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 ?
9251	2^192023-192023^2	57805	Henri Lifchitz	05/2005
9252	21^43717+2	57804	Ray Chandler	08/2011
9253	8*5^82687+7	57797	Lelio R Paula	09/2014
9254	16459^3246+3246^16459	57794	Hans Havermann	04/2019
9255	5^82680-24	57791	Lelio R Paula	10/2012
9257	(2^191915+47)/95	57771	Lelio R Paula	02/2012
9256	12019^14160-14160^12019	57771	Norbert Schneider	02/2019
9258	(74*10^57763+133)/9	57764	Robert Price	10/2017
9259	6^74227-95	57760	Lelio R Paula	10/2012
9260	2^191861+29835	57756	Lelio R Paula	10/2012
9262	1908^17605+17605^1908	57755	Serge Batalov	05/2014
9261	5*10^57754+59	57755	Robert Price	09/2016
9263	(5*2^191821-1)/8924067	57738	Lelio R Paula	01/2014
9264	14100^12431+12431^14100	57733	Hans Havermann	04/2019
9265	38^63917+5^63917-34^63917+3*2^63917	57724	Mike Oakes	11/2010
9266	41399!3-6561	57723	Robert Price	11/2015
9267	(44*10^57721-233)/9	57722	Robert Price	10/2017
9268	2^191745+17	57721	Lelio R Paula	04/2011
9269	2^191730-761	57717	Yves Minet	01/2012
9270	(2^191733-3)/2251	57715	Lelio R Paula	02/2012
9271	2^191698-111	57707	Lelio R Paula	04/2011
9272	(13*10^57691+23)/9	57692	Robert Price	02/2015
9273	2^191640-4475	57690	Yves Minet	03/2019
9274	20^44340-5423	57688	Enzo Doria	03/2013
9275	(27*2^191629+1)/125	57686	Lelio R Paula	07/2012
9276	410^57684+37^57684	57685	Mike Oakes	11/2010
9278	2*3^120898+5	57684	Lelio R Paula	04/2014
9277	10650^14323-14323^10650	57684	Norbert Schneider	05/2019
9279	(6883*2^191610-1)/7347	57681	Lelio R Paula	04/2015
9280	6^74117-49	57675	Lelio R Paula	10/2012
9281	2^191586-113201	57674	Enzo Doria	07/2014
9282	2^191580+193	57672	Lelio R Paula	04/2011
9283	(103*29^39433+10401)/4	57669	Curtis Bright	05/2015
9284	2^191560+255255	57666	Lelio R Paula	05/2011
9285	2^191515-85	57652	Lelio R Paula	04/2011
9286	2^191502-1127	57648	Yves Minet	05/2013
9287	2*5^82473-3^82473	57647	Mike Oakes	08/2010
9288	(13*10^57634-61)/3	57635	Robert Price	08/2017
9289	10635^14312-14312^10635	57631	Norbert Schneider	05/2019
9290	85^29868-29868^85	57628	Norbert Schneider	11/2017
9291	2^191430+103	57627	Lelio R Paula	04/2011
9292	3*2^191408+5	57621	Lelio R Paula	03/2014
9293	2^191382-1858931	57612	Enzo Doria	04/2016
9294	6*7^68163+5	57606	Lelio R Paula	09/2014
9295	91^29403-2	57602	Lelio R Paula	08/2013
9296	11^55308-7950	57598	Enzo Doria	02/2013
9297	2^191329+65	57596	Lelio R Paula	04/2011
9298	11^55302-240	57592	Enzo Doria	07/2012
9299	2^191299-1031467	57587	Paul Bourdelais	11/2012
9300	2^191295-111991	57586	Enzo Doria	05/2014
9301	10824^14273-14273^10824	57583	Norbert Schneider	04/2019
9302	2^191279-1297	57581	Yves Minet	08/2012
9303	14827^7630+7630^14827	57567	Hans Havermann	04/2019
9304	3*6^73961+5	57554	Lelio R Paula	09/2014
9305	16177^3610+3610^16177	57550	Hans Havermann	04/2019
9306	(3^120623+5)/52144	57548	Lelio R Paula	04/2012
9307	(17*10^57543-29)/3	57544	Robert Price	09/2017
9308	42^35445-41	57537	Norbert Schneider	06/2014
9309	(71^31079-1)/70	57534	Paul Bourdelais	08/2017
9310	2^191069-723403	57518	Paul Bourdelais	11/2012
9311	4*10^57506-3	57507	Serge Batalov	11/2010
9312	10^57501+67359	57502	Patrick De Geest	06/2016
9313	10^57501-1000000001	57501	Robert Price	05/2016
9314	10^57501-249861	57501	Patrick De Geest	06/2016
9315	(9^60251+4^60251)/13	57493	Robert Price	02/2013
9316	20^44184-6003	57485	Enzo Doria	03/2013
9317	2^190948+12705	57482	Lelio R Paula	10/2012
9318	2^190945+29	57481	Henri Lifchitz	06/2005
9319	2^190922-401	57474	Yves Minet	01/2012
9320	15^48860+46	57464	Lelio R Paula	02/2013
9321	3^120434+20	57462	Lelio R Paula	10/2012
9322	7^67964-38	57437	Lelio R Paula	10/2012
9323	2^190799-113065	57437	Enzo Doria	07/2014
9324	9*5^82159+2	57428	Lelio R Paula	09/2014
9326	(F(22898)^13-F(22897)^13)/F(22896)	57422	Wayne Halsdorf	03/2012
9325	15362^5469+5469^15362	57422	Hans Havermann	04/2019
9327	14005^12586+12586^14005	57419	Hans Havermann	04/2019
9328	10159^14330-14330^10159	57419	Norbert Schneider	05/2019
9331	lucasU(432,25,21787)-5*lucasU(432,25,21786)	57416	Mike Oakes	05/2009
9329	(103*10^57414-1)/3	57416	Serge Batalov	12/2014
9330	(1654*30^38869-1)/29	57416	Karsten Bonath	05/2017
9332	2*10^57410+9^57410	57411	Mike Oakes	04/2011
9333	2^190704-1595	57408	Lelio R Paula	05/2011
9334	11^55121-1740	57403	Enzo Doria	11/2012
9335	2^190644-185	57390	Lelio R Paula	04/2011
9336	41182!3-3^41182	57389	Robert Price	08/2015
9337	2^190629-112255	57386	Enzo Doria	06/2014
9338	(2*10^57384-71)/3	57384	Robert Price	01/2017
9340	2*6^73735+5^73735	57378	Mike Oakes	11/2009
9339	2^190605+59	57378	Lelio R Paula	04/2011
9341	6^73727-7	57371	Lelio R Paula	10/2012
9342	2^190561-112225	57365	Enzo Doria	06/2014
9343	10^57358+170899	57359	Patrick De Geest	06/2016
9344	10^57358-8001	57358	Robert Price	03/2016
9345	18^45687-11	57350	Lelio R Paula	02/2013
9346	11^55069-210	57349	Enzo Doria	07/2012
9347	11^55068-12	57348	Lelio R Paula	02/2013
9348	19^44839+54	57339	Lelio R Paula	02/2013
9349	(7*2^190468-1)/8511	57334	Lelio R Paula	01/2014
9350	(23*10^57333-59)/9	57334	Robert Price	03/2017
9351	2^190455-1155*190455	57333	Henri Lifchitz	02/2005
9352	14376^9721+9721^14376	57328	Hans Havermann	04/2019
9353	65^31620+28	57325	Lelio R Paula	01/2016
9354	2^190403+16095	57318	Lelio R Paula	05/2011
9355	(19*10^57316+119)/3	57317	Robert Price	02/2017
9358	(21*2^190393+1)/211	57314	Lelio R Paula	07/2012
9357	2^190392-112025	57314	Enzo Doria	05/2014
9356	13173^13912-13912^13173	57314	Norbert Schneider	08/2018
9359	14092^11633+11633^14092	57294	Hans Havermann	04/2019
9360	16460^3021+3021^16460	57284	Hans Havermann	04/2019
9361	(24737*2^190234+1)/9	57270	Lelio R Paula	05/2014
9362	(7*2^190230+1)/23	57265	Lelio R Paula	07/2012
9363	(10223*2^190197+1)/3211	57256	Lelio R Paula	05/2014
9364	16726^2645+2645^16726	57244	Hans Havermann	04/2019
9365	18^45590-97	57228	Lelio R Paula	02/2013
9366	(3*2^190105-1)/19205	57224	Lelio R Paula	01/2014
9367	(16*10^57219-31)/3	57220	Robert Price	03/2016
9368	(2^190074+47)/51	57217	Lelio R Paula	02/2012
9369	14899^6912+6912^14899	57207	Hans Havermann	04/2019
9370	3^119894-140	57204	Lelio R Paula	10/2012
9372	(37^36473-1)/36	57196	Robert Price	03/2012
9371	2^190000-2163	57196	Yves Minet	08/2013
9373	2^189987-2798107	57192	Enzo Doria	04/2016
9374	2^189935-112117	57177	Enzo Doria	05/2014
9375	2^189909-112231	57169	Enzo Doria	06/2014
9376	132049#+149053	57161	Makoto Morimoto	12/2015
9377	41032!3-27	57158	Robert Price	09/2014
9378	19^44694+22	57153	Lelio R Paula	02/2013
9379	16046^3645+3645^16046	57151	Hans Havermann	04/2019
9380	12^52956-17	57150	Lelio R Paula	02/2013
9381	2^189823-967	57143	Yves Minet	01/2012
9382	(25*10^57138-61)/9	57139	Robert Price	02/2015
9383	5^81743-4^(81743+1)	57136	Robert Price	04/2016
9384	14476^8843+8843^14476	57131	Hans Havermann	04/2019
9385	15327^5338+5338^15327	57130	Hans Havermann	04/2019
9386	7^67593-54	57123	Lelio R Paula	10/2012
9387	7*3^119712+2	57118	Lelio R Paula	03/2014
9388	5^81700+16	57106	Lelio R Paula	10/2012
9389	2^189700+76561	57106	Enzo Doria	05/2016
9391	2^189671+131	57097	Lelio R Paula	04/2011
9390	4*6^73374+5	57097	Lelio R Paula	09/2014
9392	(67607*2^189651+1)/43727	57091	Lelio R Paula	05/2014
9393	(29*2^189619-1)/393	57080	Lelio R Paula	01/2014
9394	3^119587+80	57058	Lelio R Paula	10/2012
9395	2^189502-113453	57046	Enzo Doria	07/2014
9396	2^189455+153	57032	Lelio R Paula	04/2011
9397	24^41317-41317^24	57027	Norbert Schneider	07/2016
9398	2^189414-17	57020	Lelio R Paula	03/2011
9399	24^41311+23	57018	Norbert Schneider	12/2013
9400	norm(Mod(x,x^4+x^3-x+1)^207341-1)/2	56998	Paul Vanderveen	05/2018
9401	14276^9819+9819^14276	56991	Hans Havermann	04/2019
9402	(4*10^56989-31)/9	56989	Erik Branger	05/2011
9403	11^54712-1620	56977	Enzo Doria	11/2012
9404	8102^14577-14577^8102	56976	Norbert Schneider	01/2019
9405	2^189237-112231	56967	Enzo Doria	06/2014
9406	17^46285-48	56952	Lelio R Paula	02/2013
9407	2^189188+75241	56952	Enzo Doria	04/2016
9408	2^189181+94395	56950	Henri Lifchitz	01/2005
9409	7001^14808-108	56940	Enzo Doria	07/2012
9410	2^189147-112639	56939	Enzo Doria	06/2014
9411	(19*10^56933-43)/3	56934	Robert Price	10/2017
9412	2^189110-3	56928	M. Frind & P. Underwood	11/2002
9413	2^189069+12909	56916	Lelio R Paula	04/2011
9414	(13*10^56909+191)/3	56910	Robert Price	08/2017
9415	(35*10^56898-17)/9	56899	Serge Batalov	02/2009
9416	2^189011-5955	56898	Lelio R Paula	04/2011
9417	6^73119-5	56898	Lelio R Paula	10/2012
9418	13^51076-90	56896	Lelio R Paula	02/2013
9419	2^188997+56897	56894	Yves Minet	02/2010
9420	5^81388-13766	56888	Enzo Doria	02/2013
9421	(104^28201+1)/105	56881	Richard Fischer	04/2018
9422	(156^25933+1)/157	56873	Eric Chen	12/2017
9423	20^43713-6403	56872	Enzo Doria	03/2013
9424	(71*10^56858-287)/9	56859	Robert Price	05/2017
9425	2^188857-254233	56852	Gary Barnes	09/2009
9427	15^48338-88	56850	Lelio R Paula	02/2013
9426	10^56849+136437	56850	Patrick De Geest	07/2017
9428	10^56849-701	56849	Robert Price	06/2017
9429	(2^188788+78557)/3	56831	Lelio R Paula	05/2012
9430	2^188771+16095	56826	Lelio R Paula	04/2011
9431	7*2^188742-9	56818	Lelio R Paula	03/2014
9432	12^52646-65	56815	Lelio R Paula	02/2013
9433	5003^15358-158	56813	Enzo Doria	07/2012
9434	2^188713+577294575	56809	Lelio R Paula	03/2013
9435	10060^14193-14193^10060	56809	Norbert Schneider	02/2019
9436	2^188693-112099	56803	Enzo Doria	05/2014
9437	(7^67211+4^67211)/11	56799	Robert Price	10/2012
9438	2^188678-94395	56798	Lelio R Paula	09/2011
9439	20^43651-8503	56792	Enzo Doria	03/2013
9441	2^188657-2371	56792	Yves Minet	10/2013
9440	152^26029-151^26029	56792	Eric Chen	04/2018
9442	(14^49549+5^49549)/19	56789	Robert Price	05/2013
9443	(45^34351-1)/44	56788	Robert Price	05/2014
9444	7*10^56785-23	56786	Robert Price	04/2016
9445	(10^56781-31)/3	56781	Serge Batalov	12/2014
9446	7*10^56779+3	56780	Erik Branger	11/2009
9447	((10^14197+1)((10^28394+10^14197)(10^14197-10^7099+3)-10^7099+2)-1)/3541/3407281	56778	Makoto Kamada	03/2019
9448	12858^13817-13817^12858	56777	Norbert Schneider	11/2018
9449	10^56765+259179	56766	Patrick De Geest	09/2013
9450	10^56765-249497	56765	Patrick De Geest	09/2013
9451	t(188706)	56764	Robert Price	04/2015
9452	2^188551-904327	56760	Paul Bourdelais	11/2012
9453	(64*10^56756+17)/9	56757	Robert Price	09/2015
9454	131101#+146291	56757	Makoto Morimoto	02/2016
9455	2^188539-112519	56756	Enzo Doria	06/2014
9456	6^72927+101	56749	Lelio R Paula	10/2012
9457	20^43617-1603	56748	Enzo Doria	03/2013
9458	(3^118892-8)/91358929	56718	Lelio R Paula	03/2012
9459	13339^13748-13748^13339	56713	Norbert Schneider	09/2018
9460	(509203*2^188338-1)/3	56701	Lelio R Paula	03/2015
9461	20^43567-5623	56682	Enzo Doria	03/2013
9462	2^188234-113183	56665	Enzo Doria	07/2014
9463	(139^26437+1)/140	56653	Richard Fischer	03/2018
9464	(7*2^188215-1)/1497315125	56651	Lelio R Paula	01/2014
9465	(1017*2^188171-1)/35	56647	Lelio R Paula	03/2015
9466	(34*10^56647-7)/9/37/263	56644	Makoto Morimoto	04/2016
9467	(2^188176-1017)/453814543	56638	Lelio R Paula	02/2012
9468	33*10^56634+7	56636	Robert Price	07/2016
9469	(F(31)^9241-F(30)^9241)/F(29)	56634	Wayne Halsdorf	08/2010
9470	14^49413+33	56634	Lelio R Paula	02/2013
9471	14240^9483+9483^14240	56632	Hans Havermann	04/2019
9472	15991^3478+3478^15991	56630	Hans Havermann	04/2019
9473	3^118680+110	56625	Lelio R Paula	10/2012
9474	(13*10^56624+161)/3	56625	Robert Price	04/2017
9475	(3^118676-2)/7516653263	56613	Lelio R Paula	03/2012
9476	(13*2^188062+1)/17	56613	Lelio R Paula	07/2012
9477	2^188056-1313	56611	Yves Minet	08/2012
9478	20^43510-5583	56608	Enzo Doria	03/2013
9479	2^188032+12285	56604	Lelio R Paula	03/2011
9480	(19*10^56597-43)/3	56598	Robert Price	10/2017
9481	(265*10^56588+17)/3	56590	Robert Price	05/2016
9482	2^187959+5775	56582	Lelio R Paula	03/2011
9483	(5*2^187959+1)/53	56581	Lelio R Paula	07/2012
9484	3*10^56575-13	56576	Robert Price	11/2017
9485	(11*2^187889-1)/351	56559	Lelio R Paula	01/2014
9486	(100049^11311+1)/100050	56553	Faysal YAtim	09/2007
9487	(19*10^56544-1)/9	56545	Serge Batalov	03/2009
9488	20^43447-8923	56526	Enzo Doria	03/2013
9489	10423^14066-14066^10423	56518	Norbert Schneider	11/2018
9490	2^187743-112177	56517	Enzo Doria	06/2014
9491	(F(5879)^47-F(5878)^47)/F(5877)	56502	Wayne Halsdorf	08/2010
9492	5^80831-22	56499	Lelio R Paula	10/2012
9493	5^80828-13166	56497	Enzo Doria	02/2013
9494	7*2^187590-5	56472	Lelio R Paula	03/2014
9495	16361^2826+2826^16361	56465	Hans Havermann	04/2019
9496	2^187555+75473	56460	Enzo Doria	04/2016
9497	2^187541-283	56456	Yves Minet	01/2012
9499	(55*10^56453-1)/9	56454	Serge Batalov	03/2009
9498	12933^13730-13730^12933	56454	Norbert Schneider	09/2018
9500	2^187506-1451	56445	Yves Minet	08/2012

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Probable Primes Top 10000

(252932 PRPs in the top)