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	3^182566+14	87107	Robert Price	09/2013
4502	(3^182385-5)/2	87020	Lelio R Paula	01/2013
4503	11^83534-8	86992	Lelio R Paula	11/2015
4504	4^144479-14267	86986	Mike Oakes	03/2011
4505	(145*10^86982-1)/9	86984	Serge Batalov	12/2014
4506	(151*10^86963-1)/3	86965	Robert Price	04/2017
4507	15^73940-58	86961	Lelio R Paula	11/2015
4508	2^288761-113143	86926	Enzo Doria	07/2014
4509	2^288747+3083	86922	Yves Minet	03/2011
4510	30^58842+29	86917	Norbert Schneider	03/2017
4511	(10^86906-13)/3	86906	Robert Price	02/2017
4512	2^288692-110027	86905	Enzo Doria	04/2014
4513	(2^288682+7)/259895449	86894	Lelio R Paula	01/2013
4514	(2^288636+47)/1293	86885	Lelio R Paula	01/2013
4515	3^182089-34	86879	Robert Price	11/2013
4516	2^288543-109801	86861	Enzo Doria	04/2014
4517	60^48847-59	86858	Norbert Schneider	10/2014
4518	2^288470-64875	86839	Lelio R Paula	10/2013
4519	10^86816+32997	86817	Patrick De Geest	07/2013
4520	10^86816-99	86816	Robert Price	05/2011
4521	(89*10^86802-539)/9	86803	Robert Price	11/2017
4522	41487!2+256	86786	Robert Price	01/2015
4523	(5*2^288301-1)/999	86785	Lelio R Paula	02/2014
4524	2^288243+76043	86770	Enzo Doria	04/2016
4525	(29*2^288232+1)/15	86767	Lelio R Paula	01/2013
4526	9*6^111495+5	86761	Lelio R Paula	10/2014
4527	(5*2^288202+1)/81	86757	Lelio R Paula	01/2013
4528	9*7^102654-2	86754	Lelio R Paula	10/2014
4529	2^288122-112841	86734	Enzo Doria	06/2014
4530	5^124062-68	86716	Lelio R Paula	10/2015
4531	(2^288007-3)/125	86697	Lelio R Paula	01/2013
4532	379*10^86691+9	86694	Arkadiusz Wesolowski	10/2011
4533	7^102555+48	86670	Lelio R Paula	10/2015
4534	77779!4+2	86660	Robert Price	08/2017
4535	2^287809-111355	86640	Enzo Doria	05/2014
4536	(47*2^287795+1)/7	86636	Lelio R Paula	04/2015
4537	9*7^102504+8	86627	Lelio R Paula	10/2014
4538	3^181551+32	86622	Robert Price	11/2013
4539	2^287735-521347	86617	Paul Bourdelais	05/2013
4540	(1017*2^287600-1)/91	86578	Lelio R Paula	04/2015
4541	2^287540-112967	86559	Enzo Doria	06/2014
4542	3^181407+20	86554	Robert Price	10/2013
4543	(13*10^86546+83)/3	86547	Robert Price	09/2016
4544	3^181378-2^(181378-1)	86540	Robert Price	01/2016
4545	83^45080-2	86513	Lelio R Paula	08/2013
4546	(78557*2^287351+1)/611	86504	Lelio R Paula	06/2014
4547	25*29^59147+20936	86498	Curtis Bright	05/2015
4548	2^287298+1871359	86486	Enzo Doria	05/2016
4549	3*10^86478+89	86479	Robert Price	03/2017
4550	2^287272-79049	86478	Paul Bourdelais	02/2012
4551	9067052((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4552	8118242((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4553	7790642((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4554	7683852((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4555	7008912((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4556	6523202((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4557	3779202((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
4558	2550602((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
4559	1871112((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
4560	(10^86453-1)/9	86453	Lew Baxter	10/2000
4561	87^44563-86^44563	86431	Robert Price	05/2015
4562	6^111057+61	86420	Lelio R Paula	12/2015
4563	2^287057-109909	86413	Enzo Doria	04/2014
4564	5^123608+22	86399	Lelio R Paula	10/2015
4565	(31*10^86364-121)/9	86365	Robert Price	06/2016
4566	2^286859+71663	86354	Enzo Doria	04/2016
4567	2^286740+29835	86318	Lelio R Paula	10/2013
4568	2*10^86310+9^86310	86311	Mike Oakes	05/2011
4569	11^82878-1860	86309	Enzo Doria	12/2012
4570	2^286547+16095	86260	Lelio R Paula	10/2013
4571	(58*10^86242+329)/9	86243	Robert Price	11/2017
4572	2^286455-110427	86232	Enzo Doria	05/2014
4573	(37*10^86230+53)/9	86231	Robert Price	05/2015
4574	8*3^180700+5	86217	Lelio R Paula	08/2014
4575	3^180697-40	86215	Lelio R Paula	12/2015
4576	(13*2^286318-1)/13257	86188	Lelio R Paula	02/2014
4577	2^286165+77	86145	Lelio R Paula	08/2012
4578	9*2^286140+7	86138	Lelio R Paula	08/2014
4579	(29*2^286108-1)/2002367	86123	Lelio R Paula	02/2014
4580	10^86110+161113	86111	Patrick De Geest	07/2013
4581	10^86110-69	86110	Robert Price	05/2011
4582	2^286036-869688105	86106	Lelio R Paula	07/2016
4583	(77*10^86072+31)/9	86073	Robert Price	10/2015
4584	2^285923+345	86072	Lelio R Paula	09/2013
4585	13^77266-90	86070	Lelio R Paula	11/2015
4586	2^285910-458903	86068	Enzo Doria	04/2015
4587	2^285904-125	86066	Lelio R Paula	08/2012
4588	2^285836+65835	86046	Lelio R Paula	09/2013
4589	(2^285766+78557)/3	86024	Lelio R Paula	01/2013
4590	(5*10^86011-107)/3	86012	Robert Price	01/2017
4591	6^110522+163	86003	Lelio R Paula	12/2015
4592	41^53323-40^53323	85999	Robert Price	07/2012
4593	2^285678-109617	85998	Enzo Doria	04/2014
4594	6^110506-16673	85991	Enzo Doria	02/2013
4596	2^285569-741	85965	Lelio R Paula	09/2013
4595	(32*10^85964+31)/9	85965	Robert Price	05/2015
4597	6*10^85910-7	85911	Dmitry Domanov	11/2010
4598	(412*10^85897-7)/9	85899	Robert Price	10/2017
4599	4*10^85881+63	85882	Robert Price	06/2016
4600	(10^85864+53)/9	85864	Robert Price	01/2015
4601	2^285230+345	85863	Lelio R Paula	09/2013
4602	(5*10^85855-473)/9	85855	Robert Price	12/2017
4603	2^285199+75683	85854	Enzo Doria	04/2016
4604	(76*10^85847-211)/9	85848	Robert Price	10/2017
4605	p(17832)#/2+512	85845	Robert Price	05/2017
4606	(16*10^85839+167)/3	85840	Robert Price	10/2017
4607	11^82426-1230	85838	Enzo Doria	11/2012
4608	2^285113-109881	85828	Enzo Doria	04/2014
4609	5^122746-92	85796	Lelio R Paula	10/2015
4610	2^285001-113461	85794	Enzo Doria	08/2014
4611	(11*10^85782-131)/3	85783	Robert Price	02/2017
4612	2^284913-110491	85768	Enzo Doria	05/2014
4613	6^110220+47	85768	Lelio R Paula	12/2015
4614	3*6^110202-5	85755	Lelio R Paula	10/2014
4615	(157^39047-1)/156	85742	Alexander Zhirkov	06/2016
4616	(3^179705+7)/250	85739	Lelio R Paula	12/2012
4617	2^284734-6555	85714	Lelio R Paula	09/2013
4618	(10^85712+53)/9	85712	Robert Price	01/2015
4619	3*10^85703+11	85704	Robert Price	11/2017
4620	(6883*2^284668-1)/3	85697	Lelio R Paula	04/2015
4621	20^65855+83	85680	Lelio R Paula	01/2016
4622	6^110105+53	85679	Lelio R Paula	12/2015
4623	(10^85666-97)/3	85666	Robert Kinser	10/2017
4625	2^284567-7605	85664	Lelio R Paula	09/2013
4624	9*5^122555-2	85664	Lelio R Paula	10/2014
4626	5^122554-14	85662	Lelio R Paula	10/2015
4627	9*5^122543+4	85655	Lelio R Paula	10/2014
4628	3^179489-2^(179489-1)	85639	Robert Price	01/2016
4629	2^284429+177	85622	Lelio R Paula	08/2012
4630	2*3^179452+5	85621	Lelio R Paula	07/2014
4631	(19^66919+3^66919)/22	85572	Robert Price	07/2013
4632	66^47023-65	85561	Norbert Schneider	11/2014
4633	6^109943+13	85553	Lelio R Paula	12/2015
4634	(2^284167-509203)/34564775	85536	Lelio R Paula	01/2013
4635	2^284133-3	85533	M. Frind & P. Underwood	07/2002
4636	2^284113+315	85527	Lelio R Paula	09/2013
4637	(28*10^85500+149)/3	85501	Robert Price	10/2017
4638	(16*10^85495-19)/3	85496	Robert Price	03/2016
4639	2^284004+177	85494	Lelio R Paula	08/2012
4640	(16*10^85473-91)/3	85474	Robert Price	06/2016
4641	3^179120+22	85462	Robert Price	12/2013
4642	2^283872-2792249	85454	Enzo Doria	03/2016
4643	(29*10^85438+259)/9	85439	Robert Price	04/2017
4644	2^283817+82875	85438	Lelio R Paula	09/2013
4645	(2^283815-5)/201	85435	Lelio R Paula	01/2013
4646	2^283796-125	85432	Lelio R Paula	08/2012
4647	(29*2^283784-1)/13	85428	Lelio R Paula	02/2014
4648	15^72592-28	85375	Lelio R Paula	11/2015
4649	2^283604-58695	85374	Lelio R Paula	09/2013
4650	(44*10^85370-503)/9	85371	Robert Price	10/2017
4651	496^31671+31671^496	85369	Norbert Schneider	07/2017
4652	(15*2^283583-1)/103051	85364	Lelio R Paula	02/2014
4653	15^72572+92	85352	Lelio R Paula	11/2015
4654	2^283473-1615	85334	Lelio R Paula	09/2013
4655	2^283466-15	85332	Lelio R Paula	08/2012
4656	11^81916-7020	85307	Enzo Doria	02/2013
4657	6^109626-7	85306	Lelio R Paula	11/2014
4658	2^283374-110327	85305	Enzo Doria	05/2014
4659	33*10^85297+7	85299	Robert Price	07/2016
4660	18^67933+41	85275	Lelio R Paula	11/2015
4661	2^283271-109341	85274	Enzo Doria	04/2014
4662	(25*10^85249-73)/3	85250	Robert Price	09/2016
4663	2*5^121959+3	85246	Lelio R Paula	10/2014
4664	19834^19834+8947	85235	Henri Lifchitz	11/2004
4665	2^283140+1915	85234	Lelio R Paula	09/2013
4666	3*10^85227-97	85228	Robert Price	08/2017
4667	(16*10^85221-31)/3	85222	Robert Price	03/2016
4668	2^283083+1869383	85217	Enzo Doria	05/2016
4669	(24737*2^283051+1)/17	85211	Lelio R Paula	06/2014
4670	(2^283032+78557)/3	85201	Lelio R Paula	01/2013
4671	2^283026-109893	85200	Enzo Doria	04/2014
4672	(2^283012+78557)/129	85193	Lelio R Paula	01/2013
4673	(10^(242589+1)+7210^42589-1)/9	85179	Robert Price	09/2017
4674	2^282860-109727	85150	Enzo Doria	04/2014
4675	2^282819+1869413	85138	Enzo Doria	05/2016
4676	3^178428+2	85132	Ray Chandler	07/2011
4677	(22699*2^282742+1)/73	85117	Lelio R Paula	06/2014
4678	(16^70687+5^70687)/21	85115	Robert Price	07/2013
4679	(3^178352-2)/7	85095	Lelio R Paula	12/2012
4680	11^81699-2790	85081	Enzo Doria	12/2012
4681	2^282612-95	85075	Lelio R Paula	08/2012
4682	2^282609-4069	85074	Yves Minet	02/2018
4683	75^45366-2	85065	Lelio R Paula	08/2013
4684	2^282511+69	85045	Lelio R Paula	08/2012
4685	69^46249+2	85045	Lelio R Paula	06/2013
4686	3^178226+10	85036	Robert Price	10/2013
4687	(182*10^85017+43)/9	85019	Robert Price	11/2017
4688	(14*10^85010+73)/3	85011	Robert Price	04/2016
4689	9*2^282338-7	84994	Lelio R Paula	08/2014
4690	(9913*2^282330-1)/1578003	84988	Lelio R Paula	04/2015
4691	2^282203+5	84952	Lelio R Paula	08/2012
4692	2^282184+13	84946	Lelio R Paula	08/2012
4693	11^81568-2400	84945	Enzo Doria	12/2012
4694	11^81562-2340	84939	Enzo Doria	12/2012
4695	(41*10^84927+31)/9	84928	Robert Price	05/2015
4696	(2*10^84904-17)/3	84904	Robert Price	08/2014
4697	(4^141017+23)/3	84901	Robert Price	02/2017
4698	6^109100-18653	84897	Enzo Doria	03/2013
4699	2^281973+1025	84883	Lelio R Paula	09/2013
4700	2^281951-109651	84876	Enzo Doria	04/2014
4701	11^81491-5430	84865	Enzo Doria	01/2013
4702	((1+sqrt(3)+sqrt(2))^79357-1)((1+sqrt(3)-sqrt(2))^79357-1)((1-sqrt(3)+sqrt(2))^79357-1)*((1-sqrt(3	84849	Mike Oakes	04/2009
4703	2^281825-1861483	84838	Enzo Doria	03/2016
4704	2^281809-97305	84833	Lelio R Paula	09/2013
4705	2^281780-114893	84825	Enzo Doria	05/2015
4706	3^177719+64	84794	Lelio R Paula	12/2015
4708	2^281675-199	84793	Lelio R Paula	08/2012
4707	2^281673-111223	84793	Enzo Doria	05/2014
4709	(4*10^84779+149)/9	84779	Robert Price	03/2017
4710	(72*10^84772-27)/9	84773	Ray Chandler	01/2011
4711	11^81398-630	84768	Enzo Doria	11/2012
4712	(25*2^281577-1)/23	84764	Lelio R Paula	02/2014
4713	2^281500-455	84740	Yves Minet	03/2012
4714	10^84725+1145141919	84726	Marisa Kirisame	03/2015
4715	10^84725+142041	84726	Patrick De Geest	10/2015
4716	10^84725-138677	84725	Patrick De Geest	02/2016
4717	76^45044+75	84720	Norbert Schneider	02/2015
4718	54^48897-53	84709	Norbert Schneider	08/2014
4719	(9913*2^281377-1)/65	84706	Lelio R Paula	04/2015
4720	Phi(171124,10)/29946701/7761329021/58560344041	84700	Maksym Voznyy	11/2015
4721	2^281337-111223	84691	Enzo Doria	05/2014
4722	2^281308+54615	84683	Lelio R Paula	09/2013
4723	7*5^121144-6	84677	Lelio R Paula	10/2014
4724	(2^281252+47)/3	84665	Lelio R Paula	01/2013
4725	11^81297-3150	84663	Enzo Doria	12/2012
4726	2^281208-303	84653	Yves Minet	02/2012
4727	197^36892-2	84648	Lelio R Paula	10/2017
4728	(21*2^281187+1)/2483	84644	Lelio R Paula	01/2013
4729	11^81247-84	84611	Lelio R Paula	10/2015
4730	17^68747-64	84590	Lelio R Paula	11/2015
4731	5^121018-15596	84588	Enzo Doria	02/2013
4732	6^108702+7	84587	Lelio R Paula	11/2014
4733	10^84582+100677	84583	Patrick De Geest	05/2016
4734	10^84582-8001	84582	Robert Price	03/2016
4735	3*5^121004-8	84579	Lelio R Paula	10/2014
4736	5^120996-84	84573	Lelio R Paula	10/2015
4737	(10223*2^280881+1)/68419	84553	Lelio R Paula	06/2014
4738	2^280852+97681	84545	Yves Minet	08/2004
4739	2^280848-1203	84544	Lelio R Paula	09/2013
4740	5^120946-24	84538	Lelio R Paula	10/2015
4741	2^280810-2111	84533	Yves Minet	08/2013
4742	11^81161-5160	84521	Enzo Doria	01/2013
4743	2^280737-93	84511	Lelio R Paula	08/2012
4744	2^280698+315	84499	Lelio R Paula	09/2013
4745	3^177099-340	84498	Lelio R Paula	12/2015
4746	(5*10^84469-107)/3	84470	Robert Price	01/2017
4747	(3^177002+7)/6696022272161744	84436	Lelio R Paula	12/2012
4748	(2^280500-1017)/823	84436	Lelio R Paula	01/2013
4749	14^73660-5	84424	Lelio R Paula	11/2015
4750	(19*10^84409-61)/3	84410	Robert Price	04/2017

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Probable Primes Top 10000

(205869 PRPs in the top)