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 ?
8251	(2^319777+2082)/2	96263	Stefano Morozzi	09/2020
8252	(2^319771+3686)/2	96261	Stefano Morozzi	09/2020
8253	2^319713-81	96244	Lelio R Paula	11/2012
8254	(55459*2^319706+1)/20167	96242	Lelio R Paula	07/2014
8255	22834^16393+16393^22834	96238	Hans Havermann	05/2020
8256	8*10^96236+27	96237	Robert Price	09/2021
8257	12^89153-43	96213	Lelio R Paula	06/2016
8258	(25048^21871-1)/25047	96202	Serge Batalov	06/2022
8260	(2*10^96195-59)/3	96195	Robert Price	05/2017
8259	9*10^96194-77	96195	Robert Price	08/2020
8261	2^319545+147	96193	Lelio R Paula	11/2012
8262	23357^13128+13128^23357	96189	Hans Havermann	02/2020
8263	(19838^22381-1)/19837	96179	Serge Batalov	06/2022
8264	(221^41023-1)/220	96172	Serge Batalov	06/2022
8265	25952^5073+5073^25952	96160	Hans Havermann	12/2019
8266	(50891^20431-1)/50890	96157	Serge Batalov	06/2022
8267	(50^56597+1)/51	96155	Robert Price	03/2014
8268	22313^20374+20374^22313	96149	Hans Havermann	12/2019
8269	22279^20668+20668^22279	96141	Hans Havermann	11/2019
8270	(41*10^96137-59)/9	96138	Robert Price	10/2017
8271	2^319353-110343	96135	Enzo Doria	05/2014
8272	11^92309-42	96130	Lelio R Paula	05/2016
8273	(21675^22171-1)/21674	96129	Serge Batalov	06/2022
8274	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
8275	(7*10^96112+143)/3	96113	Robert Price	04/2016
8276	26731^3940+3940^26731	96112	Hans Havermann	07/2020
8277	22640^17583+17583^22640	96109	Hans Havermann	07/2020
8278	(19178^22441-1)/19177	96107	Serge Batalov	06/2022
8279	2^319237+65835	96100	Lelio R Paula	03/2016
8280	2^319194-1841	96087	Yves Minet	03/2013
8281	23949^10280+10280^23949	96084	Hans Havermann	07/2020
8282	(1927^29251-1)/1926	96083	Serge Batalov	06/2022
8283	20^73847-31	96078	Lelio R Paula	05/2016
8284	(60229^20101-1)/60228	96075	Serge Batalov	06/2022
8285	(28044^21601-1)/28043	96074	Serge Batalov	06/2022
8286	50^56543-49	96065	Norbert Schneider	09/2018
8287	2^319107-109555	96061	Enzo Doria	04/2014
8288	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
8289	2^319098-112157	96059	Enzo Doria	06/2014
8290	15^81673+94	96055	Lelio R Paula	07/2016
8291	(85761^19471-1)/85760	96052	Serge Batalov	06/2022
8292	2^319074+1871749	96051	Enzo Doria	05/2016
8293	25670^5517+5517^25670	96050	Hans Havermann	06/2020
8294	6*10^96037+19	96038	Robert Price	11/2021
8295	2^319007-112111	96031	Enzo Doria	06/2014
8296	(57987^20161-1)/57986	96029	Serge Batalov	06/2022
8298	2^318946-1421	96013	Yves Minet	01/2013
8297	(68310^19861-1)/68309	96013	Serge Batalov	06/2022
8299	(20294^22291-1)/20293	96012	Serge Batalov	06/2022
8300	(304^38669-1)/303	96008	Serge Batalov	06/2022
8301	(1840^29401-1)/1839	95986	Serge Batalov	06/2022
8302	22830^16003+16003^22830	95982	Hans Havermann	02/2020
8303	2^318834-110411	95979	Enzo Doria	05/2014
8304	2^318831-1965	95978	Lelio R Paula	03/2016
8305	(5*10^95976+7)/3	95977	Erik Branger	03/2014
8306	(12797^23369-1)/12796	95975	Serge Batalov	06/2022
8307	(10534^23857-1)/10533	95963	Serge Batalov	06/2022
8308	22871^15696+15696^22871	95962	Hans Havermann	01/2020
8309	(2^318760+858)/2	95957	Stefano Morozzi	02/2021
8310	23167^13860+13860^23167	95953	Hans Havermann	01/2020
8311	(823^32911-1)/822	95946	Serge Batalov	06/2022
8313	5*3^201089-8	95945	Lelio R Paula	08/2014
8312	(81783^19531-1)/81782	95945	Serge Batalov	06/2022
8314	2^318711-139	95942	Lelio R Paula	11/2012
8315	2^318635-1167	95919	Lelio R Paula	03/2016
8316	15^81555+16	95917	Lelio R Paula	07/2016
8317	(37*10^95895+377)/9	95896	Robert Price	10/2017
8318	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
8319	2^318496-97305	95877	Lelio R Paula	03/2016
8320	22129^21496+21496^22129	95871	Hans Havermann	07/2020
8322	2^318466+15015	95868	Lelio R Paula	03/2016
8321	24847^7216+7216^24847	95868	Hans Havermann	07/2020
8323	23706^11065+11065^23706	95866	Hans Havermann	07/2020
8324	(2863^27733-1)/2862	95865	Serge Batalov	06/2022
8325	6^123187-173129	95859	Mike Oakes	04/2011
8326	2^318423-487	95855	Yves Minet	03/2012
8327	10^95848-5000000001	95848	Robert Price	09/2022
8328	(2^318359+678)/2	95836	Stefano Morozzi	09/2020
8329	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
8330	(8060^24533-1)/8059	95831	Serge Batalov	06/2022
8331	(9853^23993-1)/9852	95814	Serge Batalov	06/2022
8333	(2^318267+2550)/2	95808	Stefano Morozzi	09/2020
8332	(5048^25873-1)/5047	95808	Serge Batalov	06/2022
8335	4*10^95799+13	95800	Robert Price	02/2021
8334	(65533^19891-1)/65532	95800	Serge Batalov	06/2022
8336	45369!2+1024	95787	Robert Price	02/2015
8337	3^200758-86	95786	Lelio R Paula	05/2016
8338	(2^318271+1)/(346031404238891654090604244843)	95781	Gord Palameta	12/2018
8339	(2^318171+2030)/2	95779	Stefano Morozzi	09/2020
8340	3*10^95776-59	95777	Robert Price	10/2017
8341	(82970^19471-1)/82969	95772	Serge Batalov	06/2022
8342	193^41901-2	95768	Lelio R Paula	10/2017
8343	(2^318124+2502)/2	95765	Stefano Morozzi	09/2020
8344	(12900^23297-1)/12899	95761	Serge Batalov	06/2022
8345	4*10^95752-71	95753	Robert Price	11/2017
8346	(16955^22639-1)/16954	95743	Serge Batalov	06/2022
8347	(81795^19489-1)/81794	95740	Serge Batalov	06/2022
8348	(2742^27847-1)/2741	95737	Serge Batalov	06/2022
8349	(6072^25303-1)/6071	95726	Serge Batalov	06/2022
8350	23640^11197+11197^23640	95721	Hans Havermann	12/2019
8351	10^95712+89329	95713	Patrick De Geest	09/2022
8353	10^95712-4000001	95712	Robert Price	07/2021
8352	10^95712-989313	95712	Patrick De Geest	09/2022
8354	(60657^20011-1)/60656	95706	Serge Batalov	06/2022
8355	((10^47850-1)10000/9+6421)10^47850+(10^47850-1)/9	95704	Hans Havermann	05/2019
8356	(509203*2^317881-1)/52805	95693	Lelio R Paula	04/2015
8357	(26161^21661-1)/26160	95687	Serge Batalov	06/2022
8358	(2^317853+1086)/2	95683	Stefano Morozzi	09/2020
8359	4*10^95672+91	95673	Robert Price	11/2017
8360	6*10^95665+43	95666	Robert Price	07/2020
8361	(20819^22153-1)/20818	95663	Serge Batalov	06/2022
8362	(64464^19891-1)/64463	95658	Serge Batalov	06/2022
8363	(934^32203-1)/933	95652	Serge Batalov	06/2022
8364	(11*10^95641-113)/3	95642	Robert Price	01/2017
8365	(72330^19681-1)/72329	95632	Serge Batalov	06/2022
8366	(13224^23203-1)/13223	95624	Serge Batalov	06/2022
8367	(18211^22441-1)/18210	95602	Serge Batalov	06/2022
8368	(71975^19681-1)/71974	95590	Serge Batalov	06/2022
8369	(13*10^95588+11)/3	95589	Robert Price	05/2015
8370	Phi(191188,10)/191189	95587	Maksym Voznyy	11/2015
8371	(13368^23167-1)/13367	95585	Serge Batalov	06/2022
8372	(25874^21661-1)/25873	95583	Serge Batalov	06/2022
8373	3^200325+70	95580	Lelio R Paula	05/2016
8374	(25*10^95574-7)/9	95575	Robert Price	12/2014
8375	(2^317485-3)/21313	95569	Lelio R Paula	06/2013
8376	2^317464+31	95567	Lelio R Paula	11/2012
8377	(2^317451+2114)/2	95562	Stefano Morozzi	09/2020
8378	7^113073+82	95558	Lelio R Paula	04/2016
8379	(24728^21751-1)/24727	95552	Serge Batalov	06/2022
8380	(49764^20341-1)/49763	95536	Serge Batalov	06/2022
8381	(36155^20959-1)/36154	95531	Serge Batalov	06/2022
8382	(7725^24571-1)/7724	95526	Serge Batalov	06/2022
8383	(20546^22147-1)/20545	95510	Serge Batalov	06/2022
8384	2^317251+465	95503	Lelio R Paula	03/2016
8385	19^74684+58	95503	Lelio R Paula	06/2016
8386	(2^317250-7)/339	95500	Lelio R Paula	07/2013
8387	5*10^95498-21	95499	Robert Price	12/2021
8388	(21615^22031-1)/21614	95495	Serge Batalov	06/2022
8389	6^122718-79	95494	Lelio R Paula	05/2016
8390	22168^20291+20291^22168	95485	Hans Havermann	10/2019
8391	(77427^19531-1)/77426	95481	Serge Batalov	06/2022
8392	(13026^23203-1)/13025	95472	Serge Batalov	06/2022
8393	2^317141-110491	95469	Enzo Doria	05/2014
8394	(2^317097+3014)/2	95456	Stefano Morozzi	09/2020
8395	2^317094+76309	95455	Enzo Doria	05/2016
8396	2^317085+95	95453	Lelio R Paula	11/2012
8397	(17*10^95451-377)/9	95452	Robert Price	11/2017
8398	2^317057-109551	95444	Enzo Doria	04/2014
8399	3^200026+28	95437	Lelio R Paula	05/2016
8400	2^317024+93	95434	Donovan Johnson	06/2008
8401	(86*10^95428-437)/9	95429	Robert Price	03/2021
8402	10^95427+192591	95428	Patrick De Geest	05/2021
8405	2^316999+1605	95427	Lelio R Paula	03/2016
8404	(2^317000+3210)/2	95427	Stefano Morozzi	09/2020
8403	10^95427-10001	95427	Robert Price	02/2021
8406	2^316995-110427	95426	Enzo Doria	05/2014
8407	(69841^19699-1)/69840	95420	Serge Batalov	06/2022
8408	(59242^19993-1)/59241	95415	Serge Batalov	06/2022
8410	22300^18987+18987^22300	95410	Hans Havermann	06/2020
8409	(9478^23993-1)/9477	95410	Serge Batalov	06/2022
8411	2^316937+177	95408	Lelio R Paula	11/2012
8412	4*10^95407+91	95408	Robert Price	11/2017
8413	2^316908+1915	95399	Lelio R Paula	03/2016
8414	2^316894+99	95395	Lelio R Paula	11/2012
8415	(2^316887+2546)/2	95393	Stefano Morozzi	09/2020
8416	2*10^95374-21	95375	Robert Price	09/2020
8417	6^122547+11	95361	Lelio R Paula	05/2016
8418	2^316771+82875	95358	Lelio R Paula	03/2016
8419	(15609^22741-1)/15608	95358	Serge Batalov	06/2022
8420	(2^316765+3102)/2	95356	Stefano Morozzi	09/2020
8421	(2267^28411-1)/2266	95329	Serge Batalov	06/2022
8422	(824^32693-1)/823	95328	Serge Batalov	06/2022
8423	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
8424	1*10^95326+57	95327	Robert Price	03/2011
8425	10^95326-393687	95326	Patrick De Geest	09/2013
8426	(3^199803+4)/479539	95325	Lelio R Paula	04/2013
8427	2^316654-109481	95323	Enzo Doria	04/2014
8428	8*10^95316+51	95317	Robert Price	05/2017
8429	(50^56099+43^56099)/93	95309	Serge Batalov	12/2016
8430	(23*2^316559+1)/3925	95292	Lelio R Paula	09/2013
8432	(71*10^95277-539)/9	95278	Robert Price	11/2017
8431	23422^11691+11691^23422	95278	Hans Havermann	10/2019
8433	19^74503-56	95271	Lelio R Paula	06/2016
8434	(5038^25733-1)/5037	95267	Serge Batalov	06/2022
8435	11^91475-4380	95262	Enzo Doria	01/2013
8436	(62*10^95251-611)/9	95252	Robert Price	05/2017
8437	(160090^18301-1)/160089	95240	Serge Batalov	06/2022
8438	(173205^18181-1)/173204	95238	Serge Batalov	06/2022
8439	(158710^18313-1)/158709	95234	Serge Batalov	06/2022
8440	(9979^23813-1)/9978	95227	Serge Batalov	06/2022
8441	(57376^20011-1)/57375	95223	Serge Batalov	06/2022
8442	(2^316321-509203)/69377	95218	Lelio R Paula	06/2013
8443	26541^3868+3868^26541	95216	Hans Havermann	07/2020
8444	(79*10^95214-43)/9	95215	Erik Branger	11/2013
8445	(7176^24691-1)/7175	95202	Anonymous	11/2020
8446	(9*2^316233-1)/1751	95194	Lelio R Paula	02/2014
8447	5*2^316213+9	95191	Lelio R Paula	08/2014
8448	2*10^95188-91	95189	Robert Price	04/2020
8449	2^316205-1848163	95188	Enzo Doria	07/2015
8450	2^316185-2787913	95182	Enzo Doria	04/2016
8451	(2^316174+3538)/2	95178	Stefano Morozzi	09/2020
8452	(9787*2^316142-1)/3	95172	Lelio R Paula	04/2015
8453	2^316140-5	95168	Henri Lifchitz	02/2006
8454	(15185*2^316117-1)/3	95165	Lelio R Paula	04/2015
8455	(34*10^95153-7)/9/19/19157	95149	Makoto Morimoto	05/2016
8456	2^316069+76817	95147	Enzo Doria	05/2016
8457	(199*10^95134-7)/3	95136	Robert Price	02/2017
8458	2^316027-97305	95134	Lelio R Paula	03/2016
8459	2^316006-2798051	95128	Enzo Doria	04/2016
8460	24994^6397+6397^24994	95127	Hans Havermann	02/2020
8462	2^315921-2797603	95102	Enzo Doria	04/2016
8461	(2^315921+1314)/2	95102	Stefano Morozzi	02/2021
8463	2*10^95095+63	95096	Robert Price	10/2017
8464	2^315857+1299	95083	Lelio R Paula	03/2016
8465	(2^315858+2598)/2	95083	Stefano Morozzi	09/2020
8467	14^82955-43	95078	Lelio R Paula	06/2016
8466	(8*10^95078-269)/9	95078	Robert Price	09/2021
8468	(23*10^95074-101)/3	95075	Robert Price	04/2021
8469	2^315827-933075	95074	Paul Bourdelais	04/2021
8470	(2*10^95072-17)/3	95072	Robert Price	08/2014
8471	(286*10^95059-1)/3	95061	Robert Price	11/2020
8472	(2^315779+1610)/2	95059	Stefano Morozzi	09/2020
8473	2^315775-111546435	95058	Paul Bourdelais	10/2021
8474	21938^21513+21513^21938	95051	Hans Havermann	09/2020
8475	2^315727+65	95044	Lelio R Paula	11/2012
8476	2^315725+1885757	95043	Enzo Doria	03/2017
8477	23277^12058+12058^23277	95000	Hans Havermann	09/2020
8478	1*10^94983+21	94984	Robert Price	03/2011
8479	10^94983-717	94983	Patrick De Geest	08/2013
8480	17^77187-82	94975	Lelio R Paula	07/2016
8481	3*10^94964+37	94965	Robert Price	10/2017
8482	(2^315481-1017)/20627285	94962	Lelio R Paula	06/2013
8483	2^315423-110329	94952	Enzo Doria	05/2014
8484	11^91169-7230	94943	Enzo Doria	02/2013
8485	7*10^94938+61	94939	Robert Price	02/2017
8486	2^315351+1025	94931	Lelio R Paula	03/2016
8487	2^315350-112253	94930	Enzo Doria	06/2014
8488	(2^315343+1766)/2	94928	Stefano Morozzi	09/2020
8489	(2^315343+3066)/2	94928	Stefano Morozzi	09/2020
8492	((1001327^(15817)+1)/1001328)	94906	Faysal YAtim	10/2010
8491	2^315268+7	94906	Lelio R Paula	10/2012
8490	11^91133+62	94906	Lelio R Paula	05/2016
8493	(2^315264+1558)/2	94904	Stefano Morozzi	09/2020
8494	30^64244+41	94897	Lelio R Paula	08/2012
8495	(151*10^94885-7)/9	94887	Robert Price	07/2017
8496	4^157583+22147	94875	Mike Oakes	01/2011
8497	2^315098+123	94854	Lelio R Paula	11/2012
8498	3^198791-34	94848	Robert Price	11/2013
8499	3*2^315067+7	94846	Lelio R Paula	08/2014
8500	(9*2^315057+1)/73	94841	Lelio R Paula	09/2013

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Probable Primes Top 10000

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