2018
3956	2^414032-5	124637	Henri Lifchitz	07/2006
3955	2^414032+1872331	124637	Enzo Doria	05/2016
3957	37373^2158+2158^37373	124604	Hans Havermann	03/2021
3958	29811^15112+15112^29811	124590	Hans Havermann	03/2021
3959	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
3960	29757^15296+15296^29757	124521	Hans Havermann	03/2021
3961	35056^3561+3561^35056	124504	Hans Havermann	03/2021
3962	40588^1167+1167^40588	124487	Hans Havermann	02/2021
3963	(85*10^124485-49)/9	124486	Robert Price	12/2020
3964	64^68909-63^68909	124463	Robert Price	07/2013
3965	35016^3581+3581^35016	124448	Hans Havermann	03/2021
3966	2^413387+76253	124442	Enzo Doria	04/2016
3967	28749^21298+21298^28749	124436	Hans Havermann	03/2021
3968	2^413352+524287	124432	Paul Underwood	09/2018
3969	287117#+391613	124424	Nicolas PALAU	01/2017
3970	(4*10^124420+83)/3	124421	Robert Price	02/2018
3971	34578^3965+3965^34578	124421	Hans Havermann	03/2021
3972	(68*10^124392-329)/9	124393	Robert Price	03/2021
3973	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
3974	10^124383+58407	124384	Patrick De Geest	08/2021
3976	10^124383-8000001	124383	Robert Price	04/2021
3975	10^124383-5801	124383	Patrick De Geest	08/2021
3977	(41*10^124335-383)/9	124336	Robert Price	11/2018
3978	(304*10^124329-43)/9	124331	Robert Price	02/2020
3979	34716^3811+3811^34716	124320	Hans Havermann	03/2021
3980	2^412868-120599	124286	Paul Bourdelais	02/2012
3981	10^124248+899089	124249	Patrick De Geest	05/2021
3983	10^124248-1000001	124248	Robert Price	08/2020
3982	10^124248-501903	124248	Patrick De Geest	05/2021
3984	45^75145-2	124231	Lelio R Paula	08/2015
3985	29901^14272+14272^29901	124224	Hans Havermann	03/2021
3986	2^412645-112213	124219	Enzo Doria	06/2014
3987	29837^14500+14500^29837	124163	Hans Havermann	03/2021
3988	28074^26455+26455^28074	124158	Hans Havermann	03/2021
3989	2^412248+74611	124100	Enzo Doria	04/2016
3990	(22*10^124096-13)/9	124097	Robert Price	06/2018
3991	(455*10^124093+31)/9	124095	Robert Price	06/2021
3992	2^412192-3329	124083	Yves Minet	12/2014
3993	(25*2^412191-1)/23	124082	Lelio R Paula	05/2014
3995	(25*10^124076-67)/3	124077	Robert Price	06/2019
3994	28132^25735+25735^28132	124077	Hans Havermann	03/2021
3996	F(593689)	124074	Henri Lifchitz	01/2005
3997	(11*2^412161+1)/19	124073	Lelio R Paula	05/2014
3998	35364^3215+3215^35364	124028	Hans Havermann	03/2021
4000	(266*10^124022-11)/3	124024	Robert Price	04/2020
3999	29987^13674+13674^29987	124024	Hans Havermann	03/2021

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Probable Primes Top 10000

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