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	(19*2^248099-1)/29	74686	Lelio R Paula	01/2014
9252	20780^3927+3927^20780	74685	Hans Havermann	12/2019
9253	(86*10^74676-41)/9	74677	Robert Price	11/2015
9254	(2^248065+3650)/2	74675	Stefano Morozzi	01/2020
9255	(p(15711)#-4)/2	74672	Robert Price	09/2017
9256	10^74670+31	74671	Robert Price	01/2011
9257	10^74670-122463	74670	Patrick De Geest	05/2013
9258	2^248036-69	74667	Lelio R Paula	03/2012
9259	11^71698-6000	74666	Enzo Doria	12/2012
9260	(2^248032+406)/2	74665	Stefano Morozzi	01/2020
9261	58(10^(324887)-1)/111-1	74661	Robert Price	10/2014
9262	14^65139-45	74658	Lelio R Paula	01/2015
9263	17967^14288+14288^17967	74653	Hans Havermann	11/2019
9264	6^95921-133	74642	Lelio R Paula	01/2015
9265	11^71675+78	74642	Lelio R Paula	02/2015
9266	17875^14986+14986^17875	74641	Hans Havermann	12/2019
9267	(2^247931+1458)/2	74635	Stefano Morozzi	01/2020
9268	(166*10^74624-7)/3	74626	Robert Price	11/2020
9269	18^59449-91	74625	Lelio R Paula	01/2015
9270	(12696^18181-1)/12695	74605	Serge Batalov	08/2020
9271	6^95864-16043	74597	Enzo Doria	02/2013
9272	5*7^88261+6	74590	Lelio R Paula	10/2014
9273	9*5^106710+4	74589	Lelio R Paula	10/2014
9274	(7772^247788+1)/(11754121)	74588	Jens K. Andersen	09/2007
9275	21157^3352+3352^21157	74585	Hans Havermann	12/2019
9276	(265*10^74579+17)/3	74581	Robert Price	05/2016
9277	17798^15489+15489^17798	74575	Hans Havermann	11/2019
9278	(2^247759-1017)/3318311717	74574	Lelio R Paula	07/2012
9279	5^106682-24	74568	Lelio R Paula	08/2014
9280	(2^247686+1450)/2	74561	Stefano Morozzi	01/2020
9281	474^27863+27863^474	74556	Norbert Schneider	01/2017
9282	(14*10^74540+79)/3	74541	Robert Price	11/2017
9283	(2^247582+1630)/2	74530	Stefano Morozzi	01/2020
9284	(35365^16384+1)/2	74524	Lelio R Paula	11/2011
9285	(1705^23059-1)/1704	74518	Serge Batalov	08/2020
9286	3^156161+2660	74508	Lelio R Paula	01/2015
9288	2^247474-58695	74498	Lelio R Paula	05/2013
9287	(2^247476+886)/2	74498	Stefano Morozzi	01/2020
9289	11^71519-90	74480	Enzo Doria	07/2012
9290	(19*2^247419-1)/23202983	74475	Lelio R Paula	01/2014
9292	(2^247394-7)/3	74473	Lelio R Paula	06/2012
9291	18^59328+17	74473	Lelio R Paula	01/2015
9293	2^247379-181	74469	Lelio R Paula	03/2012
9294	(15*2^247370-1)/479	74465	Lelio R Paula	01/2014
9295	18860^8877+8877^18860	74465	Hans Havermann	12/2019
9296	17355^17564-17564^17355	74462	Norbert Schneider	11/2019
9297	2^247344+2047	74458	Lelio R Paula	05/2013
9298	2^247311-1017	74449	Lelio R Paula	05/2013
9299	(2^247288+1938)/2	74441	Stefano Morozzi	01/2020
9300	2^247280+7	74439	Lelio R Paula	03/2012
9301	(68*10^74434+13)/9	74435	Ray Chandler	11/2010
9302	3^156004-62	74433	Lelio R Paula	01/2015
9303	21865^2536+2536^21865	74432	Hans Havermann	11/2019
9304	(2^247223+1050)/2	74422	Stefano Morozzi	01/2020
9305	36095!2-64	74416	Robert Price	06/2015
9306	67699!4+16	74409	Robert Price	09/2019
9307	2^247165-3	74405	M. Frind & P. Underwood	07/2002
9308	2^247150+32769	74400	Lelio R Paula	05/2013
9309	(2^247130+3858)/2	74394	Stefano Morozzi	01/2020
9310	(2^247055+2426)/2	74371	Stefano Morozzi	01/2020
9311	12^68911+73	74368	Lelio R Paula	01/2015
9312	2^246999+74903	74355	Enzo Doria	04/2016
9313	2^246989-110643	74352	Enzo Doria	05/2014
9314	10^74350+279439	74351	Patrick De Geest	07/2017
9317	(10^74350+11)/3	74350	Robert Price	11/2014
9315	10^74350-400000001	74350	Robert Price	07/2017
9316	10^74350-716241	74350	Patrick De Geest	07/2017
9318	67647!4-512	74346	Robert Price	11/2019
9319	10^74335+13659	74336	Patrick De Geest	05/2013
9320	10^74335-53	74335	Robert Price	05/2011
9321	23360^1521+1521^23360	74335	Hans Havermann	11/2019
9322	(2^246914+3418)/2	74329	Stefano Morozzi	01/2020
9323	2^246906-1215	74327	Lelio R Paula	05/2013
9324	(2^246879+1494)/2	74318	Stefano Morozzi	01/2020
9325	2^246848+111	74309	Lelio R Paula	03/2012
9326	(2^246842+2490)/2	74307	Stefano Morozzi	01/2020
9328	6^95490-18443	74306	Enzo Doria	03/2013
9327	(2^246840+2902)/2	74306	Stefano Morozzi	01/2020
9329	18^59188-2369	74298	Enzo Doria	03/2013
9330	(13632^246767+1)/(35713^2*743)	74281	Jens K. Andersen	09/2007
9331	2^246744+40755	74278	Lelio R Paula	05/2013
9332	(29*10^74276+91)/3	74277	Robert Price	03/2016
9333	17222^17533-17533^17222	74272	Norbert Schneider	11/2019
9334	(2^246720+3606)/2	74270	Stefano Morozzi	01/2020
9335	6^95441+163	74268	Lelio R Paula	01/2015
9336	(40734^16111-1)/40733	74267	Anonymous	11/2020
9337	(14235^17881-1)/14234	74263	Serge Batalov	08/2020
9338	V(390863)	74258	Serge Batalov	03/2015
9339	10^74254+91	74255	Robert Price	03/2011
9341	(19*10^74253-1)/9	74254	Ray Chandler	02/2012
9340	10^74254-130569	74254	Patrick De Geest	05/2013
9342	771^25718+25718^771	74250	Norbert Schneider	10/2016
9343	2^246618+427	74240	Henri Lifchitz	02/2005
9344	88*10^74234+3	74236	Robert Price	11/2016
9345	8*10^74234-49	74235	Robert Price	04/2016
9346	(19648^17291-1)/19647	74232	Serge Batalov	08/2020
9347	2^246578+12285	74228	Lelio R Paula	05/2013
9348	(3^155569-5)/2	74225	Lelio R Paula	06/2012
9349	13^66628+46	74220	Lelio R Paula	01/2015
9350	(2^246534+3034)/2	74214	Stefano Morozzi	01/2020
9351	(2^246486+798)/2	74200	Stefano Morozzi	01/2020
9352	2^246476-17295	74197	Lelio R Paula	05/2013
9353	(2^246465+446)/2	74194	Stefano Morozzi	01/2020
9354	(61*10^74189-1)/3	74191	Robert Price	11/2017
9355	(15185*2^246432-1)/13	74187	Lelio R Paula	04/2015
9356	5*2^246413-3	74179	Lelio R Paula	05/2014
9357	2^246386-28635	74170	Lelio R Paula	05/2013
9358	(2^246371+3050)/2	74165	Stefano Morozzi	01/2020
9359	2^246334-111245	74154	Enzo Doria	05/2014
9360	39^77708+7^77708-24^77708-3	74153	Mike Oakes	12/2010
9361	15^63045+82	74147	Lelio R Paula	01/2015
9362	19255!+19255#+1	74140	D. Gazzoni Filho & Lucas Teixeira	06/2005
9363	(199^32251-1)/198	74139	Serge Batalov	08/2020
9364	(2^246277+2114)/2	74137	Stefano Morozzi	01/2020
9365	2^246268-110507	74135	Enzo Doria	05/2014
9366	3^155328+2660	74111	Lelio R Paula	01/2015
9368	2^246148-2786249	74098	Enzo Doria	03/2016
9367	19740^5671+5671^19740	74098	Hans Havermann	01/2020
9369	(2^246135+3386)/2	74094	Stefano Morozzi	01/2020
9370	(16*10^74092-19)/3	74093	Robert Price	03/2016
9371	2^246115-110767	74088	Enzo Doria	05/2014
9372	7^87666-68	74087	Lelio R Paula	08/2014
9373	(2^246091+1938)/2	74081	Stefano Morozzi	01/2020
9375	10^74079+1145141919	74080	Marisa Kirisame	03/2015
9374	10^74079+6219	74080	Patrick De Geest	03/2016
9376	10^74079-282707	74079	Patrick De Geest	03/2016
9377	129^35098+2	74078	Lelio R Paula	05/2013
9378	22193^2176+2176^22193	74073	Hans Havermann	12/2019
9379	17703^15278+15278^17703	74071	Hans Havermann	12/2019
9380	2^246025-112123	74061	Enzo Doria	06/2014
9381	(67*10^74045+17)/3	74047	Robert Price	02/2017
9382	(2^245944+2202)/2	74037	Stefano Morozzi	01/2020
9383	(2^245885+1446)/2	74019	Stefano Morozzi	01/2020
9384	(13769^17881-1)/13768	74004	Serge Batalov	08/2020
9385	2^245823+66831	74001	Marek Hubal	02/2017
9386	5^105869+42	74000	Lelio R Paula	08/2014
9387	(21*2^245806+1)/634555	73991	Lelio R Paula	08/2012
9388	(22699*2^245762+1)/119	73985	Lelio R Paula	06/2014
9389	(3^155048-7)/262	73975	Lelio R Paula	06/2012
9390	9998*2^245696+3	73966	Donovan Johnson	10/2004
9391	13^66400-80	73966	Lelio R Paula	01/2015
9393	(2^245704+9)/25	73963	Lelio R Paula	07/2012
9394	11^71023-7170	73963	Enzo Doria	01/2013
9392	3*10^73962+13	73963	Robert Price	08/2017
9395	(64758^15373-1)/64757	73960	Anonymous	11/2020
9396	(31*2^245660-1)/114195	73948	Lelio R Paula	01/2014
9397	2^245629-2797813	73942	Eric Chen	03/2016
9398	2^245557-153	73921	Lelio R Paula	03/2012
9399	(77*10^73917-59)/9	73918	Robert Price	11/2017
9400	15010^17699+17699^15010	73918	Norbert Schneider	11/2019
9401	(12975^17971-1)/12974	73913	Serge Batalov	08/2020
9402	2^245525+1869881	73911	Enzo Doria	06/2016
9403	2^245522+159	73910	Lelio R Paula	03/2012
9404	(2^245507+1986)/2	73905	Stefano Morozzi	01/2020
9405	(13*10^73891-43)/3	73892	Robert Price	08/2017
9406	19^57783-56	73891	Lelio R Paula	01/2015
9407	7*10^73888+79	73889	Robert Price	02/2017
9408	(2^245449+942)/2	73888	Stefano Morozzi	01/2020
9409	6^94948+174281	73884	Mike Oakes	02/2011
9410	(2^245431+3630)/2	73882	Stefano Morozzi	01/2020
9411	11^70939-4860	73876	Enzo Doria	01/2013
9412	18637^9196+9196^18637	73870	Hans Havermann	01/2020
9413	2^245372+54615	73865	Lelio R Paula	05/2013
9414	2^245362-143	73862	Lelio R Paula	03/2012
9415	7^87396+6^(87396-1)	73859	Robert Price	03/2016
9416	(22*10^73853-37)/3	73854	Robert Price	05/2017
9417	5^105646-14246	73844	Enzo Doria	02/2013
9419	2^245290-41	73840	Lelio R Paula	03/2012
9418	2^245290-94395	73840	Lelio R Paula	05/2013
9420	15770^17589+17589^15770	73836	Norbert Schneider	10/2019
9421	12352^18043+18043^12352	73828	Norbert Schneider	11/2019
9422	(2^245240+3598)/2	73825	Stefano Morozzi	01/2020
9423	(2^245242+498)/2	73825	Stefano Morozzi	01/2020
9424	8*5^105600-7	73813	Lelio R Paula	10/2014
9425	7*5^105573-4	73794	Lelio R Paula	10/2014
9426	(2^245112+1122)/2	73786	Stefano Morozzi	01/2020
9427	20151^4570+4570^20151	73751	Hans Havermann	12/2019
9428	(2^244968+1318)/2	73743	Stefano Morozzi	01/2020
9429	18^58742-4805	73738	Enzo Doria	03/2013
9430	(7*10^73729+23)/3	73730	Robert Price	06/2020
9431	13^66179+66	73720	Lelio R Paula	01/2015
9432	(2^244881+942)/2	73717	Stefano Morozzi	01/2020
9433	(2^244883+1946)/2	73717	Stefano Morozzi	01/2020
9434	(82*10^73714-1)/9	73715	Robert Price	12/2014
9435	(2^244862+3682)/2	73711	Stefano Morozzi	01/2020
9436	(29*2^244856-1)/186121	73706	Lelio R Paula	01/2014
9437	(13*2^244840-1)/2799	73702	Lelio R Paula	01/2014
9438	(13*10^73701+17)/3	73702	Robert Price	06/2015
9439	6*10^73686-29	73687	Robert Price	08/2020
9440	(2^244787-1017)/28411	73684	Lelio R Paula	07/2012
9441	21213^2974+2974^21213	73680	Hans Havermann	01/2020
9442	(3^154421-4)/23	73677	Lelio R Paula	06/2012
9443	14596^17691+17691^14596	73670	Norbert Schneider	11/2019
9444	8*7^87170+5	73669	Lelio R Paula	10/2014
9445	(29*10^73659-113)/3	73660	Robert Price	11/2017
9446	Phi(40100,-40100)	73651	Henri Lifchitz	06/2013
9447	(3883^20521-1)/3882	73650	Serge Batalov	08/2020
9448	(4*10^73647-19)/3	73648	Robert Price	06/2017
9449	2^244618-2297	73638	Yves Minet	10/2009
9450	3*5^105344+8	73633	Lelio R Paula	10/2014
9451	(2^244588+2562)/2	73629	Stefano Morozzi	01/2020
9452	5^105334-14096	73626	Enzo Doria	02/2013
9453	(2^244562+1534)/2	73621	Stefano Morozzi	01/2020
9454	(2^244584-7)/13237074243033	73614	Lelio R Paula	07/2012
9455	2^244465-110185	73592	Enzo Doria	05/2014
9456	(2^244465+2934)/2	73591	Stefano Morozzi	01/2020
9457	2^244443+40755	73585	Lelio R Paula	05/2013
9458	23155^1506+1506^23155	73583	Hans Havermann	12/2019
9459	10^73579+987654321	73580	Robert Price	12/2019
9460	10^73579+124173	73580	Patrick De Geest	02/2020
9461	10^73579-176379	73579	Patrick De Geest	02/2020
9462	2^244404+3841	73573	Yves Minet	03/2011
9463	19770^5263+5263^19770	73569	Hans Havermann	12/2019
9464	9*10^73565-41	73566	Robert Price	08/2020
9465	2^244372-110627	73564	Enzo Doria	05/2014
9466	19778^5241+5241^19778	73563	Hans Havermann	12/2019
9467	(2^244349+2186)/2	73557	Stefano Morozzi	01/2020
9468	(2^244309+3710)/2	73545	Stefano Morozzi	01/2020
9469	18428^9783+9783^18428	73537	Hans Havermann	01/2020
9470	(3*2^244255+1)/245	73527	Lelio R Paula	08/2012
9471	(11*2^244245+1)/23	73525	Lelio R Paula	08/2012
9472	18140^11301+11301^18140	73524	Hans Havermann	12/2019
9473	(15185*2^244187-1)/6111	73509	Lelio R Paula	04/2015
9474	(9699^18439-1)/9698	73508	Serge Batalov	08/2020
9475	(2^244152+2058)/2	73497	Stefano Morozzi	01/2020
9476	(2^244109+1422)/2	73484	Stefano Morozzi	01/2020
9477	17063^17362+17362^17063	73477	Norbert Schneider	04/2019
9478	(91^37507+1)/92	73476	Paul Bourdelais	08/2017
9479	18^58521+65	73460	Lelio R Paula	01/2015
9480	13^65940+36	73454	Lelio R Paula	01/2015
9481	19065^7112+7112^19065	73439	Hans Havermann	12/2019
9482	(625^26267+1)/626	73437	Richard Fischer	12/2017
9483	(16612^17401-1)/16611	73436	Serge Batalov	08/2020
9484	(2^243935+530)/2	73432	Stefano Morozzi	01/2020
9485	5^105050-14	73427	Lelio R Paula	08/2014
9486	(2^243850+1474)/2	73406	Stefano Morozzi	01/2020
9487	(((((((((((((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
9488	15^62410-46	73400	Lelio R Paula	01/2015
9489	(2^243806+2494)/2	73393	Stefano Morozzi	01/2020
9490	(2^243790+2530)/2	73388	Stefano Morozzi	01/2020
9491	(2^243766+2362)/2	73381	Stefano Morozzi	01/2020
9492	2^243733+1869707	73371	Enzo Doria	05/2016
9493	10^73365-500000001	73365	Robert Price	12/2020
9494	11^70439-5430	73355	Enzo Doria	01/2013
9495	2^243676-87	73354	Lelio R Paula	03/2012
9496	(101*10^73346-17)/3	73348	Robert Price	08/2016
9497	21639^2452+2452^21639	73346	Hans Havermann	12/2019
9498	(2^243647+2438)/2	73345	Stefano Morozzi	01/2020
9499	2^243621-113185	73338	Enzo Doria	07/2014
9500	(5*2^243610-1)/1669	73332	Lelio R Paula	01/2014

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