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	2^300874+7	90573	Lelio R Paula	10/2012
9252	10^90567+9489	90568	Patrick De Geest	11/2018
9253	10^90567-231353	90567	Patrick De Geest	07/2019
9254	(2^300857+2214)/2	90567	Stefano Morozzi	01/2020
9255	5^129568-56	90565	Lelio R Paula	04/2016
9256	2^300847-112831	90564	Enzo Doria	06/2014
9257	10^90562+790197	90563	Patrick De Geest	07/2019
9258	10^90562-2981	90562	Patrick De Geest	11/2018
9259	(7796^23269-1)/7795	90557	Serge Batalov	08/2020
9260	(31*10^90554+257)/9	90555	Robert Price	12/2021
9261	10^90549+3811	90550	Patrick De Geest	11/2018
9262	10^90549-630303	90549	Patrick De Geest	07/2019
9263	2^300790-4541	90547	Yves Minet	03/2019
9264	10^90532+8169	90533	Patrick De Geest	11/2018
9265	10^90531+9831	90532	Patrick De Geest	11/2018
9266	10^90532-154889	90532	Patrick De Geest	07/2019
9267	10^90531-1060589	90531	Patrick De Geest	07/2019
9269	2^300718+255255	90526	Lelio R Paula	02/2016
9268	(2^300719+938)/2	90526	Stefano Morozzi	01/2020
9270	10^90516+215917	90517	Patrick De Geest	07/2019
9271	10^90516-6783	90516	Patrick De Geest	11/2018
9272	10^90511+30177	90512	Patrick De Geest	07/2019
9273	10^90511-6977	90511	Patrick De Geest	11/2018
9274	(8573^23011-1)/8572	90502	Serge Batalov	08/2020
9275	2^300637+95	90501	Lelio R Paula	11/2012
9276	7^107087-24	90500	Lelio R Paula	04/2016
9277	10^90499+191547	90500	Patrick De Geest	07/2019
9278	10^90499-5823	90499	Patrick De Geest	11/2018
9280	(10^90499+3^90499)/13	90498	Robert Price	01/2013
9279	13^81241+90	90498	Lelio R Paula	06/2016
9281	(2^300600+1222)/2	90490	Stefano Morozzi	01/2020
9282	10^90480+5131	90481	Patrick De Geest	11/2018
9283	10^90480-85721	90480	Patrick De Geest	07/2019
9284	(34*10^90478-547)/9	90479	Robert Price	03/2021
9285	6^116273-85	90478	Lelio R Paula	05/2016
9286	10^90473+3139	90474	Patrick De Geest	11/2018
9287	10^90473-150599	90473	Patrick De Geest	07/2019
9288	10^90470+2319	90471	Patrick De Geest	11/2018
9289	10^90470-71637	90470	Patrick De Geest	07/2019
9290	6^116256-17573	90465	Enzo Doria	02/2013
9291	2^300502+54615	90461	Lelio R Paula	02/2016
9292	(13*2^300487+1)/45	90456	Lelio R Paula	09/2013
9293	10^90453+141843	90454	Patrick De Geest	07/2019
9295	10^90453-3969	90453	Patrick De Geest	11/2018
9294	10^90452+59317	90453	Patrick De Geest	05/2021
9296	10^90452-80000001	90452	Robert Price	04/2021
9297	10^90452-84713	90452	Patrick De Geest	05/2021
9298	10^90440+1359	90441	Patrick De Geest	11/2018
9299	10^90440-18821	90440	Patrick De Geest	07/2019
9300	(3^189545-8)/5	90436	Lelio R Paula	01/2013
9301	(7*2^300406-1)/3	90432	Lelio R Paula	02/2014
9302	10^90430+3339	90431	Patrick De Geest	11/2018
9303	10^90430-63477	90430	Patrick De Geest	07/2019
9304	(5408^24223-1)/5407	90422	Serge Batalov	08/2020
9305	10^90414+229593	90415	Patrick De Geest	07/2019
9306	10^90414-1547	90414	Patrick De Geest	11/2018
9307	10^90404+47041	90405	Patrick De Geest	07/2019
9308	10^90404-6429	90404	Patrick De Geest	11/2018
9309	10^90401+2077	90402	Patrick De Geest	11/2018
9310	10^90401-368637	90401	Patrick De Geest	07/2019
9311	24900^4271+4271^24900	90401	Hans Havermann	08/2020
9312	4*5^129332+3	90400	Lelio R Paula	10/2014
9314	10^90397+19783	90398	Patrick De Geest	07/2019
9313	23380^7353+7353^23380	90398	Hans Havermann	08/2020
9316	10^90397-323	90397	Patrick De Geest	11/2018
9315	(2^300293+2762)/2	90397	Stefano Morozzi	01/2020
9317	24058^5719+5719^24058	90394	Hans Havermann	08/2020
9318	2^300249-16245	90384	Enzo Doria	04/2013
9319	24414^5035+5035^24414	90381	Hans Havermann	08/2020
9320	(7*10^90371-313)/9	90371	Robert Price	11/2016
9321	10^90363+58677	90364	Patrick De Geest	07/2019
9322	10^90363-3557	90363	Patrick De Geest	11/2018
9323	10^90358+104641	90359	Patrick De Geest	07/2019
9326	2*6^116118+7	90358	Lelio R Paula	10/2014
9325	10^90358-4979	90358	Patrick De Geest	11/2018
9324	10^90357+112837	90358	Patrick De Geest	07/2019
9327	10^90357-189593	90357	Patrick De Geest	07/2019
9328	10^90356+53113	90357	Patrick De Geest	07/2019
9329	10^90356-7197	90356	Patrick De Geest	11/2018
9330	10^90353+603211	90354	Patrick De Geest	07/2019
9331	10^90353-1089	90353	Patrick De Geest	11/2018
9332	(24737*2^300101+1)/25	90343	Lelio R Paula	06/2014
9333	4*10^90334-21	90335	Robert Price	04/2016
9334	(4546^24697-1)/4545	90329	Serge Batalov	08/2020
9335	10^90322+137691	90323	Patrick De Geest	07/2019
9336	10^90322-9551	90322	Patrick De Geest	11/2018
9337	10^90316+9991	90317	Patrick De Geest	11/2018
9338	(4550^24691-1)/4549	90317	Serge Batalov	08/2020
9339	10^90316-45627	90316	Patrick De Geest	07/2019
9340	10^90315+32889	90316	Patrick De Geest	07/2019
9342	2^300019-110335	90315	Enzo Doria	05/2014
9341	10^90315-8561	90315	Patrick De Geest	11/2018
9343	FAB2(300001,5032)	90310	Robert Price	05/2019
9344	FAB2(300001,29405)	90310	Robert Price	05/2019
9345	(2^299965+2774)/2	90299	Stefano Morozzi	01/2020
9346	23679^6506+6506^23679	90296	Hans Havermann	08/2020
9347	2^299949-1005	90294	Lelio R Paula	11/2013
9348	(2^299947+2054)/2	90293	Stefano Morozzi	01/2020
9349	21740^14229+14229^21740	90291	Hans Havermann	08/2020
9350	10^90279+62457	90280	Patrick De Geest	07/2019
9351	10^90279-1551	90279	Patrick De Geest	09/2018
9352	(2^299892+1986)/2	90277	Stefano Morozzi	01/2020
9353	(2^299893+3866)/2	90277	Stefano Morozzi	01/2020
9354	2^299868-109613	90270	Enzo Doria	04/2014
9355	10^90259+359299	90260	Patrick De Geest	07/2019
9356	10^90259-9443	90259	Patrick De Geest	09/2018
9357	(2^299831+3786)/2	90258	Stefano Morozzi	01/2020
9358	10^90252+102873	90253	Patrick De Geest	07/2019
9359	10^90252-8103	90252	Patrick De Geest	09/2018
9360	5*2^299799-3	90250	Lelio R Paula	08/2014
9361	(2^299803+3326)/2	90250	Stefano Morozzi	01/2020
9362	13^81008-2	90239	Lelio R Paula	09/2013
9363	80697!4-256	90234	Robert Price	11/2019
9365	64^49957-63^49957	90232	Robert Price	07/2013
9364	(2^299745+2994)/2	90232	Stefano Morozzi	01/2020
9366	10^90227+56281	90228	Patrick De Geest	06/2016
9370	2^299725+315	90227	Lelio R Paula	11/2013
9367	10^90227-1000000001	90227	Robert Price	05/2016
9368	10^90227-68763	90227	Patrick De Geest	06/2016
9369	9*10^90226+29	90227	Robert Price	03/2022
9371	5^129082+48	90225	Lelio R Paula	03/2016
9372	2^299699+195	90219	Lelio R Paula	10/2012
9373	(55*10^90211-1)/9	90212	Ray Chandler	02/2012
9374	22131^11918+11918^22131	90211	Hans Havermann	08/2020
9375	10^90209+8971	90210	Patrick De Geest	09/2018
9376	10^90209-724797	90209	Patrick De Geest	07/2019
9377	10^90208+189531	90209	Patrick De Geest	07/2019
9378	10^90208-2247	90208	Patrick De Geest	09/2018
9379	(629^32233-1)/628	90207	Michael Stocker	05/2020
9380	116^43693-115	90203	Norbert Schneider	08/2018
9381	10^90202+3553	90203	Patrick De Geest	09/2018
9382	3^189053+280	90202	Lelio R Paula	04/2016
9383	10^90202-67793	90202	Patrick De Geest	07/2019
9384	2^299639-187	90201	Lelio R Paula	10/2012
9385	10^90199+254031	90200	Patrick De Geest	07/2019
9386	10^90199-2891	90199	Patrick De Geest	09/2018
9388	2^299631+183	90198	Lelio R Paula	10/2012
9387	21567^15212+15212^21567	90198	Hans Havermann	08/2020
9389	10^90196+187539	90197	Patrick De Geest	07/2019
9391	10^90196-9683	90196	Patrick De Geest	09/2018
9390	21708^14287+14287^21708	90196	Hans Havermann	08/2020
9392	10^90193+104973	90194	Patrick De Geest	07/2019
9393	10^90193-9809	90193	Patrick De Geest	09/2018
9394	(21*2^299611-1)/29	90192	Lelio R Paula	02/2014
9395	(2277^26863-1)/2276	90186	Serge Batalov	08/2020
9396	2^299567+113	90179	Lelio R Paula	10/2012
9397	2^299550+189	90174	Lelio R Paula	10/2012
9398	10^90170+376063	90171	Patrick De Geest	07/2019
9399	10^90170-6749	90170	Patrick De Geest	09/2018
9400	(2^299535+3)/29	90168	Lelio R Paula	01/2013
9401	(2^299521+13)/15	90164	Stefano Morozzi	03/2020
9402	22316^10971+10971^22316	90163	Hans Havermann	08/2020
9403	10^90160+271947	90161	Patrick De Geest	07/2019
9404	10^90160-5613	90160	Patrick De Geest	09/2018
9405	(97*10^90155-1)/3	90157	Serge Batalov	12/2014
9406	(29*10^90153+583)/9	90154	Robert Price	06/2021
9408	3^188938+8680	90147	Lelio R Paula	04/2016
9407	10^90146+160209	90147	Patrick De Geest	07/2019
9409	10^90146-2027	90146	Patrick De Geest	09/2018
9410	6^115840-55	90142	Lelio R Paula	05/2016
9411	(5*10^90142-473)/9	90142	Robert Price	12/2017
9412	8*7^106659+5	90139	Lelio R Paula	10/2014
9413	2^299406-16653	90131	Enzo Doria	05/2013
9414	(317057^16384+1)/2	90131	Richard Fischer	10/2019
9415	(2^299409+834)/2	90131	Stefano Morozzi	01/2020
9416	10^90128+288673	90129	Patrick De Geest	07/2019
9418	208049#+(216091#)/(208049#)	90128	Makoto Morimoto	04/2016
9417	10^90128-8387	90128	Patrick De Geest	09/2018
9420	(F(5)^128941-F(4)^128941)/F(3)	90126	Wayne Halsdorf	03/2012
9419	(5^128941-3^128941)/2	90126	Kellen Shenton	05/2022
9421	6^115819-53	90125	Lelio R Paula	05/2016
9422	10^90123+6313	90124	Patrick De Geest	09/2018
9423	6^115816-16853	90123	Enzo Doria	02/2013
9424	10^90123-22617	90123	Patrick De Geest	07/2019
9425	6^115813-23	90121	Lelio R Paula	05/2016
9426	2^299351-933075	90114	Paul Bourdelais	04/2021
9427	(22*10^90110+161)/3	90111	Robert Price	02/2017
9429	(2^299330-509203)/69	90106	Lelio R Paula	01/2013
9428	10^90105+915759	90106	Patrick De Geest	07/2019
9430	10^90105-767	90105	Patrick De Geest	09/2018
9431	10^90104+48189	90105	Patrick De Geest	07/2019
9432	(6050^23827-1)/6049	90105	Serge Batalov	08/2020
9434	10^90104-7703	90104	Patrick De Geest	09/2018
9435	10^90103+9159	90104	Patrick De Geest	09/2018
9433	(797*10^90102-23)/9	90104	Robert Price	01/2022
9436	10^90103-208457	90103	Patrick De Geest	07/2019
9437	10^90102+73011	90103	Patrick De Geest	07/2019
9438	10^90102-602433	90102	Patrick De Geest	07/2019
9439	10^90101+1225537	90102	Patrick De Geest	07/2019
9441	10^90101-3207	90101	Patrick De Geest	09/2018
9440	21730^14007+14007^21730	90101	Hans Havermann	08/2020
9442	(29*10^90096-17)/3	90097	Erik Branger	09/2014
9443	(49*10^90094+221)/9	90095	Robert Price	02/2022
9444	10^90089+143181	90090	Patrick De Geest	07/2019
9445	10^90089-3573	90089	Patrick De Geest	09/2018
9446	2^299247+1870529	90083	Enzo Doria	05/2016
9447	10^90079+1609	90080	Patrick De Geest	09/2018
9448	10^90079-230043	90079	Patrick De Geest	07/2019
9449	2^299229-2797783	90077	Enzo Doria	04/2016
9450	2^299220-16317	90075	Enzo Doria	04/2013
9451	11^86491-1350	90072	Enzo Doria	12/2012
9452	10^90071+52333	90072	Patrick De Geest	07/2019
9454	10^90071-1233	90071	Patrick De Geest	09/2018
9453	(314401^16384+1)/2	90071	Richard Fischer	10/2019
9455	10^90069+158527	90070	Patrick De Geest	07/2019
9456	10^90069-7841	90069	Patrick De Geest	09/2018
9457	(31*10^90064-1)/3	90066	Robert Price	03/2017
9458	10^90060+149431	90061	Patrick De Geest	07/2019
9459	10^90060-839	90060	Patrick De Geest	09/2018
9460	10^90052+2361	90053	Patrick De Geest	09/2018
9461	10^90052-90929	90052	Patrick De Geest	07/2019
9462	10^90047+619	90048	Patrick De Geest	09/2018
9463	10^90047-151071	90047	Patrick De Geest	07/2019
9464	L(430949)/861899/1440387561539	90045	Serge Batalov	07/2017
9465	22996^8233+8233^22996	90043	Hans Havermann	08/2020
9466	2^299112+73951	90042	Enzo Doria	04/2016
9467	8^99702+7^(99702-1)	90040	Robert Price	02/2016
9468	10^90038+157803	90039	Patrick De Geest	07/2019
9469	10^90038-9687	90038	Patrick De Geest	09/2018
9471	5*10^90033+3	90034	Dmitry Domanov	11/2010
9470	(17574^21211-1)/17573	90034	Serge Batalov	08/2020
9472	10^90030+225813	90031	Patrick De Geest	07/2019
9473	10^90030-1461	90030	Patrick De Geest	09/2018
9474	243^37738+37738^243	90029	Norbert Schneider	01/2015
9475	10^90025+70569	90026	Patrick De Geest	07/2019
9476	10^90025-8703	90025	Patrick De Geest	09/2018
9477	2^299048-113297	90023	Enzo Doria	07/2014
9478	10^90015+849	90016	Patrick De Geest	09/2018
9479	10^90015-228387	90015	Patrick De Geest	07/2019
9480	10^90010+6811	90011	Patrick De Geest	09/2018
9481	10^90010-183597	90010	Patrick De Geest	11/2018
9482	10^90009+58321	90010	Patrick De Geest	11/2018
9483	10^90008+847	90009	Patrick De Geest	09/2018
9484	10^90009-356013	90009	Patrick De Geest	11/2018
9485	25696^3183+3183^25696	90009	Hans Havermann	08/2020
9487	3^188648+92	90008	Lelio R Paula	12/2015
9486	10^90008-706049	90008	Patrick De Geest	11/2018
9488	5*2^298991+7	90006	Lelio R Paula	08/2014
9489	(25*2^298997+1)/3267	90005	Lelio R Paula	01/2013
9490	10^90000+8869	90001	Patrick De Geest	12/2009
9492	10^89999+82939	90000	Dirk Augustin	04/2007
9491	10^90000-140343	90000	Patrick De Geest	12/2009
9493	10^89999-194891	89999	Patrick De Geest	11/2009
9494	(2^298918+1798)/2	89983	Stefano Morozzi	01/2020
9495	19^70365-78	89980	Lelio R Paula	12/2015
9496	Phi(186062,10)/134609632483003347004451	89977	Makoto Kamada	04/2021
9497	NaturalLogarithmOf2(89973)	89973	Eric W. Weisstein	10/2015
9498	2^298852-64875	89964	Lelio R Paula	11/2013
9499	(2^298825+1010)/2	89955	Stefano Morozzi	01/2020
9500	18^71659+37	89952	Lelio R Paula	12/2015

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PRP Records

Probable Primes Top 10000

(291192 PRPs in the top)