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 ?
9001	10^73579-176379	73579	Patrick De Geest	02/2020
9002	2^244404+3841	73573	Yves Minet	03/2011
9003	19770^5263+5263^19770	73569	Hans Havermann	12/2019
9004	9*10^73565-41	73566	Robert Price	08/2020
9005	2^244372-110627	73564	Enzo Doria	05/2014
9006	19778^5241+5241^19778	73563	Hans Havermann	12/2019
9007	(2^244349+2186)/2	73557	Stefano Morozzi	01/2020
9008	(2^244309+3710)/2	73545	Stefano Morozzi	01/2020
9009	18428^9783+9783^18428	73537	Hans Havermann	01/2020
9010	(3*2^244255+1)/245	73527	Lelio R Paula	08/2012
9011	(11*2^244245+1)/23	73525	Lelio R Paula	08/2012
9012	18140^11301+11301^18140	73524	Hans Havermann	12/2019
9013	(15185*2^244187-1)/6111	73509	Lelio R Paula	04/2015
9014	(9699^18439-1)/9698	73508	Serge Batalov	08/2020
9015	(2^244152+2058)/2	73497	Stefano Morozzi	01/2020
9016	(2^244109+1422)/2	73484	Stefano Morozzi	01/2020
9017	17063^17362+17362^17063	73477	Norbert Schneider	04/2019
9018	(91^37507+1)/92	73476	Paul Bourdelais	08/2017
9019	18^58521+65	73460	Lelio R Paula	01/2015
9020	13^65940+36	73454	Lelio R Paula	01/2015
9021	19065^7112+7112^19065	73439	Hans Havermann	12/2019
9022	(625^26267+1)/626	73437	Richard Fischer	12/2017
9023	(16612^17401-1)/16611	73436	Serge Batalov	08/2020
9024	(2^243935+530)/2	73432	Stefano Morozzi	01/2020
9025	5^105050-14	73427	Lelio R Paula	08/2014
9026	(2^243850+1474)/2	73406	Stefano Morozzi	01/2020
9027	(((((((((((((30201^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	73401	Serge Batalov	07/2016
9028	15^62410-46	73400	Lelio R Paula	01/2015
9029	(2^243806+2494)/2	73393	Stefano Morozzi	01/2020
9030	(2^243790+2530)/2	73388	Stefano Morozzi	01/2020
9031	(2^243766+2362)/2	73381	Stefano Morozzi	01/2020
9032	2^243733+1869707	73371	Enzo Doria	05/2016
9033	11^70439-5430	73355	Enzo Doria	01/2013
9034	2^243676-87	73354	Lelio R Paula	03/2012
9035	(101*10^73346-17)/3	73348	Robert Price	08/2016
9036	21639^2452+2452^21639	73346	Hans Havermann	12/2019
9037	(2^243647+2438)/2	73345	Stefano Morozzi	01/2020
9038	2^243621-113185	73338	Enzo Doria	07/2014
9039	(5*2^243610-1)/1669	73332	Lelio R Paula	01/2014
9040	19857^4928+4928^19857	73326	Hans Havermann	12/2019
9041	2*5^104888-7	73314	Lelio R Paula	10/2014
9042	(58695*2^243516-1)/983	73308	Lelio R Paula	04/2015
9043	(3^153648-2)/33423138097	73299	Lelio R Paula	06/2012
9044	(2^243467+470)/2	73291	Stefano Morozzi	01/2020
9045	(2^243460+2410)/2	73289	Stefano Morozzi	01/2020
9046	18^58376-5255	73278	Enzo Doria	03/2013
9047	11^70363+32	73276	Lelio R Paula	02/2015
9048	2^243413+4257	73275	Lelio R Paula	05/2013
9049	104824^5+5^104824	73269	Andrey Kulsha	07/2010
9050	7^86689-6^86689	73261	Predrag Minovic	09/2004
9051	(2^243355+3846)/2	73257	Stefano Morozzi	01/2020
9052	(15954^17431-1)/15953	73257	Serge Batalov	08/2020
9053	2^243296+90195	73240	Lelio R Paula	05/2013
9054	2^243281-4843	73235	Yves Minet	05/2019
9056	p(15433)#/2-4	73218	Robert Price	12/2016
9055	(59*10^73217-77)/9	73218	Robert Price	11/2017
9057	(18160^17191-1)/18159	73215	Serge Batalov	08/2020
9058	2^243127+71355	73189	Lelio R Paula	05/2013
9059	2^243116-249419	73186	Paul Bourdelais	03/2013
9060	(58695*2^243085-1)/11	73180	Lelio R Paula	04/2015
9061	(2^243084+3406)/2	73176	Stefano Morozzi	01/2020
9062	11^70262-98	73171	Lelio R Paula	02/2015
9063	(2^243034+47)/722703303	73152	Lelio R Paula	07/2012
9064	(2^242966+47)/46887	73136	Lelio R Paula	07/2012
9065	(43^44773-1)/42	73134	Robert Price	04/2014
9066	6^93980-158359	73131	Mike Oakes	02/2011
9067	19953^4616+4616^19953	73114	Hans Havermann	11/2019
9068	(2^242855+2546)/2	73107	Stefano Morozzi	01/2020
9069	(2^242845+3926)/2	73104	Stefano Morozzi	01/2020
9070	6^93915+53	73081	Lelio R Paula	01/2015
9071	(5*10^73079+211)/9	73079	Robert Price	12/2017
9072	(74*10^73076+43)/9	73077	Robert Price	10/2015
9073	(3^153125+2)/1144955	73054	Lelio R Paula	06/2012
9074	2^242632-112199	73040	Enzo Doria	06/2014
9075	V(351646)	73029	Serge Batalov	03/2015
9076	(2^242598+1090)/2	73029	Stefano Morozzi	01/2020
9077	18^58175-85	73026	Lelio R Paula	01/2015
9078	p(15395)#/2-4	73019	Robert Price	12/2016
9079	(4^121271+3^121271)/7	73012	Jean-Louis Charton	03/2011
9080	8*6^93825-5	73011	Lelio R Paula	10/2014
9081	(28123^16411-1)/28122	73010	Serge Batalov	08/2020
9082	19090^6673+6673^19090	73007	Hans Havermann	11/2019
9084	(F(220)^1601-F(219)^1601)/F(218)	73005	Wayne Halsdorf	08/2013
9083	(73^39181+1)/74	73005	Paul Bourdelais	08/2017
9085	6^93815+143	73003	Lelio R Paula	01/2015
9087	6^93812+5	73000	Wojciech Florek	03/2006
9086	17874^12137+12137^17874	73000	Hans Havermann	11/2019
9088	19^57078-62	72989	Lelio R Paula	01/2015
9089	(29*10^72985+91)/3	72986	Robert Price	03/2016
9090	20691^3368+3368^20691	72985	Hans Havermann	10/2019
9091	(2^242451+558)/2	72985	Stefano Morozzi	01/2020
9092	11^70082-2520	72983	Enzo Doria	12/2012
9093	(2^242429+2142)/2	72979	Stefano Morozzi	01/2020
9094	(27992^16411-1)/27991	72976	Serge Batalov	08/2020
9095	6^93773+133	72970	Lelio R Paula	01/2015
9096	(2^242392+3762)/2	72967	Stefano Morozzi	01/2020
9097	2^242328-59	72948	Lelio R Paula	03/2012
9098	5^104358-13016	72944	Enzo Doria	02/2013
9099	(75*10^72941-57)/99	72941	Ray Chandler	03/2011
9100	12^67585-95	72937	Lelio R Paula	02/2015
9101	(2^242261+3834)/2	72928	Stefano Morozzi	01/2020
9102	2^242230-113285	72919	Enzo Doria	07/2014
9103	(2^242229+2742)/2	72918	Stefano Morozzi	01/2020
9104	(5*10^72916-11)/3	72917	Erik Branger	12/2013
9105	2^242220-110399	72916	Enzo Doria	05/2014
9106	2^242205-113413	72911	Enzo Doria	07/2014
9107	(3^152809+3^76405+1)/7	72908	Serge Batalov	03/2014
9108	2^242175+74243	72902	Yves Minet	03/2011
9109	(2^242168+3406)/2	72900	Stefano Morozzi	01/2020
9110	2^242150+17659	72895	Lelio R Paula	11/2009
9111	18902^7179+7179^18902	72888	Hans Havermann	11/2019
9112	(17366^17191-1)/17365	72881	Serge Batalov	08/2020
9113	11^69982-2340	72879	Enzo Doria	12/2012
9114	(23*2^242093+1)/10117	72875	Lelio R Paula	08/2012
9115	(67607*2^242043+1)/33263	72863	Lelio R Paula	06/2014
9116	2^242032+87	72859	Lelio R Paula	03/2012
9117	(194*10^72852-17)/3	72854	Robert Price	09/2020
9118	(2^241983+2690)/2	72844	Stefano Morozzi	01/2020
9120	2^241968-110595	72840	Enzo Doria	05/2014
9119	(2^241968+598)/2	72840	Stefano Morozzi	01/2020
9121	18850^7313+7313^18850	72839	Hans Havermann	11/2019
9122	(2^241921+3290)/2	72826	Stefano Morozzi	01/2020
9123	(10^72821+71)/9	72821	Robert Price	11/2014
9124	2^241852-64875	72805	Lelio R Paula	05/2013
9125	F(348307)/20562890865908093	72776	Donovan Johnson	07/2007
9126	13952^17559+17559^13952	72776	Norbert Schneider	09/2019
9127	(67*10^72772+23)/9	72773	Ray Chandler	11/2010
9128	(8*10^72759+67)/3	72760	Robert Price	01/2017
9129	2^241670+145	72750	Lelio R Paula	03/2012
9130	5^104074+52	72745	Lelio R Paula	08/2014
9131	(3^152466-5)/724	72742	Lelio R Paula	06/2012
9132	20^55908-41	72738	Lelio R Paula	01/2015
9133	(73*10^72735+53)/9	72736	Robert Price	10/2015
9134	10^72730+224011	72731	Patrick De Geest	05/2013
9135	10^72730-99	72730	Robert Price	05/2011
9136	3*10^72723+67	72724	Robert Price	11/2017
9138	(11^69833+3^69833)/14	72723	Robert Price	03/2013
9137	(10^72723-79)/3	72723	Robert Price	10/2017
9139	18706^7719+7719^18706	72721	Hans Havermann	11/2019
9140	(88*10^72711-43)/9	72712	Robert Price	11/2015
9141	3^152379+280	72704	Lelio R Paula	01/2015
9143	(25*10^72703-241)/9	72704	Robert Price	01/2017
9142	(2^241517+3774)/2	72704	Stefano Morozzi	01/2020
9144	(2^241515+3518)/2	72703	Stefano Morozzi	01/2020
9145	(47*10^72696+133)/9	72697	Robert Price	04/2017
9146	17^59077-90	72692	Lelio R Paula	01/2015
9147	65^40096+58	72691	Lelio R Paula	01/2016
9148	(29*2^241446-1)/245	72682	Lelio R Paula	01/2014
9150	11^69783-38400000	72672	Enzo Doria	01/2013
9149	2^241409-112903	72672	Enzo Doria	06/2014
9151	18895^7014+7014^18895	72670	Hans Havermann	11/2019
9152	(3^152287+1)/4	72659	Paul Bourdelais	04/2008
9153	(2^241353+3186)/2	72655	Stefano Morozzi	01/2020
9154	17638^13137+13137^17638	72643	Hans Havermann	11/2019
9155	3^152249-56	72642	Lelio R Paula	01/2015
9156	10^72631+37	72632	Robert Price	01/2011
9157	10^72631-8813	72631	Patrick De Geest	05/2013
9158	(19*2^241254+1)/101	72624	Lelio R Paula	08/2012
9159	(32202^16111-1)/32201	72622	Serge Batalov	08/2020
9160	(9^76103+8^76103)/17	72620	Robert Price	12/2012
9162	2^241220-112337	72615	Enzo Doria	06/2014
9161	7*10^72614+33	72615	Robert Price	06/2020
9163	(82*10^72612+449)/9	72613	Robert Price	02/2017
9164	2^241169-15793	72600	Enzo Doria	04/2013
9165	9*10^72595+11	72596	Robert Kinser	01/2017
9166	(2^241152+2478)/2	72594	Stefano Morozzi	01/2020
9167	(2^241143+2438)/2	72591	Stefano Morozzi	01/2020
9168	(2^241115+1598)/2	72583	Stefano Morozzi	01/2020
9169	(1003^24179-1)/1002	72566	Serge Batalov	07/2020
9170	(25*2^241048+1)/89	72563	Lelio R Paula	08/2012
9171	(2^241045+1550)/2	72562	Stefano Morozzi	01/2020
9172	(22*10^72560+17)/3	72561	Robert Price	09/2015
9173	2^241032-23	72558	Lelio R Paula	02/2012
9174	34485*10^72550+2^241004-3	72555	Gilbert Mozzo	12/2012
9175	19460^5349+5349^19460	72553	Hans Havermann	11/2019
9176	(2^241016+3850)/2	72553	Stefano Morozzi	01/2020
9177	2^241004-3	72550	M. Frind & P. Underwood	07/2002
9178	22061^1942+1942^22061	72543	Hans Havermann	11/2019
9179	9*10^72528-89	72529	Robert Price	04/2020
9181	97*10^72522-3	72524	Robert Price	01/2017
9180	(29*10^72523-107)/3	72524	Robert Price	08/2020
9182	(68*10^72516+7)/3	72518	Robert Price	03/2016
9183	(13993^17491-1)/13992	72512	Serge Batalov	08/2020
9184	(78557*2^240844+1)/63	72505	Lelio R Paula	06/2014
9185	67^39701-66	72497	Norbert Schneider	11/2014
9186	(185*10^72484+7)/3	72486	Robert Price	02/2017
9187	(2^240780+2686)/2	72482	Stefano Morozzi	01/2020
9188	(2^240759+1106)/2	72476	Stefano Morozzi	01/2020
9190	(293*27^50631-1736)/13	72473	Curtis Bright	05/2015
9189	103^36005-102	72473	Norbert Schneider	10/2016
9191	15^61616+88	72467	Lelio R Paula	01/2015
9192	45^43831+2	72462	Lelio R Paula	05/2013
9193	2^240692-492389	72456	Paul Bourdelais	03/2013
9194	(646*10^72446-7)/9	72448	Robert Price	07/2016
9195	9*6^93083+7	72434	Lelio R Paula	10/2014
9196	2^240617-3645	72433	Lelio R Paula	05/2013
9197	(9391^18229-1)/9390	72415	Serge Batalov	08/2020
9198	11^69531-24000	72410	Enzo Doria	12/2012
9199	18714^7367+7367^18714	72373	Hans Havermann	11/2019
9200	(22699*2^240396+1)/55	72370	Lelio R Paula	06/2014
9201	6^92995+13	72365	Lelio R Paula	01/2015
9202	(11*10^72362-149)/3	72363	Robert Price	01/2017
9203	18567^7892+7892^18567	72360	Hans Havermann	11/2019
9204	(2^240381+3)/51655	72358	Lelio R Paula	05/2012
9205	6^92974-55	72348	Lelio R Paula	01/2015
9206	2^240295+11	72337	Lelio R Paula	02/2012
9207	(2^240294+1342)/2	72336	Stefano Morozzi	01/2020
9208	(14*10^72326-53)/3	72327	Robert Price	12/2016
9209	15^61493-46	72322	Lelio R Paula	01/2015
9210	(2^240245+2094)/2	72321	Stefano Morozzi	01/2020
9211	(2^240237+1554)/2	72319	Stefano Morozzi	01/2020
9212	lucasU(46,1,43497)-lucasU(46,1,43496)	72315	Mike Oakes	04/2009
9213	(2^240211+1514)/2	72311	Stefano Morozzi	01/2020
9215	5*10^72302+9	72303	Dmitry Domanov	11/2010
9214	(9787*2^240179-1)/265	72303	Lelio R Paula	04/2015
9216	(2^240171+3246)/2	72299	Stefano Morozzi	01/2020
9217	11^69419-3120	72293	Enzo Doria	12/2012
9218	18069^10016+10016^18069	72289	Hans Havermann	11/2019
9219	(25883^16381-1)/25882	72286	Serge Batalov	08/2020
9220	(2^240095+594)/2	72276	Stefano Morozzi	01/2020
9221	(25848^16381-1)/25847	72276	Serge Batalov	08/2020
9222	4*10^72274-83	72275	Robert Price	10/2017
9223	(2^240075+2790)/2	72270	Stefano Morozzi	01/2020
9224	10^72267+33	72268	Robert Price	01/2011
9225	10^72267-553947	72267	Patrick De Geest	05/2013
9226	(2^240066+1030)/2	72267	Stefano Morozzi	01/2020
9228	11^69389-1380	72262	Enzo Doria	12/2012
9229	(16^60013-5^60013)/11	72262	Robert Price	07/2013
9227	7^85507-30	72262	Lelio R Paula	08/2014
9230	(19*2^240026-1)/15	72256	Lelio R Paula	02/2014
9231	(3^151426-2)/661337	72243	Lelio R Paula	06/2012
9232	(2^239940+3850)/2	72229	Stefano Morozzi	01/2020
9233	gcd(V(1296375),5F(259275)(F(259275)-1)+1)	72227	Serge Batalov	04/2015
9234	(2789^20959-1)/2788	72210	Serge Batalov	08/2020
9235	2^239863-112267	72206	Enzo Doria	06/2014
9236	2^239853-114853	72203	Enzo Doria	05/2015
9237	(14068^17401-1)/14067	72180	Serge Batalov	08/2020
9238	(5669^19231-1)/5668	72180	Serge Batalov	08/2020
9239	(4*10^72174+149)/9	72174	Robert Price	03/2017
9241	(2^239671+9)/296131	72143	Lelio R Paula	05/2012
9240	2^239651-110665	72143	Enzo Doria	05/2014
9242	(29*2^239650-1)/3305	72140	Lelio R Paula	01/2014
9243	(17099^17041-1)/17098	72130	Serge Batalov	08/2020
9245	241^30280+30280^241	72128	Norbert Schneider	11/2014
9244	(2^239603+950)/2	72128	Stefano Morozzi	01/2020
9246	(2^239594+3058)/2	72125	Stefano Morozzi	01/2020
9247	(68*10^72120-23)/9	72121	Robert Price	10/2015
9248	(9^75571+8^75571)/17	72112	Robert Price	12/2012
9249	(15661^17191-1)/15660	72109	Serge Batalov	08/2020
9250	(3508^20341-1)/3507	72107	Serge Batalov	08/2020

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