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 ?
3501	6*10^127158+19	127159	Robert Price	11/2021
3502	30469^14902+14902^30469	127155	Hans Havermann	03/2021
3503	5*10^127153+77	127154	Robert Price	12/2018
3504	29941^17620+17620^29941	127130	Hans Havermann	02/2021
3505	31607^10516+10516^31607	127119	Hans Havermann	03/2021
3506	(19*10^127118-97)/3	127119	Robert Price	10/2021
3507	(29*10^127111+691)/9	127112	Robert Price	08/2021
3508	736^44335+44335^736	127104	Norbert Schneider	07/2019
3509	33040^7023+7023^33040	127090	Hans Havermann	03/2021
3510	(4*10^127081+167)/9	127081	Robert Price	03/2022
3511	29748^18661+18661^29748	127052	Hans Havermann	03/2021
3512	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
3513	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
3514	(14*10^127014-137)/3	127015	Robert Price	04/2021
3515	31436^10965+10965^31436	127002	Hans Havermann	03/2021
3516	28905^24758+24758^28905	127001	Hans Havermann	03/2021
3517	2^421860-113285	126993	Enzo Doria	07/2014
3518	(10^127030+7)/81234833/9230384921/6092460488946445358851	126991	Alfred Reich	07/2021
3519	(2^421827-7)/11	126982	Lelio R Paula	05/2015
3520	11^121910-840	126957	Enzo Doria	12/2012
3521	(56*10^126935+187)/9	126936	Robert Price	10/2021
3522	28915^24538+24538^28915	126933	Hans Havermann	03/2021
3523	(29*10^126928-77)/3	126929	Robert Price	02/2020
3524	(259*10^126919-1)/3	126921	Robert Price	12/2020
3525	10^126919+204567	126920	Patrick De Geest	05/2021
3526	(2^421617+100280245065)	126920	Paul Bourdelais	05/2022
3527	10^126919-100001	126919	Robert Price	07/2020
3528	28340^28503+28503^28340	126907	Norbert Schneider	02/2021
3529	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
3530	(5*10^126871-119)/3	126872	Robert Price	03/2018
3531	331^50339-10004	126846	Enzo Doria	07/2012
3532	2^421363-2790757	126843	Enzo Doria	03/2016
3533	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
3534	37938^2203+2203^37938	126828	Hans Havermann	03/2021
3535	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
3536	(14*10^126784-83)/3	126785	Robert Price	12/2018
3537	2^421161-286183	126783	Enzo Doria	06/2015
3538	(106*10^126726+17)/3	126728	Robert Price	04/2021
3539	30718^13347+13347^30718	126724	Hans Havermann	03/2021
3540	2^420939-113935	126716	Enzo Doria	10/2014
3541	177^56363-2	126703	Lelio R Paula	10/2017
3542	2^420741-113659	126656	Enzo Doria	08/2014
3543	2^420694-21	126642	Lelio R Paula	05/2017
3544	(13*10^126638+437)/9	126639	Robert Price	04/2018
3545	(167*10^126637-17)/3	126639	Robert Price	03/2020
3546	4*10^126625+87	126626	Robert Price	08/2018
3547	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
3548	7*10^126600-99	126601	Robert Price	06/2019
3549	2^420424-59189	126561	Enzo Doria	10/2015
3550	28717^25534+25534^28717	126560	Hans Havermann	03/2021
3551	(86*10^126542+103)/9	126543	Robert Price	12/2021
3552	28922^23655+23655^28922	126503	Hans Havermann	03/2021
3553	2^420126+71893	126471	Enzo Doria	04/2016
3554	(43*10^126441+47)/9	126442	Robert Price	12/2018
3555	8*10^126408+71	126409	Robert Price	05/2022
3556	2^419866+1877059	126393	Enzo Doria	07/2016
3557	29315^20484+20484^29315	126390	Hans Havermann	03/2021
3558	29433^19676+19676^29433	126384	Hans Havermann	03/2021
3559	F(604711)	126377	Henri Lifchitz	02/2005
3560	2^419757+72707	126360	Enzo Doria	04/2016
3561	2^419720-21569	126349	Enzo Doria	07/2013
3562	2^419637+29	126324	Henri Lifchitz	02/2006
3563	31004^11865+11865^31004	126319	Hans Havermann	03/2021
3564	2^419612+1876741	126316	Enzo Doria	07/2016
3565	2^419520+2793271	126289	Enzo Doria	03/2016
3566	(2^419447-5)/369	126264	Lelio R Paula	05/2014
3567	2^419328-1859939	126231	Enzo Doria	03/2016
3568	2^419282-1851507	126217	Enzo Doria	08/2015
3569	(133*10^126212+17)/3	126214	Robert Price	11/2021
3570	2^419251+1866143	126208	Enzo Doria	03/2016
3571	11^121185+2	126202	Robert Price	05/2014
3572	28203^28352+28352^28203	126175	Norbert Schneider	01/2021
3573	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
3574	2^418851+23	126087	Robert Price	09/2015
3575	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
3576	2^418829+167	126081	Lelio R Paula	01/2012
3577	31037^11530+11530^31037	126067	Hans Havermann	03/2021
3578	4*10^126064-69	126065	Robert Price	01/2022
3579	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
3580	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
3581	(35*10^126048-323)/9	126049	Robert Price	10/2021
3582	33016^6551+6551^33016	126000	Hans Havermann	03/2021
3583	2^418548-111546435	125996	Paul Bourdelais	10/2021
3584	34736^4227+4227^34736	125954	Hans Havermann	03/2021
3585	2^418319-109501	125927	Enzo Doria	04/2014
3586	2^418316-112373	125926	Enzo Doria	06/2014
3587	40398^1309+1309^40398	125919	Hans Havermann	03/2021
3588	(8*10^125894-29)/3	125895	Robert Price	07/2018
3589	(26*10^125886-413)/9	125887	Robert Price	05/2018
3590	55*10^125847+9	125849	Robert Price	03/2022
3591	4*10^125832+57	125833	Robert Price	05/2022
3592	2^417968+1869811	125821	Enzo Doria	06/2016
3593	2^417902+63	125802	Lelio R Paula	09/2015
3594	(10^125792-91)/9	125792	Serge Batalov	12/2014
3595	30438^13573+13573^30438	125791	Hans Havermann	03/2021
3596	32867^6714+6714^32867	125782	Hans Havermann	03/2021
3597	31155^10892+10892^31155	125777	Hans Havermann	03/2021
3598	(35*10^125754-593)/9	125755	Robert Price	07/2018
3599	30455^13464+13464^30455	125754	Hans Havermann	03/2021
3600	(32*10^125751-77)/9	125752	Robert Price	06/2018
3601	2^417704+77011	125742	Enzo Doria	05/2016
3602	29755^16816+16816^29755	125737	Hans Havermann	03/2021
3603	(22*10^125734+203)/9	125735	Robert Price	10/2021
3604	29918^15915+15915^29918	125710	Hans Havermann	03/2021
3605	(10^125706+149)/3	125706	Serge Batalov	12/2014
3606	28531^25368+25368^28531	125659	Hans Havermann	03/2021
3607	2^417419-115309	125656	Enzo Doria	07/2015
3608	(46*10^125642+593)/9	125643	Robert Price	04/2022
3609	2^417300+77281	125620	Enzo Doria	05/2016
3610	30638^12537+12537^30638	125561	Hans Havermann	03/2021
3611	2^417095-1657	125559	Yves Minet	07/2014
3612	30162^14525+14525^30162	125538	Hans Havermann	03/2021
3613	(56*10^125535+583)/9	125536	Robert Price	08/2021
3614	(23*10^125517-179)/3	125518	Robert Price	06/2022
3615	9*10^125516+29	125517	Robert Price	03/2022
3616	(88*10^125492-637)/9	125493	Robert Price	11/2020
3617	28958^21525+21525^28958	125474	Hans Havermann	02/2021
3619	2^416773-25	125462	Lelio R Paula	09/2015
3618	(10^125482+7)/162685667/1639829194459	125462	Alfred Reich	07/2021
3620	33889^5032+5032^33889	125449	Hans Havermann	03/2021
3621	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
3622	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
3623	(289511#+1896)/(23^3797801939911849)	125434	Makoto Morimoto	06/2019
3624	2^416641-2*416641+1	125422	Robert Price	05/2018
3625	33392^5697+5697^33392	125409	Hans Havermann	03/2021
3626	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
3627	2^416530+1870429	125389	Enzo Doria	05/2016
3628	(56*10^125385+691)/9	125386	Robert Price	05/2019
3629	27953^28198+28198^27953	125381	Norbert Schneider	01/2021
3630	31074^10837+10837^31074	125381	Hans Havermann	03/2021
3631	33745^5194+5194^33745	125380	Hans Havermann	03/2021
3632	2^416490+1875109	125376	Enzo Doria	09/2016
3633	28360^26331+26331^28360	125365	Hans Havermann	03/2021
3634	2^416416-114929	125354	Enzo Doria	05/2015
3635	(77*10^125330-293)/9	125331	Robert Price	09/2019
3636	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
3637	2^416134+1865899	125269	Enzo Doria	03/2016
3638	153^57337-152	125264	Norbert Schneider	12/2018
3639	(599*10^125224+13)/9	125226	Robert Price	02/2022
3640	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
3641	30054^14657+14657^30054	125207	Hans Havermann	03/2021
3642	(23^91943-1)/22	125201	Robert Price	01/2012
3643	2^415884-933075	125194	Paul Bourdelais	06/2021
3644	43125^27010-106	125185	Enzo Doria	08/2012
3645	(38*10^125166+349)/9	125167	Robert Price	10/2018
3646	10^125166-5001	125166	Robert Price	12/2021
3647	2^415765-112603	125158	Enzo Doria	06/2014
3648	8*10^125088-13	125089	Robert Price	08/2019
3649	(25*10^125076-13)/3	125077	Robert Price	09/2019
3650	(11*10^125054+73)/3	125055	Robert Price	08/2021
3651	(29*10^125021-113)/3	125022	Robert Price	10/2019
3652	2^415290-113591	125015	Enzo Doria	08/2014
3653	2^415276-460919	125011	Enzo Doria	06/2015
3654	2^415259+77243	125006	Enzo Doria	05/2016
3655	(67*10^124990+77)/9	124991	Robert Price	10/2021
3656	2^415144-3683	124971	Yves Minet	10/2011
3657	2^415092+111546435	124956	Paul Bourdelais	10/2021
3658	31936^8173+8173^31936	124946	Hans Havermann	03/2021
3659	5^178715-4	124916	Tyler NeSmith	07/2021
3660	29767^15700+15700^29767	124900	Hans Havermann	03/2021
3661	2^414874+79	124890	Lelio R Paula	01/2015
3662	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
3663	2^414618+79459	124813	Enzo Doria	06/2016
3664	(61*10^124809-1)/3	124811	Robert Price	01/2020
3665	(29*10^124765-71)/3	124766	Robert Price	07/2021
3666	2^414432-1846709	124757	Enzo Doria	07/2015
3667	2*10^124751-51	124752	Robert Price	04/2018
3668	(56*10^124735+367)/9	124736	Robert Price	06/2019
3669	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
3670	(23*10^124690+37)/3	124691	Robert Price	02/2022
3671	56*10^124656-3	124658	Robert Price	03/2020
3672	(7*10^124648+197)/3	124649	Robert Price	07/2018
3674	2^414032-5	124637	Henri Lifchitz	07/2006
3673	2^414032+1872331	124637	Enzo Doria	05/2016
3675	37373^2158+2158^37373	124604	Hans Havermann	03/2021
3676	29811^15112+15112^29811	124590	Hans Havermann	03/2021
3677	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
3678	29757^15296+15296^29757	124521	Hans Havermann	03/2021
3679	35056^3561+3561^35056	124504	Hans Havermann	03/2021
3680	40588^1167+1167^40588	124487	Hans Havermann	02/2021
3681	(85*10^124485-49)/9	124486	Robert Price	12/2020
3682	64^68909-63^68909	124463	Robert Price	07/2013
3683	35016^3581+3581^35016	124448	Hans Havermann	03/2021
3684	2^413387+76253	124442	Enzo Doria	04/2016
3685	28749^21298+21298^28749	124436	Hans Havermann	03/2021
3686	2^413352+524287	124432	Paul Underwood	09/2018
3687	287117#+391613	124424	Nicolas PALAU	01/2017
3688	(4*10^124420+83)/3	124421	Robert Price	02/2018
3689	34578^3965+3965^34578	124421	Hans Havermann	03/2021
3690	(68*10^124392-329)/9	124393	Robert Price	03/2021
3691	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
3692	10^124383+58407	124384	Patrick De Geest	08/2021
3694	10^124383-8000001	124383	Robert Price	04/2021
3693	10^124383-5801	124383	Patrick De Geest	08/2021
3695	(41*10^124335-383)/9	124336	Robert Price	11/2018
3696	(304*10^124329-43)/9	124331	Robert Price	02/2020
3697	34716^3811+3811^34716	124320	Hans Havermann	03/2021
3698	2^412868-120599	124286	Paul Bourdelais	02/2012
3699	10^124248+899089	124249	Patrick De Geest	05/2021
3701	10^124248-1000001	124248	Robert Price	08/2020
3700	10^124248-501903	124248	Patrick De Geest	05/2021
3702	45^75145-2	124231	Lelio R Paula	08/2015
3703	29901^14272+14272^29901	124224	Hans Havermann	03/2021
3704	2^412645-112213	124219	Enzo Doria	06/2014
3705	29837^14500+14500^29837	124163	Hans Havermann	03/2021
3706	28074^26455+26455^28074	124158	Hans Havermann	03/2021
3707	2^412248+74611	124100	Enzo Doria	04/2016
3708	(22*10^124096-13)/9	124097	Robert Price	06/2018
3709	(455*10^124093+31)/9	124095	Robert Price	06/2021
3710	2^412192-3329	124083	Yves Minet	12/2014
3711	(25*2^412191-1)/23	124082	Lelio R Paula	05/2014
3713	(25*10^124076-67)/3	124077	Robert Price	06/2019
3712	28132^25735+25735^28132	124077	Hans Havermann	03/2021
3714	F(593689)	124074	Henri Lifchitz	01/2005
3715	(11*2^412161+1)/19	124073	Lelio R Paula	05/2014
3716	35364^3215+3215^35364	124028	Hans Havermann	03/2021
3718	(266*10^124022-11)/3	124024	Robert Price	04/2020
3717	29987^13674+13674^29987	124024	Hans Havermann	03/2021
3719	2^411932-111546435	124004	Paul Bourdelais	10/2021
3720	2^411884-113279	123990	Enzo Doria	07/2014
3721	(2^411832+1)/257	123972	Lelio R Paula	05/2014
3722	(2^411833+2)/514	123972	Stefano Morozzi	03/2020
3723	(26*10^123970-89)/9	123971	Robert Price	06/2018
3724	2^411790-1853531	123962	Enzo Doria	08/2015
3725	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
3726	(101*10^123950+7)/9	123952	Robert Price	02/2022
3727	2^411711-113257	123938	Enzo Doria	07/2014
3728	(23*2^411675-1)/3	123928	Lelio R Paula	05/2014
3729	36289^2598+2598^36289	123914	Hans Havermann	03/2021
3730	(11*10^123899-179)/3	123900	Robert Price	09/2018
3731	32276^6879+6879^32276	123860	Hans Havermann	02/2021
3732	2^411325-351103	123822	Enzo Doria	06/2015
3733	(646*10^123817+11)/9	123819	Robert Price	10/2021
3734	30738^10643+10643^30738	123784	Hans Havermann	03/2021
3735	31074^9607+9607^31074	123755	Hans Havermann	03/2021
3736	2^411052+1872481	123739	Enzo Doria	05/2016
3737	34365^3986+3986^34365	123733	Hans Havermann	03/2021
3738	2^410997+39	123723	Lelio R Paula	05/2014
3739	(649^43987-1)/648	123700	Michael Stocker	05/2020
3740	(148*10^123688-1)/3	123690	Robert Price	03/2020
3741	36825^2284+2284^36825	123684	Hans Havermann	03/2021
3742	29582^15171+15171^29582	123683	Hans Havermann	03/2021
3743	10^123671+3593037	123672	Paul Bourdelais	10/2021
3744	8*10^123657+87	123658	Robert Price	10/2019
3745	30505^11302+11302^30505	123642	Hans Havermann	03/2021
3746	29956^13401+13401^29956	123633	Hans Havermann	03/2021
3747	155^56438+154	123618	Norbert Schneider	01/2019
3748	2^410596-39	123602	Lelio R Paula	05/2014
3749	(41*10^123600-221)/9	123601	Robert Price	10/2021
3750	28995^18302+18302^28995	123592	Hans Havermann	03/2021

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Probable Primes Top 10000

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