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 ?
4501	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
4502	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
4503	2^388180+93	116854	Donovan Johnson	07/2008
4504	(2^388167+2510)/2	116850	Stefano Morozzi	09/2020
4505	(85*10^116842+293)/9	116843	Robert Price	12/2019
4506	35296^2043+2043^35296	116840	Hans Havermann	02/2021
4507	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
4508	38633^1056+1056^38633	116814	Hans Havermann	02/2021
4509	2^387946-113261	116784	Enzo Doria	07/2014
4510	28*36^75009+305	116739	Eric Chen	12/2022
4511	28363^13056+13056^28363	116737	Hans Havermann	02/2021
4512	2^387745+75557	116723	Enzo Doria	04/2016
4513	(29*10^116719+313)/9	116720	Robert Price	04/2021
4514	29622^8699+8699^29622	116695	Hans Havermann	02/2021
4515	(206*10^116687-17)/9	116689	Robert Price	01/2020
4516	(7*10^116684+179)/3	116685	Robert Price	09/2018
4517	2^387554+71455	116666	Enzo Doria	04/2016
4518	(602*10^116647-71)/9	116649	Robert Price	12/2021
4519	3^244461-10	116638	Tyler NeSmith	09/2022
4520	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
4521	(2*10^116620+43)/9	116620	Serge Batalov	11/2022
4522	(19*10^116617+287)/9/12893	116614	Alfred Reich	11/2022
4523	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
4524	(25*10^116601-331)/9	116602	Robert Price	08/2018
4525	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
4526	(2^387284+3726)/2	116584	Stefano Morozzi	09/2020
4527	2^387211+111546435	116563	Paul Bourdelais	10/2021
4528	10^116557+987654321	116558	Robert Price	12/2019
4529	10^116557+9141	116558	Patrick De Geest	02/2020
4530	10^116557-609431	116557	Patrick De Geest	02/2020
4531	(28*10^116546+41)/3	116547	Robert Price	07/2021
4532	(2^387123+1814)/2	116536	Stefano Morozzi	02/2021
4533	(2^387076+2046)/2	116522	Stefano Morozzi	09/2020
4534	(2^387073+2570)/2	116521	Stefano Morozzi	09/2020
4535	(7*10^116514-1)/3	116515	Robert Price	08/2022
4536	28846^10931+10931^28846	116500	Hans Havermann	02/2021
4537	10^116496+3593037	116497	Paul Bourdelais	10/2021
4538	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
4539	2^386947+1869143	116483	Enzo Doria	05/2016
4540	(30^78857-1)/29	116480	Robert Price	12/2011
4541	(2^386903-3)/5	116469	Lelio R Paula	03/2014
4542	28107^13892+13892^28107	116441	Hans Havermann	02/2021
4543	29110^9957+9957^29110	116386	Hans Havermann	02/2021
4544	26469^24838+24838^26469	116335	Hans Havermann	01/2021
4545	2^386389-1864783	116315	Enzo Doria	03/2016
4546	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
4547	297^47012+47012^297	116250	Norbert Schneider	07/2018
4548	(35*10^116223-341)/9	116224	Robert Price	08/2021
4549	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
4550	(2^386054+714)/2	116214	Stefano Morozzi	09/2020
4551	(10^116201+7)/39623	116197	Alfred Reich	06/2021
4552	2^385969-823	116189	Yves Minet	05/2012
4553	57^66162+2	116173	Lelio R Paula	08/2013
4554	2^385854+75049	116154	Enzo Doria	04/2016
4555	(2^385832+2590)/2	116147	Stefano Morozzi	09/2020
4556	2^385775-109587	116130	Enzo Doria	04/2014
4557	(14*10^116112-101)/3	116113	Robert Price	02/2019
4558	Phi(236354,10)/24817171	116109	Makoto Kamada	08/2019
4559	3*10^116107+23	116108	Robert Price	03/2022
4560	28729^10990+10990^28729	116094	Hans Havermann	02/2021
4561	2^385622+71839	116084	Enzo Doria	04/2016
4562	2^385564+781	116067	Lelio R Paula	01/2012
4563	(2^385565+1562)/2	116067	Stefano Morozzi	09/2020
4564	(2^385563+378)/2	116066	Stefano Morozzi	02/2021
4565	(2^385557+2214)/2	116064	Stefano Morozzi	09/2020
4566	29431^8776+8776^29431	116056	Hans Havermann	01/2021
4567	(266*10^116024-17)/3	116026	Robert Price	07/2020
4568	30263^6820+6820^30263	116022	Hans Havermann	02/2021
4569	2^385410+71893	116020	Enzo Doria	04/2016
4570	38225^1084+1084^38225	116014	Hans Havermann	02/2021
4571	26548^23433+23433^26548	116011	Hans Havermann	02/2021
4572	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
4573	(11*10^115910-131)/3	115911	Robert Price	09/2018
4574	2^384953-111943	115883	Paul Bourdelais	02/2012
4575	43^70942-2	115882	Lelio R Paula	04/2014
4576	(94*10^115879-7)/3	115881	Robert Price	03/2020
4577	7*10^115863+3	115864	Robert Price	08/2015
4578	2^384834+93	115847	Donovan Johnson	07/2008
4579	2^384809+71297	115840	Enzo Doria	04/2016
4580	(55*10^115829+323)/9	115830	Robert Price	10/2021
4581	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
4582	31348^4951+4951^31348	115822	Hans Havermann	02/2021
4583	(793*10^115810+53)/9	115812	Robert Price	01/2022
4584	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
4585	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
4586	31115^5266+5266^31115	115794	Hans Havermann	02/2021
4587	2*10^115784-27	115785	Robert Price	05/2018
4588	10^115773+126739	115774	Patrick De Geest	04/2018
4590	10^115773-1000000001	115773	Robert Price	03/2018
4589	10^115773-396221	115773	Patrick De Geest	04/2018
4591	(2^384582+778)/2	115771	Stefano Morozzi	09/2020
4592	30537^6178+6178^30537	115762	Hans Havermann	01/2021
4593	2^384530+1874305	115756	Enzo Doria	06/2016
4594	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
4595	28275^12406+12406^28275	115748	Hans Havermann	01/2021
4596	(44*10^115697-413)/9	115698	Robert Price	03/2019
4597	31408^4825+4825^31408	115692	Hans Havermann	02/2021
4598	(2^384317+1026)/2	115691	Stefano Morozzi	09/2020
4599	2^384312+81091	115690	Yves Minet	02/2010
4600	(2^384265+2150)/2	115675	Stefano Morozzi	09/2020
4601	(2^384246+2182)/2	115670	Stefano Morozzi	09/2020
4602	(4*10^115668-79)/3	115669	Robert Price	02/2018
4603	(2^384193+242)/2	115654	Stefano Morozzi	09/2020
4604	(266947#+1267)/(7^2*181)	115647	Makoto Morimoto	06/2019
4605	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
4606	18^92125-92125^18	115642	Dylan Delgado	08/2019
4607	3^242337-4042	115625	Enzo Doria	05/2014
4608	(2^383931+674)/2	115575	Stefano Morozzi	09/2020
4609	7*10^115561+79	115562	Robert Price	07/2019
4610	(2^383872+3046)/2	115557	Stefano Morozzi	09/2020
4611	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
4612	2^383780-3149	115530	Yves Minet	10/2014
4613	(41*10^115523-383)/9	115524	Robert Price	11/2018
4614	27316^16923+16923^27316	115506	Hans Havermann	02/2021
4615	(2^383618+618)/2	115481	Stefano Morozzi	09/2020
4616	2^383560-455	115464	Yves Minet	03/2012
4617	(2^383544+5)/3	115458	Lelio R Paula	03/2014
4618	(22*10^115454+119)/3	115455	Robert Price	04/2021
4619	89^59221-88^59221	115445	Robert Price	06/2015
4620	2^383347+1869413	115399	Enzo Doria	05/2016
4621	(103*10^115366+17)/3	115368	Robert Price	08/2020
4622	(2^383232+750)/2	115365	Stefano Morozzi	09/2020
4623	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
4624	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
4625	29961^7060+7060^29961	115315	Hans Havermann	01/2021
4627	2^383039+1869509	115307	Enzo Doria	05/2016
4626	32918^3183+3183^32918	115307	Hans Havermann	01/2021
4628	36964^1315+1315^36964	115288	Hans Havermann	02/2021
4629	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
4630	(22*10^115282+29)/3	115283	Robert Price	02/2021
4631	(2^382945+2046)/2	115278	Stefano Morozzi	09/2020
4632	(2^382789+3182)/2	115231	Stefano Morozzi	09/2020
4633	30416^6141+6141^30416	115224	Hans Havermann	02/2021
4634	6*10^115211+79	115212	Robert Price	09/2020
4635	(2^382722+3598)/2	115211	Stefano Morozzi	09/2020
4636	27987^13078+13078^27987	115210	Hans Havermann	02/2021
4637	(2^382699+2090)/2	115204	Stefano Morozzi	09/2020
4638	(22*10^115188-193)/9	115189	Robert Price	07/2022
4639	2^382633+73697	115185	Enzo Doria	04/2016
4640	2^382509-113593	115147	Enzo Doria	08/2014
4641	2^382502-2791721	115145	Enzo Doria	03/2016
4642	(2^382495+1274)/2	115143	Stefano Morozzi	01/2021
4643	26752^20065+20065^26752	115099	Hans Havermann	02/2021
4644	26383^23008+23008^26383	115080	Hans Havermann	02/2021
4645	9^120590-120590	115073	Robert Price	03/2014
4646	28203^12016+12016^28203	115062	Hans Havermann	02/2021
4647	2^382198+9	115054	Lelio R Paula	03/2013
4648	30101^6630+6630^30101	115032	Hans Havermann	01/2021
4649	(89*10^115030-179)/9	115031	Robert Price	12/2019
4650	(2^381935+2774)/2	114974	Stefano Morozzi	02/2021
4651	27300^16271+16271^27300	114972	Hans Havermann	02/2021
4652	2^381883-59197	114959	Enzo Doria	10/2015
4653	27423^15542+15542^27423	114944	Hans Havermann	02/2021
4654	(2^381820+1626)/2	114939	Stefano Morozzi	09/2020
4656	2^381806-4481	114936	Yves Minet	07/2011
4655	2^381808-1851507	114936	Enzo Doria	08/2015
4657	(2^381792+2502)/2	114931	Stefano Morozzi	09/2020
4658	2^381774-112373	114926	Enzo Doria	06/2014
4659	26341^22980+22980^26341	114883	Hans Havermann	01/2021
4660	2^381555-109051	114860	Enzo Doria	04/2014
4661	2^381546-113501	114857	Enzo Doria	08/2014
4662	(7*10^114845-19)/3	114846	Robert Price	10/2020
4663	26675^20178+20178^26675	114833	Hans Havermann	02/2021
4664	(2^381436+1182)/2	114824	Stefano Morozzi	09/2020
4665	3^240644+16	114817	Robert Price	04/2020
4666	2^381360-110429	114801	Enzo Doria	05/2014
4667	(17*10^114795+79)/3	114796	Robert Price	04/2019
4668	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
4669	2^381252-115079	114769	Enzo Doria	06/2015
4670	(2^381251+3186)/2	114768	Stefano Morozzi	09/2020
4671	2^381209-29323	114756	Enzo Doria	07/2015
4672	2^381207-111546435	114755	Paul Bourdelais	10/2021
4673	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
4674	2^381201+1873205	114753	Enzo Doria	06/2016
4675	(85*10^114737+293)/9	114738	Robert Price	12/2019
4676	(265*10^114736+17)/3	114738	Robert Price	03/2020
4677	(2^381062+2170)/2	114711	Stefano Morozzi	09/2020
4678	2^380974-112991	114685	Enzo Doria	07/2014
4679	37097^1234+1234^37097	114679	Hans Havermann	02/2021
4680	88^58949-87	114626	Norbert Schneider	11/2015
4681	(2^380773+662)/2	114624	Stefano Morozzi	09/2020
4682	29913^6782+6782^29913	114608	Hans Havermann	02/2021
4683	(331*10^114605-7)/9	114607	Robert Price	04/2022
4684	2^380700+91	114603	Lelio R Paula	03/2013
4685	(2^380632+2578)/2	114582	Stefano Morozzi	09/2020
4686	7*10^114577+27	114578	Robert Price	11/2020
4688	10^114575+3^114576	114576	Mike Oakes	09/2010
4687	10^114575+66561	114576	Patrick De Geest	02/2017
4689	10^114575-581081	114575	Patrick De Geest	02/2017
4690	2^380587-115315	114569	Enzo Doria	06/2015
4691	31874^3927+3927^31874	114558	Hans Havermann	02/2021
4692	2^380513-216925	114546	Enzo Doria	05/2014
4693	2^380451-1840087	114528	Enzo Doria	06/2015
4694	(2^380426+1510)/2	114520	Stefano Morozzi	09/2020
4695	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
4696	2^380279-461347	114476	Enzo Doria	07/2015
4697	(331*10^114454-7)/9	114456	Robert Price	04/2022
4698	27121^16590+16590^27121	114447	Hans Havermann	01/2021
4699	25966^25555+25555^25966	114445	Hans Havermann	01/2021
4700	(11*10^114400+529)/9	114401	Robert Price	09/2021
4701	2^380021+1871147	114398	Enzo Doria	05/2016
4702	2^380005+1869707	114393	Enzo Doria	05/2016
4703	2^379958-113297	114379	Enzo Doria	07/2014
4704	(2^379897+1274)/2	114361	Stefano Morozzi	01/2021
4705	2^379881-109105	114356	Enzo Doria	04/2014
4706	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
4707	(4*10^114340+83)/3	114341	Robert Price	02/2018
4708	(26*10^114317-77)/3	114318	Robert Price	11/2019
4709	(4*10^114296+149)/9	114296	Robert Price	04/2018
4710	88^58773-87	114284	Norbert Schneider	11/2015
4711	27764^13065+13065^27764	114280	Hans Havermann	01/2021
4712	2^379529-2790283	114250	Enzo Doria	03/2016
4713	2^379522+1869115	114248	Enzo Doria	05/2016
4714	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
4715	2^379317-115033	114186	Enzo Doria	06/2015
4716	(22*10^114178+47)/3	114179	Robert Price	06/2021
4717	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
4718	(2^379192+226)/2	114148	Stefano Morozzi	09/2020
4719	6*10^114091+23	114092	Robert Price	09/2020
4720	(4*10^114076+143)/3	114077	Robert Price	03/2018
4721	(2^378820+3226)/2	114036	Stefano Morozzi	01/2021
4722	(2^378754+2058)/2	114017	Stefano Morozzi	09/2020
4723	13643^27572-27572^13643	114008	Norbert Schneider	12/2022
4725	(46*10^113969+683)/9	113970	Robert Price	03/2019
4724	(83*10^113969+133)/9	113970	Robert Price	08/2021
4726	32226^3439+3439^32226	113966	Hans Havermann	02/2021
4727	(77*10^113963-149)/9	113964	Robert Price	03/2022
4728	78*10^113954-7	113956	Robert Price	10/2020
4729	2*10^113941+9	113942	Dmitry Domanov	11/2010
4730	10^113933+145897	113934	Patrick De Geest	02/2021
4733	(2^378478+1642)/2	113933	Stefano Morozzi	09/2020
4731	10^113933-8000000001	113933	Robert Price	11/2020
4732	10^113933-66167	113933	Patrick De Geest	02/2021
4734	2339662057597*10^113903+9	113916	Robert Price	03/2021
4735	4*10^113905+91	113906	Robert Price	08/2018
4736	10^113894+76609	113895	Patrick De Geest	02/2021
4738	10^113894-10000001	113894	Robert Price	09/2020
4737	10^113894-373947	113894	Patrick De Geest	02/2021
4739	33933^2270+2270^33933	113881	Hans Havermann	02/2021
4740	4*10^113874-21	113875	Robert Price	09/2018
4741	2^378272-16565	113872	Enzo Doria	04/2013
4742	2^378217-109075	113855	Enzo Doria	04/2014
4743	2^378198+67	113849	Lelio R Paula	03/2013
4744	2^378173-3249	113842	Yves Minet	12/2014
4745	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
4746	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
4747	30030^6173+6173^30030	113829	Hans Havermann	01/2021
4748	2^378128-262977	113828	Enzo Doria	05/2014
4749	2^378123-113215	113827	Enzo Doria	07/2014
4750	6^146274-18893	113824	Enzo Doria	03/2013

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