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	(41*10^93207+49)/9	93208	Robert Price	04/2016
4502	14^81312-57	93194	Lelio R Paula	06/2016
4503	41^57783-40	93192	Theodore Burton	02/2007
4504	3*10^93179-97	93180	Robert Price	08/2017
4505	5*7^110252-4	93175	Lelio R Paula	11/2014
4506	2^309380-27	93133	Lelio R Paula	11/2012
4507	23*10^93116-7	93118	Robert Price	03/2016
4508	(29*10^93082+1)/3	93083	Robert Price	11/2015
4509	(58*10^93062-13)/9	93063	Robert Price	09/2015
4510	2^309131+1869383	93058	Enzo Doria	05/2016
4511	2^309066-93	93039	Lelio R Paula	11/2012
4512	2^309063-113269	93038	Enzo Doria	07/2014
4513	3^194965+16	93022	Robert Price	10/2013
4514	2^308979+1869143	93012	Enzo Doria	05/2016
4515	5^133064+54	93008	Lelio R Paula	04/2016
4516	(2^308905-509203)/119	92988	Lelio R Paula	06/2013
4517	(94*10^92981-49)/99	92981	Ray Chandler	07/2011
4518	(2*10^92976-17)/3	92976	Robert Price	08/2014
4519	2^308809+37967	92961	Phil Moore	03/2008
4520	(3^194825+5)/11656	92952	Lelio R Paula	04/2013
4521	(2^308679+5)/1573	92919	Lelio R Paula	06/2013
4522	2^308650+513	92913	Lelio R Paula	02/2016
4523	5*7^109936+6	92908	Lelio R Paula	10/2014
4524	2*10^92897+89	92898	Robert Price	07/2016
4525	12^86073-29	92889	Lelio R Paula	06/2016
4526	2^308566-117	92888	Lelio R Paula	11/2012
4527	(17*10^92869-11)/3	92870	Robert Price	07/2015
4528	2^308459+75431	92856	Enzo Doria	04/2016
4529	2^308426-1866377	92846	Enzo Doria	03/2016
4530	(96^46831-1)/95	92830	Paul Bourdelais	09/2017
4531	2^308349-112111	92823	Enzo Doria	06/2014
4532	9*10^92821+19	92822	Robert Price	05/2016
4533	2^308337-75	92819	Lelio R Paula	11/2012
4534	4*3^194508+7	92805	Lelio R Paula	08/2014
4535	22*25^66379-113	92796	Curtis Bright	05/2015
4536	11^89101-1080	92790	Enzo Doria	12/2012
4537	2^308236-1867859	92789	Enzo Doria	04/2016
4538	12^85963+25	92770	Lelio R Paula	06/2016
4539	7^109750-66	92750	Lelio R Paula	04/2016
4540	9*10^92742+11	92743	Robert Kinser	01/2017
4541	(21*2^308046-1)/8857	92729	Lelio R Paula	02/2014
4542	2^307997-110655	92717	Enzo Doria	05/2014
4543	L(443609)	92709	Renaud Lifchitz	11/2003
4544	10^92691+9	92692	Robert Price	03/2011
4545	10^92691-252291	92691	Patrick De Geest	08/2013
4546	2^307879-2521	92681	Yves Minet	07/2014
4547	(2^307780-7)/19959669	92644	Lelio R Paula	06/2013
4548	14^80831+47	92643	Lelio R Paula	06/2016
4549	15^78744+92	92611	Lelio R Paula	07/2016
4550	65^51083-64	92610	Norbert Schneider	11/2014
4551	131^43737-130	92604	Norbert Schneider	02/2019
4552	6^118996-16943	92597	Enzo Doria	02/2013
4553	(16*10^92591+41)/3	92592	Robert Price	10/2017
4554	(3^194014-7)/2	92568	Lelio R Paula	04/2013
4555	(63^51439+1)/64	92555	Paul Bourdelais	08/2017
4556	(26*10^92546-77)/3	92547	Robert Price	02/2017
4557	3^193954+340	92540	Lelio R Paula	04/2016
4558	2^307407-307407^2	92539	Henri Lifchitz	05/2005
4559	(17*10^92513-11)/3	92514	Robert Price	07/2015
4560	2^307318-4211	92512	Yves Minet	06/2011
4561	2^307280+193	92501	Lelio R Paula	11/2012
4562	20^71075-33	92471	Lelio R Paula	05/2016
4563	2^307126-78795	92455	Lelio R Paula	02/2016
4564	2^307125-49789	92454	Henri Lifchitz	08/2005
4565	2^307099+23	92447	Lelio R Paula	11/2012
4566	129^43798+128	92440	Norbert Schneider	01/2019
4567	Phi(277314,10)/3327769	92430	Makoto Kamada	05/2019
4568	7*10^92414-69	92415	Robert Price	01/2017
4569	(9787*2^306975-1)/2129155	92407	Lelio R Paula	04/2015
4570	2^306915+1873373	92391	Enzo Doria	06/2016
4571	2^306908+12915	92389	Lelio R Paula	02/2016
4572	19^72244-80	92383	Lelio R Paula	06/2016
4574	2^306849+75	92371	Lelio R Paula	11/2012
4573	(397*10^92369+53)/9	92371	Robert Price	11/2017
4575	2^306813-869688105	92360	Lelio R Paula	08/2016
4576	2^306672-109059	92318	Enzo Doria	04/2014
4577	6^118604-17063	92292	Enzo Doria	02/2013
4578	(31*2^306487-1)/2291	92260	Lelio R Paula	02/2014
4579	2^306467-1835611	92256	Enzo Doria	04/2015
4580	2^306433+76427	92246	Enzo Doria	05/2016
4582	2^306430-113313	92245	Enzo Doria	07/2014
4581	(23*10^92244-59)/9	92245	Robert Price	03/2017
4583	(47*2^306398+1)/1384803	92231	Lelio R Paula	04/2015
4584	(25*10^92186+59)/3	92187	Robert Price	05/2016
4585	2^306213-286183	92180	Enzo Doria	06/2015
4586	10^92178+61	92179	Robert Price	04/2011
4587	10^92178-175509	92178	Patrick De Geest	07/2013
4588	2^306200+1185	92176	Lelio R Paula	02/2016
4589	2^306153+11	92162	Lelio R Paula	11/2012
4590	(2^306141-7)/5	92157	Lelio R Paula	06/2013
4591	(26*10^92152-23)/3	92153	Robert Price	08/2016
4592	(2*10^92152+67)/3	92152	Robert Price	04/2017
4593	410^92099+37^92099	92100	Mike Oakes	12/2010
4594	115^44684+114	92081	Norbert Schneider	07/2018
4595	(2^305867-2^152934+1)/5	92075		11/2006
4596	2^305851-109495	92071	Enzo Doria	04/2014
4598	12^85300+35	92055	Lelio R Paula	06/2016
4597	((10^46026-1)1000/9+739)10^46026+(10^46026-1)/9	92055	Hans Havermann	05/2019
4599	3^192911+92	92042	Lelio R Paula	04/2016
4600	2^305723-276271	92032	Enzo Doria	07/2015
4601	2^305676+93	92018	Donovan Johnson	06/2008
4602	3^192819+4	91999	Lelio R Paula	04/2013
4603	(38*10^91997-83)/99	91997	Ray Chandler	07/2011
4604	2^305539+72911	91977	Enzo Doria	04/2016
4605	Phi(212014,10)	91960	Makoto Kamada	04/2019
4606	(2^305427-5)/1297998213	91934	Lelio R Paula	06/2013
4607	85^47642+84	91922	Norbert Schneider	10/2015
4608	10^91920+187651	91921	Patrick De Geest	07/2013
4609	10^91920-39	91920	Robert Price	05/2011
4610	(22*10^91903+41)/9	91904	Robert Price	02/2015
4612	2^305275-27	91897	Lelio R Paula	11/2012
4611	3^192607-7726	91897	Enzo Doria	05/2014
4613	(7*10^91856-61)/9	91856	Erik Branger	12/2009
4614	(89*10^91839-53)/9	91840	Robert Price	11/2015
4615	8*5^131351+7	91812	Lelio R Paula	10/2014
4616	3^192426-68	91811	Lelio R Paula	04/2016
4617	2^304973+117	91807	Lelio R Paula	11/2012
4618	2^304939-1863727	91796	Enzo Doria	03/2016
4619	2^304902+8415	91785	Lelio R Paula	02/2016
4620	18^73119+61	91785	Lelio R Paula	06/2016
4621	(78557*2^304740+1)/159	91739	Lelio R Paula	06/2014
4622	2^304747+71355	91738	Lelio R Paula	02/2016
4623	8*3^192251+5	91728	Lelio R Paula	08/2014
4624	2^304674-87	91717	Lelio R Paula	11/2012
4625	(28*10^91715+701)/9	91716	Robert Price	11/2017
4626	(2^304698+9)/1362809953	91715	Lelio R Paula	06/2013
4627	(5*10^91707-119)/3	91708	Robert Price	04/2016
4628	2^304633-112771	91704	Enzo Doria	06/2014
4629	9*10^91693+23	91694	Robert Price	11/2017
4630	2^304578-16713	91688	Enzo Doria	05/2013
4631	6^117824-18713	91685	Enzo Doria	03/2013
4632	(17^74509-1)/16	91679	Paul Bourdelais	03/2010
4633	(2^304551-7)/8912231	91673	Lelio R Paula	06/2013
4634	(2^304532-3)/3013	91670	Lelio R Paula	06/2013
4635	2^304507-16645	91666	Enzo Doria	04/2013
4636	(29*2^304489+1)/31	91661	Lelio R Paula	09/2013
4637	2^304471-1836127	91655	Enzo Doria	04/2015
4638	2^304433+32769	91644	Lelio R Paula	02/2016
4639	2^304410-16625	91637	Enzo Doria	04/2013
4640	183^40500-2	91630	Lelio R Paula	10/2017
4641	(203*10^91613+1)/3	91615	Robert Price	09/2017
4642	4*5^131052+7	91603	Lelio R Paula	10/2014
4643	2^304278-4001	91597	Yves Minet	04/2017
4644	2^304272-1866377	91595	Enzo Doria	03/2016
4645	2^304268+19683	91594	Lelio R Paula	02/2016
4646	2^304162-161	91562	Lelio R Paula	11/2012
4647	5*7^108331+6	91552	Lelio R Paula	10/2014
4648	2^304082-2787821	91538	Enzo Doria	03/2016
4649	2^304015+64133	91518	David Broadhurst	06/2002
4650	(7*2^303963+1)/3	91503	Lelio R Paula	09/2013
4651	(2^303945-9)/3617	91494	Lelio R Paula	06/2013
4652	2^303930+1880527	91493	Enzo Doria	10/2016
4653	3^191684-68	91457	Lelio R Paula	04/2016
4654	(21*2^303813-1)/169	91456	Lelio R Paula	02/2014
4655	11^87797-120	91432	Enzo Doria	07/2012
4656	2^303698-1847231	91423	Enzo Doria	07/2015
4657	(38^28933-1)^2-2	91416	Norbert Schneider	06/2016
4658	2^303554+77299	91379	Enzo Doria	05/2016
4659	2^303542+12705	91376	Lelio R Paula	02/2016
4660	31^61269-2	91375	Lelio R Paula	09/2013
4661	2^303516-64875	91368	Lelio R Paula	02/2016
4662	(24737*2^303428+1)/3	91345	Lelio R Paula	06/2014
4663	(21181*2^303357+1)/32361	91320	Lelio R Paula	06/2014
4664	2^303344-2786969	91316	Enzo Doria	03/2016
4665	6^117346+65	91313	Lelio R Paula	05/2016
4666	2^303321+855	91309	Lelio R Paula	02/2016
4667	12^84606+47	91306	Lelio R Paula	06/2016
4668	2^303288+1874311	91299	Enzo Doria	06/2016
4669	197^39788-2	91293	Lelio R Paula	10/2017
4670	11^87663-1710	91292	Enzo Doria	12/2012
4671	2^303224+2533	91280	Henri Lifchitz	05/2005
4672	6^117302+143	91279	Lelio R Paula	05/2016
4673	3^191306-112880	91277	Enzo Doria	07/2014
4674	2^303207+12915	91275	Lelio R Paula	02/2016
4675	2^303191-111259	91270	Enzo Doria	05/2014
4676	10^91230+9^(91230+1)	91231	Robert Price	08/2016
4677	10^91230+7921	91231	Patrick De Geest	11/2016
4678	10^91230-911141	91230	Patrick De Geest	11/2016
4679	10^91229+348793	91230	Patrick De Geest	07/2019
4680	10^91229-2471	91229	Patrick De Geest	01/2019
4681	10^91225+5271	91226	Patrick De Geest	01/2019
4683	6^117232-17423	91225	Enzo Doria	02/2013
4682	10^91225-147219	91225	Patrick De Geest	07/2019
4685	7*10^91215+3	91216	Erik Branger	11/2009
4684	10^91215+230611	91216	Patrick De Geest	07/2019
4686	10^91215-4539	91215	Patrick De Geest	01/2019
4687	10^91210+2421	91211	Patrick De Geest	01/2019
4688	10^91210-1737	91210	Patrick De Geest	01/2019
4689	97*10^91205-3	91207	Robert Price	01/2017
4690	2^302979-161181	91206	Enzo Doria	04/2013
4691	2^302949+81	91197	Henri Lifchitz	02/2007
4692	10^91194+200361	91195	Patrick De Geest	07/2019
4694	4*6^117192-5	91194	Lelio R Paula	10/2014
4693	10^91194-8663	91194	Patrick De Geest	01/2019
4695	2^302918+99	91188	Lelio R Paula	11/2012
4696	10^91186+268111	91187	Patrick De Geest	07/2019
4697	10^91186-7763	91186	Patrick De Geest	01/2019
4698	10^91181+550471	91182	Patrick De Geest	07/2019
4699	10^91181-1367	91181	Patrick De Geest	01/2019
4700	10^91178+71883	91179	Patrick De Geest	07/2019
4701	10^91178-4719	91178	Patrick De Geest	01/2019
4702	10^91165+3043	91166	Patrick De Geest	01/2019
4703	10^91165-399413	91165	Patrick De Geest	07/2019
4704	10^91156+3861	91157	Patrick De Geest	01/2019
4705	10^91156-231497	91156	Patrick De Geest	07/2019
4706	2^302797+1869587	91151	Enzo Doria	05/2016
4707	265^37614+37614^265	91148	Norbert Schneider	01/2015
4708	7^107852+82	91146	Lelio R Paula	04/2016
4709	(38*10^91144-11)/9	91145	Robert Price	05/2015
4710	(55*10^91142+377)/9	91143	Robert Price	10/2017
4711	10^91128+9961	91129	Patrick De Geest	01/2019
4713	249^38030+38030^249	91128	Norbert Schneider	01/2015
4712	10^91128-189153	91128	Patrick De Geest	07/2019
4714	6^117094-211049	91117	Mike Oakes	05/2011
4716	2^302602-1867181	91093	Enzo Doria	03/2016
4715	10^91092+56127	91093	Patrick De Geest	07/2019
4717	10^91092-9107	91092	Patrick De Geest	01/2019
4718	(1017*2^302592-1)/53	91091	Lelio R Paula	04/2015
4719	15^77445-16	91083	Lelio R Paula	07/2016
4720	2^302505+81	91064	Henri Lifchitz	02/2007
4721	2^302496-112349	91061	Enzo Doria	06/2014
4722	17^73999-72	91052	Lelio R Paula	07/2016
4723	10^91047+9331	91048	Patrick De Geest	01/2019
4724	10^91047-671169	91047	Patrick De Geest	07/2019
4725	10^91044+2077	91045	Patrick De Geest	01/2019
4726	10^91044-136359	91044	Patrick De Geest	07/2019
4727	10^91041+9349	91042	Patrick De Geest	01/2019
4728	10^91041-7823	91041	Patrick De Geest	01/2019
4729	10^91040+4077	91041	Patrick De Geest	01/2019
4730	10^91040-119421	91040	Patrick De Geest	07/2019
4731	10^91037+2769	91038	Patrick De Geest	01/2019
4732	10^91037-22649	91037	Patrick De Geest	07/2019
4733	(16*10^91032+41)/3	91033	Robert Price	10/2017
4734	10^91023+58039	91024	Patrick De Geest	07/2019
4735	10^91023-6471	91023	Patrick De Geest	01/2019
4736	10^91018+7873	91019	Patrick De Geest	01/2019
4737	10^91018-333177	91018	Patrick De Geest	07/2019
4738	10^91017+68767	91018	Patrick De Geest	07/2019
4739	10^91017-428327	91017	Patrick De Geest	07/2019
4740	10^91016+73111	91017	Patrick De Geest	07/2019
4741	10^91016-7973	91016	Patrick De Geest	01/2019
4742	2^302332+577294575	91012	Lelio R Paula	08/2016
4743	10^91004+9073	91005	Patrick De Geest	01/2019
4744	10^91004-491519	91004	Patrick De Geest	07/2019
4745	10^91003+74269	91004	Patrick De Geest	07/2019
4746	10^91003-3903	91003	Patrick De Geest	01/2019
4747	2^302274+74209	90994	Enzo Doria	04/2016
4748	10^90991+81147	90992	Patrick De Geest	07/2019
4749	10^90991-6279	90991	Patrick De Geest	01/2019
4750	10^90983+1393	90984	Patrick De Geest	01/2019

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Probable Primes Top 10000

(253476 PRPs in the top)