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	fibonacci(751442)-2	157042	Jon Grantham	08/2023
3502	2^521401-29593	156958	Enzo Doria	08/2015
3503	7*10^156956+87	156957	Robert Price	07/2019
3504	2^521348-23397	156942	Enzo Doria	08/2013
3505	10^156902+34509	156903	Patrick De Geest	08/2021
3507	10^156902-80000001	156902	Robert Price	04/2021
3506	10^156902-69789	156902	Patrick De Geest	08/2021
3508	(98^78797+1)/99	156901	Paul Bourdelais	12/2017
3509	65^86522+64	156857	Lelio R Paula	04/2016
3510	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
3511	2^520977-1858183	156830	Enzo Doria	10/2015
3512	(8*10^156718-101)/3	156719	Robert Price	08/2018
3513	(10^156640+7)/53	156639	Alfred Reich	07/2021
3514	2^520314-1849481	156631	Enzo Doria	08/2015
3515	(16*10^156563-637)/9	156564	Robert Price	09/2022
3516	(13*10^156522+89)/3	156523	Robert Price	09/2018
3518	(2^(6*86654+1)-5)/3	156513	Kevin Acres	12/2013
3517	(2^519925-5)/3	156513	Stefano Morozzi	08/2022
3519	(4*10^156501+119)/3	156502	Robert Price	12/2021
3520	(83*10^156476-101)/9	156477	Robert Price	08/2021
3521	3*10^156435-97	156436	Robert Price	07/2018
3522	10^156428+111	156429	Boyan Hu	10/2024
3523	(8*10^156371-77)/3	156372	Robert Price	07/2018
3524	53^90679-52^90679	156356	Robert Price	01/2013
3525	31267^34782-34782^31267	156349	Frank Doornink	01/2024
3526	(418*10^156309-31)/9	156311	Robert Price	05/2022
3527	2^519106-59141	156267	Enzo Doria	10/2015
3528	25929^35404-35404^25929	156266	Frank Doornink	03/2024
3529	2^519053+6077	156251	Enzo Doria	02/2016
3530	31199^34764-34764^31199	156235	Frank Doornink	01/2024
3531	2^518968-1860989	156225	Enzo Doria	11/2015
3532	(25*10^156221-7)/9	156222	Robert Price	05/2018
3533	2^518931-2782297	156214	Enzo Doria	09/2015
3534	2^518608-2939	156117	Yves Minet	09/2014
3535	10*27^109005+697	156027	Curtis Bright	05/2015
3536	(49*10^155933-319)/9	155934	Robert Price	10/2021
3537	2^517967-113485	155924	Enzo Doria	08/2014
3538	(103*10^155904+17)/3	155906	Robert Price	08/2020
3539	(8*10^155887-719)/9	155887	Robert Price	03/2021
3540	2^517789+29231	155871	Enzo Doria	02/2024
3541	4*10^155853-39	155854	Robert Price	09/2020
3542	2^517698+4429	155843	Lelio R Paula	01/2013
3543	32015^34584-34584^32015	155814	Frank Doornink	01/2024
3544	2^517543-113257	155796	Enzo Doria	07/2014
3545	(14*10^155740-143)/3	155741	Robert Price	11/2018
3546	31959^34564-34564^31959	155697	Frank Doornink	01/2024
3547	31^104309-30^104309	155563	Henri Lifchitz	08/2013
3548	2^516742-39851	155555	Enzo Doria	09/2015
3549	(22*10^155543+47)/3	155544	Robert Price	06/2021
3550	(19*10^155504+131)/3	155505	Robert Price	06/2020
3551	7*10^155496+61	155497	Robert Price	08/2019
3552	2^516440+1878421	155464	Enzo Doria	08/2016
3553	26012^35173-35173^26012	155295	Frank Doornink	03/2024
3554	2^515863-1867237	155291	Enzo Doria	03/2016
3555	2^515786-461861	155268	Enzo Doria	07/2015
3556	2^515644-113247	155225	Enzo Doria	07/2014
3557	(7*10^155203+107)/3	155204	Robert Price	02/2018
3558	10^155163+206871	155164	Patrick De Geest	05/2021
3559	10^155163-40001	155163	Robert Price	01/2021
3560	(17*10^155133-89)/9	155134	Robert Price	07/2018
3561	26024^35131-35131^26024	155117	Frank Doornink	03/2024
3562	2^515249+214457	155106	Enzo Doria	10/2023
3563	2^515227-114997	155099	Enzo Doria	06/2015
3564	26510^35061-35061^26510	155090	Frank Doornink	03/2024
3566	EPrime(155025)	155025	Eric W. Weisstein	10/2010
3565	(14*10^155024-221)/9	155025	Robert Price	04/2018
3567	(4*10^155022+173)/3	155023	Robert Price	02/2018
3568	2^514652+6561	154926	Henri Lifchitz	11/2024
3569	(266*10^154897+1)/3	154899	Robert Price	04/2020
3570	(115*10^154869-1)/3	154871	Serge Batalov	12/2014
3571	(86*10^154853-221)/9	154854	Robert Price	09/2019
3572	2^514361+78167	154839	Enzo Doria	05/2016
3573	2^514281-115033	154815	Enzo Doria	06/2015
3574	25701^35104-35104^25701	154807	Frank Doornink	02/2024
3575	2^514194-3311	154788	Yves Minet	12/2014
3576	25930^35067-35067^25930	154779	Frank Doornink	03/2024
3577	(14*10^154773+37)/3	154774	Robert Price	12/2018
3578	(16*10^154748+131)/3	154749	Robert Price	03/2022
3579	6*10^154742-31	154743	Robert Price	07/2020
3580	(14*10^154645+139)/9	154646	Robert Price	11/2021
3581	2^513690+216949	154637	Enzo Doria	12/2023
3582	5*10^154618-79	154619	Robert Price	03/2021
3583	(167*10^154595+1)/3	154597	Robert Price	04/2021
3584	2^513437+1879337	154560	Enzo Doria	09/2016
3585	2^513306-113201	154521	Enzo Doria	07/2014
3586	26415^34942-34942^26415	154509	Frank Doornink	03/2024
3587	18^120818+19^120818-2	154497	Harsh Aggarwal	05/2024
3588	(10^154494-13)/3	154494	Robert Price	12/2017
3589	23462^35343+35343^23462	154462	Norbert Schneider	04/2023
3590	2^513042-113787	154442	Enzo Doria	09/2014
3591	(151*10^154434-7)/9	154436	Robert Price	01/2020
3592	(118*10^154428+11)/3	154430	Robert Price	03/2022
3593	2^512987+29153	154425	Enzo Doria	02/2024
3594	(14*10^154413+139)/9	154414	Robert Price	11/2021
3595	(77*10^154389-149)/9	154390	Robert Price	03/2022
3596	32184^34247-34247^32184	154374	Frank Doornink	02/2024
3597	10^154359+49	154360	Robert Price	02/2023
3598	2^512628-114053	154317	Enzo Doria	11/2014
3599	2^512529-49783	154287	Enzo Doria	10/2015
3600	(355573#+6991)/(6991*2031599)	154285	Makoto Morimoto	06/2019
3601	2^512315-115297	154223	Enzo Doria	06/2015
3602	(47*10^154221+241)/9	154222	Robert Price	06/2022
3603	(7*10^154211+173)/9	154211	Robert Price	01/2022
3604	2^512243+22703	154201	Enzo Doria	09/2023
3605	2^512168+79561	154178	Enzo Doria	06/2016
3606	(77*10^154175+67)/9	154176	Robert Price	12/2021
3607	(59*19^120562-5)/18	154170	Anonymous	12/2023
3608	(5*10^154158-311)/9	154158	Robert Price	12/2021
3609	27169^34758-34758^27169	154120	Frank Doornink	01/2024
3610	(89*10^154103-737)/9	154104	Robert Price	01/2022
3611	2^511857+23327	154085	Enzo Doria	10/2023
3612	4*10^154078-57	154079	Robert Price	10/2018
3613	26242^34863-34863^26242	154060	Frank Doornink	03/2024
3614	(355049#+1859)/(111310148891*62587751)	154051	Makoto Morimoto	06/2019
3615	7*10^154038-57	154039	Robert Price	06/2020
3616	2^511658-114371	154025	Enzo Doria	02/2015
3617	(57^87719+1)/58	154022	Paul Bourdelais	11/2017
3618	2^511580-1846679	154001	Enzo Doria	07/2015
3619	(259*10^153998-1)/3	154000	Robert Price	12/2020
3620	2^511541-113713	153990	Enzo Doria	09/2014
3621	49958^32768+49957^32768	153965	Kellen Shenton	11/2020
3622	10^153935+970801	153936	Patrick De Geest	05/2021
3623	10^153935-1000001	153935	Robert Price	08/2020
3624	(16*10^153868-73)/3	153869	Robert Price	07/2020
3625	9*10^153851-67	153852	Robert Price	11/2020
3626	2^511077-112723	153850	Enzo Doria	06/2014
3627	69^83653-68^83653	153826	Robert Price	12/2013
3628	2^510963-113707	153816	Enzo Doria	09/2014
3629	(154*10^153810-1)/9	153812	Serge Batalov	12/2014
3630	(181*25^109991-75077)/8	153763	Curtis Bright	05/2015
3631	2*10^153746-3	153747	Robert Price	07/2015
3632	2^510626+1179379	153714	Enzo Doria	05/2016
3633	(7*10^153664+113)/3	153665	Robert Price	02/2018
3634	2^510448+24991	153661	Enzo Doria	11/2023
3635	2^510420+81121	153652	Enzo Doria	07/2016
3636	(197*7^181761-1)/2	153608	Karsten Bonath	05/2017
3637	2^509894-459161	153494	Enzo Doria	05/2015
3638	(74*10^153489+673)/9	153490	Robert Price	02/2022
3639	(49*10^153484-211)/9	153485	Robert Price	06/2022
3640	2^509841+71657	153478	Enzo Doria	04/2016
3641	9*10^153446+41	153447	Robert Price	08/2020
3642	2^509533-1846723	153385	Enzo Doria	07/2015
3643	2^509468-39989	153366	Enzo Doria	09/2015
3644	70^83117-69^83117	153360	Robert Price	01/2014
3645	(209246*34^99997-81)/11	153148	Eric Chen	08/2023
3646	(7*10^153116-1)/3	153117	Robert Price	08/2022
3647	(112*10^153025-1)/3	153027	Serge Batalov	12/2014
3648	31912^33975-33975^31912	153022	Frank Doornink	01/2024
3649	(19*10^153010+131)/3	153011	Robert Price	06/2020
3650	2^508174-1855151	152976	Enzo Doria	09/2015
3651	181^67757-2	152974	Lelio R Paula	12/2017
3652	2^508160-1864829	152972	Enzo Doria	01/2016
3653	10^152960+412563	152961	Patrick De Geest	05/2021
3654	10^152960-50000000001	152960	Robert Price	12/2020
3655	10^152960-423749	152960	Patrick De Geest	05/2021
3656	(71*10^152933-143)/9	152934	Robert Price	10/2021
3657	32109^33932-33932^32109	152919	Frank Doornink	02/2024
3658	2^507857-1848199	152881	Enzo Doria	07/2015
3659	2^507638-115361	152815	Enzo Doria	07/2015
3660	2^507551-114025	152789	Enzo Doria	11/2014
3661	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
3662	(22*10^152670-13)/9	152671	Robert Price	06/2018
3663	2^507085+28517	152648	Enzo Doria	01/2024
3664	2^506917+28847	152598	Enzo Doria	02/2024
3665	2^506451-22339	152457	Enzo Doria	07/2013
3666	26463^34460-34460^26463	152405	Frank Doornink	03/2024
3667	31898^33837-33837^31898	152394	Frank Doornink	01/2024
3668	2^505995-113185	152320	Enzo Doria	07/2014
3669	(8*10^152260-17)/9	152260	Serge Batalov	11/2022
3670	(4*10^152253+149)/9	152253	Robert Price	04/2018
3671	33530^33643-33643^33530	152250	Norbert Schneider	04/2024
3672	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
3673	2^505431-505431	152150	Henri Lifchitz	04/2005
3674	(203*10^152143+1)/3	152145	Robert Price	03/2020
3675	31730^33787-33787^31730	152092	Frank Doornink	01/2024
3676	2^505089+217787	152047	Enzo Doria	01/2024
3677	33565^33594-33594^33565	152043	Norbert Schneider	04/2024
3678	2^505053+73097	152037	Enzo Doria	04/2016
3679	22*10^151998+3	152000	Robert Price	01/2020
3680	(238*10^151979-1)/3	151981	Robert Price	04/2020
3681	(2^504793-7)/46765	151954	Lelio R Paula	12/2017
3682	3^318465+4	151947	Aurel Gibier	09/2024
3683	350377#+797581	151937	Nicolas PALAU	08/2017
3684	(79*10^151906-529)/9	151907	Robert Price	01/2022
3685	2^504618-343991	151906	Enzo Doria	07/2015
3686	2^504259+211193	151798	Enzo Doria	08/2023
3687	2^504212-461939	151783	Enzo Doria	07/2015
3688	7*10^151772-41	151773	Robert Price	08/2021
3689	2^504054-2231	151736	Yves Minet	10/2011
3690	25237^34458-34458^25237	151686	Frank Doornink	11/2023
3691	(28*10^151682+191)/3	151683	Robert Price	02/2020
3692	2^503817+23961	151665	Enzo Doria	10/2023
3693	2^503475-933075	151562	Paul Bourdelais	06/2021
3694	2^503371+26289	151530	Enzo Doria	12/2023
3695	2^503361-39883	151527	Enzo Doria	09/2015
3696	2^503225+382667	151486	Enzo Doria	10/2016
3697	(206*10^151483-11)/3	151485	Robert Price	02/2022
3698	(844*10^151396-7)/9	151398	Robert Price	05/2021
3699	(26*10^151391-503)/9	151392	Robert Price	07/2018
3700	2^502769+1877567	151349	Enzo Doria	08/2016
3701	2^502576-4019	151291	Yves Minet	10/2011
3702	5*10^151257+41	151258	Robert Price	03/2019
3703	2^502290-2792501	151205	Enzo Doria	02/2016
3704	2^502181+1868417	151172	Enzo Doria	04/2016
3705	2^502055+22583	151134	Enzo Doria	09/2023
3706	(3*23^110967+41)/22	151106	Anonymous	12/2023
3707	6*10^151063-77	151064	Robert Price	09/2021
3708	2^501781-1850503	151052	Enzo Doria	08/2015
3709	(5*10^151007+37)/3	151008	Robert Price	03/2018
3710	3^316494+5*2^316494	151007	Jon Grantham	08/2023
3711	2^501627-991	151005	Yves Minet	02/2014
3712	2^501577-115333	150990	Enzo Doria	07/2015
3713	25239^34298-34298^25239	150983	Frank Doornink	12/2023
3714	(19*10^150977-7)/3	150978	Robert Price	12/2023
3715	8*10^150975+3	150976	Robert Price	08/2015
3716	2^501512-113669	150971	Enzo Doria	09/2014
3717	34180^26101+26101^34180	150962	Norman Luhn	04/2024
3718	U(1083477)/2166953	150949	Serge Batalov	07/2024
3719	(83*10^150908+493)/9	150909	Robert Price	12/2021
3720	36267^14482+14482^36267	150901	Norman Luhn	04/2024
3721	2*10^150818+83	150819	Robert Price	12/2021
3722	48753^1240+1240^48753	150814	Norman Luhn	04/2024
3723	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
3724	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
3725	2^500899-500899	150786	Henri Lifchitz	04/2005
3726	2^500832+1876801	150766	Enzo Doria	07/2016
3727	(23*10^150763-59)/9	150764	Robert Price	05/2018
3728	46002^1891+1891^46002	150735	Norman Luhn	04/2024
3729	32001^33458-33458^32001	150734	Frank Doornink	01/2024
3730	2^500699+1884953	150726	Enzo Doria	02/2017
3731	(13*10^150675-37)/3	150676	Robert Price	01/2019
3732	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
3733	35365^18204+18204^35365	150661	Norman Luhn	05/2024
3735	2^500337-71101	150617	Enzo Doria	04/2016
3734	(74*10^150616+133)/9	150617	Robert Price	06/2019
3736	(2*10^150612-17)/3	150612	Serge Batalov	11/2022
3737	4*10^150577+91	150578	Robert Price	08/2018
3738	5649^40132+40132^5649	150575	Norbert Schneider	04/2024
3739	2^500160+80071	150564	Enzo Doria	06/2016
3740	(2^500120+5)/9	150551	Lelio R Paula	12/2017
3742	(43*10^150515-421)/9	150516	Robert Price	01/2019
3741	4695^40994+40994^4695	150516	Norbert Schneider	11/2023
3743	2^499999+15981	150515	Norman Luhn	08/2023
3744	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
3745	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
3746	26614^34005-34005^26614	150476	Frank Doornink	03/2024
3747	2^499861-29503	150474	Enzo Doria	08/2015
3748	2^499653-113533	150411	Enzo Doria	08/2014
3749	(14*10^150391-191)/3	150392	Robert Price	10/2020
3750	29033^33696+33696^29033	150382	Norbert Schneider	10/2023

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