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 (> 30000)	Who ?	When ?
4501	(19*2^291534-1)/178696395	87754	Lelio R Paula	02/2014
4502	(3^183915+5)/128	87748	Lelio R Paula	01/2013
4503	19^68619+24	87747	Lelio R Paula	12/2015
4505	2^291480+1185	87745	Lelio R Paula	10/2013
4504	2^291482+1867369	87745	Enzo Doria	03/2016
4506	2^291467-937	87741	Yves Minet	05/2013
4507	(25*10^87726+161)/3	87727	Robert Price	01/2017
4508	11^84239-2850	87726	Enzo Doria	12/2012
4509	10^87720+215541	87721	Patrick De Geest	01/2011
4510	10^87720-3	87720	Markus Tervooren	07/2010
4511	(5*10^87712-473)/9	87712	Robert Price	12/2017
4512	(2^291357+5)/6847	87704	Lelio R Paula	01/2013
4514	93^44541-2	87679	Lelio R Paula	09/2013
4513	2^291261-109561	87679	Enzo Doria	04/2014
4515	(4*10^87669+149)/9	87669	Robert Price	03/2017
4516	2^291217+4257	87666	Lelio R Paula	10/2013
4517	2*12^81214-5^81214	87645	Mike Oakes	12/2010
4518	(5*10^87622-473)/9	87622	Robert Price	12/2017
4519	12^81188+85	87617	Lelio R Paula	11/2015
4520	(21*2^290980-1)/5	87595	Lelio R Paula	02/2014
4521	2^290958+127	87588	Lelio R Paula	09/2012
4522	2^290923-67	87577	Lelio R Paula	09/2012
4523	3*10^87573-97	87574	Robert Price	08/2017
4524	(13*10^87565+11)/3	87566	Robert Price	05/2015
4525	(2^290857-7)/55	87555	Lelio R Paula	01/2013
4526	2^290802+82875	87541	Lelio R Paula	10/2013
4527	(509203*2^290792-1)/7560987	87536	Lelio R Paula	04/2015
4528	3^183441+236	87524	Lelio R Paula	12/2015
4529	2^290618-33	87485	Lelio R Paula	09/2012
4530	(184*10^87473-1)/3	87475	Robert Price	02/2017
4531	2^290534-115151	87460	Enzo Doria	06/2015
4532	2^290512-109757	87453	Enzo Doria	04/2014
4533	(32*10^87448-41)/9	87449	Robert Price	05/2015
4534	(2^290491+9)/3179	87444	Lelio R Paula	01/2013
4535	(25*2^290489-1)/51809	87443	Lelio R Paula	02/2014
4536	2^290426+82875	87427	Lelio R Paula	11/2013
4537	3*2^290415-7	87425	Lelio R Paula	08/2014
4538	10^87408+57	87409	Robert Price	03/2011
4539	2^290366+74779	87409	Enzo Doria	04/2016
4540	10^87408-123569	87408	Patrick De Geest	07/2013
4541	2^290265+58905	87379	Lelio R Paula	10/2013
4542	7^103391+16	87376	Lelio R Paula	10/2015
4543	(115*10^87368-7)/9	87370	Robert Price	11/2017
4544	(92^44491-1)/91	87369	Paul Bourdelais	08/2017
4545	8*7^103379+3	87367	Lelio R Paula	10/2014
4546	(2^290226+7)/71	87365	Lelio R Paula	01/2013
4547	13^78407-30	87341	Lelio R Paula	11/2015
4548	4*10^87337-99	87338	Robert Price	12/2016
4549	7*10^87319+39	87320	Robert Price	07/2016
4550	3*5^124921+2	87317	Lelio R Paula	10/2014
4551	3^182984+88	87306	Lelio R Paula	12/2015
4552	4*10^87287-99	87288	Robert Price	12/2016
4553	11^83813-1860	87283	Enzo Doria	12/2012
4554	734^30453+30453^734	87270	Norbert Schneider	04/2017
4555	12^80855+29	87258	Lelio R Paula	11/2015
4556	3*6^112119-5	87247	Lelio R Paula	10/2014
4557	12^80806+79	87205	Lelio R Paula	11/2015
4558	91382^9+9^91382	87201	Andrey Kulsha	11/2004
4559	(21181*2^289657+1)/81	87198	Lelio R Paula	06/2014
4560	6^112054-47	87195	Lelio R Paula	12/2015
4561	(55459*2^289632+1)/55	87191	Lelio R Paula	06/2014
4562	15^74131-68	87185	Lelio R Paula	11/2015
4563	2^289583-741	87174	Lelio R Paula	10/2013
4564	7^103146+12	87169	Lelio R Paula	10/2015
4565	5*2^289556-3	87166	Lelio R Paula	08/2014
4566	2^289543-112735	87162	Enzo Doria	06/2014
4567	8*3^182655-7	87150	Lelio R Paula	08/2014
4568	2*10^87144+81	87145	Robert Price	01/2017
4569	7^103106+2*3^103106	87135	Mike Oakes	08/2010
4570	8*3^182614+7	87130	Lelio R Paula	08/2014
4571	(2^289368-509203)/9	87108	Lelio R Paula	01/2013
4572	3^182566+14	87107	Robert Price	09/2013
4573	(3^182385-5)/2	87020	Lelio R Paula	01/2013
4574	11^83534-8	86992	Lelio R Paula	11/2015
4575	4^144479-14267	86986	Mike Oakes	03/2011
4576	(145*10^86982-1)/9	86984	Serge Batalov	12/2014
4577	(151*10^86963-1)/3	86965	Robert Price	04/2017
4578	15^73940-58	86961	Lelio R Paula	11/2015
4579	2^288761-113143	86926	Enzo Doria	07/2014
4580	2^288747+3083	86922	Yves Minet	03/2011
4581	30^58842+29	86917	Norbert Schneider	03/2017
4582	(10^86906-13)/3	86906	Robert Price	02/2017
4583	2^288692-110027	86905	Enzo Doria	04/2014
4584	(2^288682+7)/259895449	86894	Lelio R Paula	01/2013
4585	(2^288636+47)/1293	86885	Lelio R Paula	01/2013
4586	3^182089-34	86879	Robert Price	11/2013
4587	2^288543-109801	86861	Enzo Doria	04/2014
4588	60^48847-59	86858	Norbert Schneider	10/2014
4589	2^288470-64875	86839	Lelio R Paula	10/2013
4590	10^86816+32997	86817	Patrick De Geest	07/2013
4591	10^86816-99	86816	Robert Price	05/2011
4592	(89*10^86802-539)/9	86803	Robert Price	11/2017
4593	41487!2+256	86786	Robert Price	01/2015
4594	(5*2^288301-1)/999	86785	Lelio R Paula	02/2014
4595	2^288243+76043	86770	Enzo Doria	04/2016
4596	(29*2^288232+1)/15	86767	Lelio R Paula	01/2013
4597	9*6^111495+5	86761	Lelio R Paula	10/2014
4598	(5*2^288202+1)/81	86757	Lelio R Paula	01/2013
4599	9*7^102654-2	86754	Lelio R Paula	10/2014
4600	2^288122-112841	86734	Enzo Doria	06/2014
4601	5^124062-68	86716	Lelio R Paula	10/2015
4602	(2^288007-3)/125	86697	Lelio R Paula	01/2013
4603	379*10^86691+9	86694	Arkadiusz Wesolowski	10/2011
4604	7^102555+48	86670	Lelio R Paula	10/2015
4605	77779!4+2	86660	Robert Price	08/2017
4606	2^287809-111355	86640	Enzo Doria	05/2014
4607	(47*2^287795+1)/7	86636	Lelio R Paula	04/2015
4608	9*7^102504+8	86627	Lelio R Paula	10/2014
4609	3^181551+32	86622	Robert Price	11/2013
4610	2^287735-521347	86617	Paul Bourdelais	05/2013
4611	(1017*2^287600-1)/91	86578	Lelio R Paula	04/2015
4612	2^287540-112967	86559	Enzo Doria	06/2014
4613	3^181407+20	86554	Robert Price	10/2013
4614	(13*10^86546+83)/3	86547	Robert Price	09/2016
4615	3^181378-2^(181378-1)	86540	Robert Price	01/2016
4616	83^45080-2	86513	Lelio R Paula	08/2013
4617	(78557*2^287351+1)/611	86504	Lelio R Paula	06/2014
4618	25*29^59147+20936	86498	Curtis Bright	05/2015
4619	2^287298+1871359	86486	Enzo Doria	05/2016
4620	3*10^86478+89	86479	Robert Price	03/2017
4621	2^287272-79049	86478	Paul Bourdelais	02/2012
4622	9067052((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4623	8118242((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4624	7790642((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4625	7683852((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4626	7008912((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4627	6523202((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4628	3779202((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
4629	2550602((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
4630	1871112((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
4631	(10^86453-1)/9	86453	Lew Baxter	10/2000
4632	87^44563-86^44563	86431	Robert Price	05/2015
4633	6^111057+61	86420	Lelio R Paula	12/2015
4634	2^287057-109909	86413	Enzo Doria	04/2014
4635	5^123608+22	86399	Lelio R Paula	10/2015
4636	(31*10^86364-121)/9	86365	Robert Price	06/2016
4637	2^286859+71663	86354	Enzo Doria	04/2016
4638	2^286740+29835	86318	Lelio R Paula	10/2013
4639	2*10^86310+9^86310	86311	Mike Oakes	05/2011
4640	11^82878-1860	86309	Enzo Doria	12/2012
4641	2^286547+16095	86260	Lelio R Paula	10/2013
4642	(58*10^86242+329)/9	86243	Robert Price	11/2017
4643	2^286455-110427	86232	Enzo Doria	05/2014
4644	(37*10^86230+53)/9	86231	Robert Price	05/2015
4645	8*3^180700+5	86217	Lelio R Paula	08/2014
4646	3^180697-40	86215	Lelio R Paula	12/2015
4647	(13*2^286318-1)/13257	86188	Lelio R Paula	02/2014
4648	2^286165+77	86145	Lelio R Paula	08/2012
4649	9*2^286140+7	86138	Lelio R Paula	08/2014
4650	(29*2^286108-1)/2002367	86123	Lelio R Paula	02/2014
4651	10^86110+161113	86111	Patrick De Geest	07/2013
4652	10^86110-69	86110	Robert Price	05/2011
4653	2^286036-869688105	86106	Lelio R Paula	07/2016
4654	(77*10^86072+31)/9	86073	Robert Price	10/2015
4655	2^285923+345	86072	Lelio R Paula	09/2013
4656	13^77266-90	86070	Lelio R Paula	11/2015
4657	2^285910-458903	86068	Enzo Doria	04/2015
4658	2^285904-125	86066	Lelio R Paula	08/2012
4659	2^285836+65835	86046	Lelio R Paula	09/2013
4660	(2^285766+78557)/3	86024	Lelio R Paula	01/2013
4661	(5*10^86011-107)/3	86012	Robert Price	01/2017
4662	6^110522+163	86003	Lelio R Paula	12/2015
4663	41^53323-40^53323	85999	Robert Price	07/2012
4664	2^285678-109617	85998	Enzo Doria	04/2014
4665	6^110506-16673	85991	Enzo Doria	02/2013
4667	2^285569-741	85965	Lelio R Paula	09/2013
4666	(32*10^85964+31)/9	85965	Robert Price	05/2015
4668	6*10^85910-7	85911	Dmitry Domanov	11/2010
4669	(412*10^85897-7)/9	85899	Robert Price	10/2017
4670	4*10^85881+63	85882	Robert Price	06/2016
4671	(10^85864+53)/9	85864	Robert Price	01/2015
4672	2^285230+345	85863	Lelio R Paula	09/2013
4673	(5*10^85855-473)/9	85855	Robert Price	12/2017
4674	2^285199+75683	85854	Enzo Doria	04/2016
4675	(76*10^85847-211)/9	85848	Robert Price	10/2017
4676	p(17832)#/2+512	85845	Robert Price	05/2017
4677	(16*10^85839+167)/3	85840	Robert Price	10/2017
4678	11^82426-1230	85838	Enzo Doria	11/2012
4679	2^285113-109881	85828	Enzo Doria	04/2014
4680	5^122746-92	85796	Lelio R Paula	10/2015
4681	2^285001-113461	85794	Enzo Doria	08/2014
4682	(11*10^85782-131)/3	85783	Robert Price	02/2017
4683	2^284913-110491	85768	Enzo Doria	05/2014
4684	6^110220+47	85768	Lelio R Paula	12/2015
4685	3*6^110202-5	85755	Lelio R Paula	10/2014
4686	(157^39047-1)/156	85742	Alexander Zhirkov	06/2016
4687	(3^179705+7)/250	85739	Lelio R Paula	12/2012
4688	2^284734-6555	85714	Lelio R Paula	09/2013
4689	(10^85712+53)/9	85712	Robert Price	01/2015
4690	3*10^85703+11	85704	Robert Price	11/2017
4691	(6883*2^284668-1)/3	85697	Lelio R Paula	04/2015
4692	20^65855+83	85680	Lelio R Paula	01/2016
4693	6^110105+53	85679	Lelio R Paula	12/2015
4694	(10^85666-97)/3	85666	Robert Kinser	10/2017
4695	2^284567-7605	85664	Lelio R Paula	09/2013
4696	9*5^122555-2	85664	Lelio R Paula	10/2014
4697	5^122554-14	85662	Lelio R Paula	10/2015
4698	9*5^122543+4	85655	Lelio R Paula	10/2014
4699	3^179489-2^(179489-1)	85639	Robert Price	01/2016
4700	2^284429+177	85622	Lelio R Paula	08/2012
4701	2*3^179452+5	85621	Lelio R Paula	07/2014
4702	(19^66919+3^66919)/22	85572	Robert Price	07/2013
4703	66^47023-65	85561	Norbert Schneider	11/2014
4704	6^109943+13	85553	Lelio R Paula	12/2015
4705	(2^284167-509203)/34564775	85536	Lelio R Paula	01/2013
4706	2^284133-3	85533	M. Frind & P. Underwood	07/2002
4707	2^284113+315	85527	Lelio R Paula	09/2013
4708	(28*10^85500+149)/3	85501	Robert Price	10/2017
4709	(16*10^85495-19)/3	85496	Robert Price	03/2016
4710	2^284004+177	85494	Lelio R Paula	08/2012
4711	(16*10^85473-91)/3	85474	Robert Price	06/2016
4712	3^179120+22	85462	Robert Price	12/2013
4713	2^283872-2792249	85454	Enzo Doria	03/2016
4714	(29*10^85438+259)/9	85439	Robert Price	04/2017
4715	2^283817+82875	85438	Lelio R Paula	09/2013
4716	(2^283815-5)/201	85435	Lelio R Paula	01/2013
4717	2^283796-125	85432	Lelio R Paula	08/2012
4718	(29*2^283784-1)/13	85428	Lelio R Paula	02/2014
4719	15^72592-28	85375	Lelio R Paula	11/2015
4720	2^283604-58695	85374	Lelio R Paula	09/2013
4721	(44*10^85370-503)/9	85371	Robert Price	10/2017
4722	496^31671+31671^496	85369	Norbert Schneider	07/2017
4723	(15*2^283583-1)/103051	85364	Lelio R Paula	02/2014
4724	15^72572+92	85352	Lelio R Paula	11/2015
4725	2^283473-1615	85334	Lelio R Paula	09/2013
4726	2^283466-15	85332	Lelio R Paula	08/2012
4727	11^81916-7020	85307	Enzo Doria	02/2013
4728	6^109626-7	85306	Lelio R Paula	11/2014
4729	2^283374-110327	85305	Enzo Doria	05/2014
4730	33*10^85297+7	85299	Robert Price	07/2016
4731	18^67933+41	85275	Lelio R Paula	11/2015
4732	2^283271-109341	85274	Enzo Doria	04/2014
4733	(25*10^85249-73)/3	85250	Robert Price	09/2016
4734	2*5^121959+3	85246	Lelio R Paula	10/2014
4735	19834^19834+8947	85235	Henri Lifchitz	11/2004
4736	2^283140+1915	85234	Lelio R Paula	09/2013
4737	3*10^85227-97	85228	Robert Price	08/2017
4738	(16*10^85221-31)/3	85222	Robert Price	03/2016
4739	2^283083+1869383	85217	Enzo Doria	05/2016
4740	(24737*2^283051+1)/17	85211	Lelio R Paula	06/2014
4741	(2^283032+78557)/3	85201	Lelio R Paula	01/2013
4742	2^283026-109893	85200	Enzo Doria	04/2014
4743	(2^283012+78557)/129	85193	Lelio R Paula	01/2013
4744	(10^(242589+1)+7210^42589-1)/9	85179	Robert Price	09/2017
4745	2^282860-109727	85150	Enzo Doria	04/2014
4746	2^282819+1869413	85138	Enzo Doria	05/2016
4747	3^178428+2	85132	Ray Chandler	07/2011
4748	(22699*2^282742+1)/73	85117	Lelio R Paula	06/2014
4749	(16^70687+5^70687)/21	85115	Robert Price	07/2013
4750	(3^178352-2)/7	85095	Lelio R Paula	12/2012

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Probable Primes Top 10000

(212140 PRPs in the top)