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 ?
9501	19857^4928+4928^19857	73326	Hans Havermann	12/2019
9502	2*5^104888-7	73314	Lelio R Paula	10/2014
9503	(58695*2^243516-1)/983	73308	Lelio R Paula	04/2015
9504	(3^153648-2)/33423138097	73299	Lelio R Paula	06/2012
9505	(2^243467+470)/2	73291	Stefano Morozzi	01/2020
9506	(2^243460+2410)/2	73289	Stefano Morozzi	01/2020
9507	18^58376-5255	73278	Enzo Doria	03/2013
9508	11^70363+32	73276	Lelio R Paula	02/2015
9509	2^243413+4257	73275	Lelio R Paula	05/2013
9510	104824^5+5^104824	73269	Andrey Kulsha	07/2010
9511	7^86689-6^86689	73261	Predrag Minovic	09/2004
9512	(2^243355+3846)/2	73257	Stefano Morozzi	01/2020
9513	(15954^17431-1)/15953	73257	Serge Batalov	08/2020
9514	2^243296+90195	73240	Lelio R Paula	05/2013
9515	2^243281-4843	73235	Yves Minet	05/2019
9517	p(15433)#/2-4	73218	Robert Price	12/2016
9516	(59*10^73217-77)/9	73218	Robert Price	11/2017
9518	(18160^17191-1)/18159	73215	Serge Batalov	08/2020
9519	2*10^73199+23	73200	Robert Price	12/2020
9520	2^243127+71355	73189	Lelio R Paula	05/2013
9521	2^243116-249419	73186	Paul Bourdelais	03/2013
9522	(58695*2^243085-1)/11	73180	Lelio R Paula	04/2015
9523	(2^243084+3406)/2	73176	Stefano Morozzi	01/2020
9524	11^70262-98	73171	Lelio R Paula	02/2015
9525	(2^243034+47)/722703303	73152	Lelio R Paula	07/2012
9526	(2^242966+47)/46887	73136	Lelio R Paula	07/2012
9527	(43^44773-1)/42	73134	Robert Price	04/2014
9528	6^93980-158359	73131	Mike Oakes	02/2011
9529	19953^4616+4616^19953	73114	Hans Havermann	11/2019
9530	(2^242855+2546)/2	73107	Stefano Morozzi	01/2020
9531	(2^242845+3926)/2	73104	Stefano Morozzi	01/2020
9532	6^93915+53	73081	Lelio R Paula	01/2015
9533	(5*10^73079+211)/9	73079	Robert Price	12/2017
9534	(74*10^73076+43)/9	73077	Robert Price	10/2015
9535	(3^153125+2)/1144955	73054	Lelio R Paula	06/2012
9536	2^242632-112199	73040	Enzo Doria	06/2014
9537	V(351646)	73029	Serge Batalov	03/2015
9538	(2^242598+1090)/2	73029	Stefano Morozzi	01/2020
9539	18^58175-85	73026	Lelio R Paula	01/2015
9540	p(15395)#/2-4	73019	Robert Price	12/2016
9541	(4^121271+3^121271)/7	73012	Jean-Louis Charton	03/2011
9542	8*6^93825-5	73011	Lelio R Paula	10/2014
9543	(28123^16411-1)/28122	73010	Serge Batalov	08/2020
9544	19090^6673+6673^19090	73007	Hans Havermann	11/2019
9546	(F(220)^1601-F(219)^1601)/F(218)	73005	Wayne Halsdorf	08/2013
9545	(73^39181+1)/74	73005	Paul Bourdelais	08/2017
9547	6^93815+143	73003	Lelio R Paula	01/2015
9549	6^93812+5	73000	Wojciech Florek	03/2006
9548	17874^12137+12137^17874	73000	Hans Havermann	11/2019
9550	19^57078-62	72989	Lelio R Paula	01/2015
9551	(29*10^72985+91)/3	72986	Robert Price	03/2016
9552	20691^3368+3368^20691	72985	Hans Havermann	10/2019
9553	(2^242451+558)/2	72985	Stefano Morozzi	01/2020
9554	11^70082-2520	72983	Enzo Doria	12/2012
9555	(2^242429+2142)/2	72979	Stefano Morozzi	01/2020
9556	(27992^16411-1)/27991	72976	Serge Batalov	08/2020
9557	6^93773+133	72970	Lelio R Paula	01/2015
9558	(2^242392+3762)/2	72967	Stefano Morozzi	01/2020
9559	2^242328-59	72948	Lelio R Paula	03/2012
9560	5^104358-13016	72944	Enzo Doria	02/2013
9561	(75*10^72941-57)/99	72941	Ray Chandler	03/2011
9562	12^67585-95	72937	Lelio R Paula	02/2015
9563	(2^242261+3834)/2	72928	Stefano Morozzi	01/2020
9564	2^242230-113285	72919	Enzo Doria	07/2014
9565	(2^242229+2742)/2	72918	Stefano Morozzi	01/2020
9566	(5*10^72916-11)/3	72917	Erik Branger	12/2013
9567	2^242220-110399	72916	Enzo Doria	05/2014
9568	2^242205-113413	72911	Enzo Doria	07/2014
9569	(3^152809+3^76405+1)/7	72908	Serge Batalov	03/2014
9570	2^242175+74243	72902	Yves Minet	03/2011
9571	(2^242168+3406)/2	72900	Stefano Morozzi	01/2020
9572	2^242150+17659	72895	Lelio R Paula	11/2009
9573	18902^7179+7179^18902	72888	Hans Havermann	11/2019
9574	(17366^17191-1)/17365	72881	Serge Batalov	08/2020
9575	11^69982-2340	72879	Enzo Doria	12/2012
9576	(23*2^242093+1)/10117	72875	Lelio R Paula	08/2012
9577	(67607*2^242043+1)/33263	72863	Lelio R Paula	06/2014
9578	2^242032+87	72859	Lelio R Paula	03/2012
9579	(194*10^72852-17)/3	72854	Robert Price	09/2020
9580	(2^241983+2690)/2	72844	Stefano Morozzi	01/2020
9582	2^241968-110595	72840	Enzo Doria	05/2014
9581	(2^241968+598)/2	72840	Stefano Morozzi	01/2020
9583	18850^7313+7313^18850	72839	Hans Havermann	11/2019
9584	(2^241921+3290)/2	72826	Stefano Morozzi	01/2020
9585	(10^72821+71)/9	72821	Robert Price	11/2014
9586	2^241852-64875	72805	Lelio R Paula	05/2013
9587	F(348307)/20562890865908093	72776	Donovan Johnson	07/2007
9588	13952^17559+17559^13952	72776	Norbert Schneider	09/2019
9589	(67*10^72772+23)/9	72773	Ray Chandler	11/2010
9590	(8*10^72759+67)/3	72760	Robert Price	01/2017
9591	2^241670+145	72750	Lelio R Paula	03/2012
9592	5^104074+52	72745	Lelio R Paula	08/2014
9593	(3^152466-5)/724	72742	Lelio R Paula	06/2012
9594	20^55908-41	72738	Lelio R Paula	01/2015
9595	(73*10^72735+53)/9	72736	Robert Price	10/2015
9596	10^72730+224011	72731	Patrick De Geest	05/2013
9597	10^72730-99	72730	Robert Price	05/2011
9598	3*10^72723+67	72724	Robert Price	11/2017
9600	(11^69833+3^69833)/14	72723	Robert Price	03/2013
9599	(10^72723-79)/3	72723	Robert Price	10/2017
9601	18706^7719+7719^18706	72721	Hans Havermann	11/2019
9602	(88*10^72711-43)/9	72712	Robert Price	11/2015
9603	3^152379+280	72704	Lelio R Paula	01/2015
9605	(25*10^72703-241)/9	72704	Robert Price	01/2017
9604	(2^241517+3774)/2	72704	Stefano Morozzi	01/2020
9606	(2^241515+3518)/2	72703	Stefano Morozzi	01/2020
9607	(47*10^72696+133)/9	72697	Robert Price	04/2017
9608	17^59077-90	72692	Lelio R Paula	01/2015
9609	65^40096+58	72691	Lelio R Paula	01/2016
9610	(29*2^241446-1)/245	72682	Lelio R Paula	01/2014
9612	11^69783-38400000	72672	Enzo Doria	01/2013
9611	2^241409-112903	72672	Enzo Doria	06/2014
9613	18895^7014+7014^18895	72670	Hans Havermann	11/2019
9614	(3^152287+1)/4	72659	Paul Bourdelais	04/2008
9615	(2^241353+3186)/2	72655	Stefano Morozzi	01/2020
9616	17638^13137+13137^17638	72643	Hans Havermann	11/2019
9617	3^152249-56	72642	Lelio R Paula	01/2015
9618	10^72631+37	72632	Robert Price	01/2011
9619	10^72631-8813	72631	Patrick De Geest	05/2013
9620	(19*2^241254+1)/101	72624	Lelio R Paula	08/2012
9621	(32202^16111-1)/32201	72622	Serge Batalov	08/2020
9622	(9^76103+8^76103)/17	72620	Robert Price	12/2012
9624	2^241220-112337	72615	Enzo Doria	06/2014
9623	7*10^72614+33	72615	Robert Price	06/2020
9625	(82*10^72612+449)/9	72613	Robert Price	02/2017
9626	2^241169-15793	72600	Enzo Doria	04/2013
9627	9*10^72595+11	72596	Robert Kinser	01/2017
9628	(2^241152+2478)/2	72594	Stefano Morozzi	01/2020
9629	(2^241143+2438)/2	72591	Stefano Morozzi	01/2020
9630	(2^241115+1598)/2	72583	Stefano Morozzi	01/2020
9631	(1003^24179-1)/1002	72566	Serge Batalov	07/2020
9632	(25*2^241048+1)/89	72563	Lelio R Paula	08/2012
9633	(2^241045+1550)/2	72562	Stefano Morozzi	01/2020
9634	(22*10^72560+17)/3	72561	Robert Price	09/2015
9635	2^241032-23	72558	Lelio R Paula	02/2012
9636	34485*10^72550+2^241004-3	72555	Gilbert Mozzo	12/2012
9637	19460^5349+5349^19460	72553	Hans Havermann	11/2019
9638	(2^241016+3850)/2	72553	Stefano Morozzi	01/2020
9639	2^241004-3	72550	M. Frind & P. Underwood	07/2002
9640	22061^1942+1942^22061	72543	Hans Havermann	11/2019
9641	9*10^72528-89	72529	Robert Price	04/2020
9643	97*10^72522-3	72524	Robert Price	01/2017
9642	(29*10^72523-107)/3	72524	Robert Price	08/2020
9644	(68*10^72516+7)/3	72518	Robert Price	03/2016
9645	(13993^17491-1)/13992	72512	Serge Batalov	08/2020
9646	(78557*2^240844+1)/63	72505	Lelio R Paula	06/2014
9647	67^39701-66	72497	Norbert Schneider	11/2014
9648	(185*10^72484+7)/3	72486	Robert Price	02/2017
9649	(2^240780+2686)/2	72482	Stefano Morozzi	01/2020
9650	(2^240759+1106)/2	72476	Stefano Morozzi	01/2020
9652	(293*27^50631-1736)/13	72473	Curtis Bright	05/2015
9651	103^36005-102	72473	Norbert Schneider	10/2016
9653	15^61616+88	72467	Lelio R Paula	01/2015
9654	45^43831+2	72462	Lelio R Paula	05/2013
9655	2^240692-492389	72456	Paul Bourdelais	03/2013
9656	(646*10^72446-7)/9	72448	Robert Price	07/2016
9657	9*6^93083+7	72434	Lelio R Paula	10/2014
9658	2^240617-3645	72433	Lelio R Paula	05/2013
9659	(9391^18229-1)/9390	72415	Serge Batalov	08/2020
9660	11^69531-24000	72410	Enzo Doria	12/2012
9661	(259*10^72400-1)/3	72402	Robert Price	12/2020
9662	18714^7367+7367^18714	72373	Hans Havermann	11/2019
9663	(22699*2^240396+1)/55	72370	Lelio R Paula	06/2014
9664	6^92995+13	72365	Lelio R Paula	01/2015
9665	(11*10^72362-149)/3	72363	Robert Price	01/2017
9666	18567^7892+7892^18567	72360	Hans Havermann	11/2019
9667	(2^240381+3)/51655	72358	Lelio R Paula	05/2012
9668	6^92974-55	72348	Lelio R Paula	01/2015
9669	2^240295+11	72337	Lelio R Paula	02/2012
9670	(2^240294+1342)/2	72336	Stefano Morozzi	01/2020
9671	(14*10^72326-53)/3	72327	Robert Price	12/2016
9672	15^61493-46	72322	Lelio R Paula	01/2015
9673	(2^240245+2094)/2	72321	Stefano Morozzi	01/2020
9674	(2^240237+1554)/2	72319	Stefano Morozzi	01/2020
9675	lucasU(46,1,43497)-lucasU(46,1,43496)	72315	Mike Oakes	04/2009
9676	(2^240211+1514)/2	72311	Stefano Morozzi	01/2020
9678	5*10^72302+9	72303	Dmitry Domanov	11/2010
9677	(9787*2^240179-1)/265	72303	Lelio R Paula	04/2015
9679	(2^240171+3246)/2	72299	Stefano Morozzi	01/2020
9680	11^69419-3120	72293	Enzo Doria	12/2012
9681	18069^10016+10016^18069	72289	Hans Havermann	11/2019
9682	(25883^16381-1)/25882	72286	Serge Batalov	08/2020
9683	(2^240095+594)/2	72276	Stefano Morozzi	01/2020
9684	(25848^16381-1)/25847	72276	Serge Batalov	08/2020
9685	4*10^72274-83	72275	Robert Price	10/2017
9686	(2^240075+2790)/2	72270	Stefano Morozzi	01/2020
9687	10^72267+33	72268	Robert Price	01/2011
9688	10^72267-553947	72267	Patrick De Geest	05/2013
9689	(2^240066+1030)/2	72267	Stefano Morozzi	01/2020
9691	11^69389-1380	72262	Enzo Doria	12/2012
9692	(16^60013-5^60013)/11	72262	Robert Price	07/2013
9690	7^85507-30	72262	Lelio R Paula	08/2014
9693	(19*2^240026-1)/15	72256	Lelio R Paula	02/2014
9694	(3^151426-2)/661337	72243	Lelio R Paula	06/2012
9695	(2^239940+3850)/2	72229	Stefano Morozzi	01/2020
9696	gcd(V(1296375),5F(259275)(F(259275)-1)+1)	72227	Serge Batalov	04/2015
9697	(2789^20959-1)/2788	72210	Serge Batalov	08/2020
9698	2^239863-112267	72206	Enzo Doria	06/2014
9699	2^239853-114853	72203	Enzo Doria	05/2015
9700	(14068^17401-1)/14067	72180	Serge Batalov	08/2020
9701	(5669^19231-1)/5668	72180	Serge Batalov	08/2020
9702	(4*10^72174+149)/9	72174	Robert Price	03/2017
9703	4*10^72166+67	72167	Robert Price	01/2021
9705	(2^239671+9)/296131	72143	Lelio R Paula	05/2012
9704	2^239651-110665	72143	Enzo Doria	05/2014
9706	(29*2^239650-1)/3305	72140	Lelio R Paula	01/2014
9707	(17099^17041-1)/17098	72130	Serge Batalov	08/2020
9709	241^30280+30280^241	72128	Norbert Schneider	11/2014
9708	(2^239603+950)/2	72128	Stefano Morozzi	01/2020
9710	(2^239594+3058)/2	72125	Stefano Morozzi	01/2020
9711	(68*10^72120-23)/9	72121	Robert Price	10/2015
9712	(9^75571+8^75571)/17	72112	Robert Price	12/2012
9713	(15661^17191-1)/15660	72109	Serge Batalov	08/2020
9714	(3508^20341-1)/3507	72107	Serge Batalov	08/2020
9715	(15*2^239530-1)/173	72105	Lelio R Paula	01/2014
9716	(2^239523+2378)/2	72104	Stefano Morozzi	01/2020
9717	2^239513-112519	72101	Enzo Doria	06/2014
9718	(10^72097+149)/3	72097	Serge Batalov	12/2014
9719	2^239442-6555	72080	Lelio R Paula	05/2012
9720	2*5^103106+3	72069	Lelio R Paula	10/2014
9721	2^239402-197	72068	Lelio R Paula	02/2012
9722	2^239356-111875	72054	Enzo Doria	05/2014
9723	(38*10^72050-119)/9	72051	Robert Price	11/2016
9724	2^239339+15015	72049	Lelio R Paula	01/2013
9725	159^32728+2	72048	Lelio R Paula	05/2013
9726	15^61259-38	72047	Lelio R Paula	01/2015
9727	92^36683-91^36683	72038	Robert Price	08/2015
9728	2^239280+54615	72031	Lelio R Paula	05/2012
9729	(47*2^239267+1)/77	72027	Lelio R Paula	04/2015
9730	(85*10^72025-1)/3	72027	Robert Price	07/2017
9731	(2^239269+1730)/2	72027	Stefano Morozzi	01/2020
9732	2^239236-97305	72018	Lelio R Paula	05/2012
9734	144^33361-143	72006	Norbert Schneider	11/2018
9733	(2^239198+1422)/2	72006	Stefano Morozzi	01/2020
9735	2^239169+59	71998	Lelio R Paula	02/2012
9736	lucasU(2010,1,21796)-lucasU(2010,1,21795)	71994	Mike Oakes	05/2009
9737	(15*2^239171-1)/106301	71994	Lelio R Paula	01/2014
9738	(2^239121+1926)/2	71983	Stefano Morozzi	01/2020
9740	(29^49211-1)/28	71965	Robert Price	04/2012
9739	(299*10^71963+1)/3	71965	Robert Price	11/2017
9741	(58729^15091-1)/58728	71962	Anonymous	11/2020
9743	L(344293)	71953	Renaud Lifchitz	09/2003
9742	V(344293)	71953	Serge Batalov	03/2015
9744	6*10^71951+7	71952	Dmitry Domanov	11/2010
9745	3^150798+40	71949	Lelio R Paula	01/2015
9746	2^238961+95	71935	Lelio R Paula	02/2012
9747	12511^17556+17556^12511	71933	Norbert Schneider	09/2019
9748	2^238936-407	71927	Yves Minet	02/2012
9749	(2^238930+2982)/2	71925	Stefano Morozzi	01/2020
9750	2^238923-28635	71923	Lelio R Paula	05/2012

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