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	19376^10365+10365^19376	77806	Hans Havermann	04/2020
8252	65^42916+28	77803	Lelio R Paula	01/2016
8253	(2^258405+3302)/2	77788	Stefano Morozzi	01/2020
8254	(89*10^77781-17)/9	77782	Robert Price	11/2015
8255	2^258382-110405	77781	Enzo Doria	05/2014
8257	5^111278-14996	77780	Enzo Doria	02/2013
8256	(2^258378+2314)/2	77780	Stefano Morozzi	01/2020
8258	14^67862+61	77779	Lelio R Paula	02/2015
8259	10^77777+48483	77778	Patrick De Geest	11/2010
8260	10^77777-183243	77777	Patrick De Geest	11/2010
8261	(27*2^258352+1)/43	77772	Lelio R Paula	08/2012
8262	(22329^17881-1)/22328	77758	Serge Batalov	08/2020
8263	(2^258294+2454)/2	77754	Stefano Morozzi	01/2020
8264	337^30756-10002	77740	Enzo Doria	07/2012
8265	10^77726+99	77727	Robert Price	03/2011
8266	10^77726-85947	77726	Patrick De Geest	06/2013
8267	89^39870-2	77723	Lelio R Paula	08/2013
8268	7^91966-32	77721	Lelio R Paula	02/2015
8269	35^50327+2	77709	Lelio R Paula	05/2013
8270	24^56298+23	77704	Norbert Schneider	12/2016
8271	(2^258128+3502)/2	77704	Stefano Morozzi	01/2020
8273	(2^258105+78557)/19	77697	Lelio R Paula	10/2012
8272	(2^258102+2842)/2	77697	Stefano Morozzi	01/2020
8274	2^258079+179	77690	Lelio R Paula	03/2012
8276	2^258062-113111	77685	Enzo Doria	07/2014
8275	(21752^17911-1)/21751	77685	Serge Batalov	08/2020
8277	(2^258022+2422)/2	77673	Stefano Morozzi	01/2020
8278	10^77669+123456789	77670	Robert Price	10/2019
8279	10^77669+59127	77670	Patrick De Geest	12/2019
8280	10^77669-109103	77669	Patrick De Geest	12/2019
8281	(2^258002+3822)/2	77667	Stefano Morozzi	01/2020
8282	80^40807-79	77660	Norbert Schneider	03/2015
8283	70385!4-4	77658	Robert Price	11/2019
8284	(10^77637+359)/9	77637	Serge Batalov	12/2014
8285	2^257862-165	77625	Lelio R Paula	03/2012
8286	(25*2^257853+1)/3	77623	Lelio R Paula	07/2012
8287	(2^257832+1362)/2	77615	Stefano Morozzi	01/2020
8288	(2^257869+1)/(3*18645362967379)	77613	Henri Lifchitz	04/2005
8289	6^99728+71	77604	Lelio R Paula	01/2015
8290	2^257778-112767	77599	Enzo Doria	06/2014
8291	(31*2^257771+1)/537	77596	Lelio R Paula	07/2012
8292	(2^257762+2214)/2	77594	Stefano Morozzi	01/2020
8293	2^257729-73	77585	Lelio R Paula	03/2012
8294	(2^257728+1890)/2	77584	Stefano Morozzi	01/2020
8296	2^257689-63	77573	Lelio R Paula	03/2012
8295	(47*10^77572+493)/9	77573	Robert Price	11/2017
8297	(78557*2^257665+1)/6108725	77564	Lelio R Paula	06/2014
8298	(5570^20707-1)/5569	77562	Serge Batalov	08/2020
8299	(3^162563+8)/2885	77559	Lelio R Paula	10/2012
8301	2^257636-110235	77557	Enzo Doria	05/2014
8302	(23*10^77556+97)/3	77557	Robert Price	02/2017
8300	(2^257639+2630)/2	77557	Stefano Morozzi	01/2020
8303	(2^257625+3354)/2	77553	Stefano Morozzi	01/2020
8304	2^257621-110071	77552	Enzo Doria	04/2014
8305	19580^9129+9129^19580	77546	Hans Havermann	03/2020
8306	2^257567-64875	77536	Lelio R Paula	06/2013
8307	(18098^18211-1)/18097	77532	Serge Batalov	08/2020
8308	(2^257429+2394)/2	77494	Stefano Morozzi	01/2020
8309	(2^257373+1206)/2	77477	Stefano Morozzi	01/2020
8310	2*7^91674+9	77474	Lelio R Paula	10/2014
8311	(2^257248+2442)/2	77440	Stefano Morozzi	01/2020
8312	(17*10^77427-47)/3	77428	Robert Price	05/2017
8313	10^77418+841683	77419	Patrick De Geest	06/2013
8314	10^77418-33	77418	Robert Price	05/2011
8315	19^60539-36	77415	Lelio R Paula	03/2015
8316	(9562^19447-1)/9561	77406	Serge Batalov	08/2020
8317	37401!!-1024	77397	Robert Price	11/2015
8318	(2^257095+1410)/2	77394	Stefano Morozzi	01/2020
8319	11^74313-18750	77390	Enzo Doria	12/2012
8320	2^257044-112883	77378	Enzo Doria	06/2014
8321	8*10^77377+51	77378	Robert Price	05/2017
8322	Phi(258121,2)/719	77375	Jeppe Stig Nielsen	09/2020
8323	2*7^91553+9	77372	Lelio R Paula	10/2014
8324	713^27118+27118^713	77371	Norbert Schneider	12/2016
8325	(22711^17761-1)/22710	77367	Serge Batalov	08/2020
8326	18652^14043+14043^18652	77359	Hans Havermann	03/2020
8327	(11391^19069-1)/11390	77351	Serge Batalov	08/2020
8328	6*10^77346-29	77347	Robert Price	08/2020
8329	2^256920-111155	77341	Enzo Doria	05/2014
8330	2^256896-6555	77334	Lelio R Paula	06/2013
8331	(52*10^77322-7)/9	77323	Robert Price	12/2014
8332	2^256849-112939	77320	Enzo Doria	06/2014
8333	17275^18246+18246^17275	77316	Norbert Schneider	01/2020
8334	(4*10^77309-31)/9	77309	Erik Branger	05/2011
8335	20936^4923+4923^20936	77301	Hans Havermann	04/2020
8336	(25376^17551-1)/25375	77298	Serge Batalov	08/2020
8337	(3^161988+7)/41864	77284	Lelio R Paula	10/2012
8338	(14^67421-1)/13	77272	Paul Bourdelais	09/2008
8339	(2^256679+3554)/2	77268	Stefano Morozzi	01/2020
8341	5*3^161923-4	77258	Lelio R Paula	06/2014
8340	20465^5958+5958^20465	77258	Hans Havermann	02/2020
8342	(2^256591+954)/2	77242	Stefano Morozzi	01/2020
8343	24806^1299+1299^24806	77237	Hans Havermann	05/2020
8344	2^256552-1499	77230	Yves Minet	05/2013
8345	18339^16258+16258^18339	77227	Hans Havermann	04/2020
8346	21243^4316+4316^21243	77221	Hans Havermann	04/2020
8347	(2^256493+3126)/2	77212	Stefano Morozzi	01/2020
8348	2^256460-112757	77203	Enzo Doria	06/2014
8349	(2^256444+2578)/2	77198	Stefano Morozzi	01/2020
8350	2^256398+23299	77184	Yves Minet	02/2011
8351	2^256391-1155*256391	77182	Henri Lifchitz	03/2005
8352	(2^256391-9)/56593	77177	Lelio R Paula	10/2012
8353	(7665^19867-1)/7664	77170	Serge Batalov	08/2020
8354	(2^256338+3834)/2	77166	Stefano Morozzi	01/2020
8355	(2^256339+546)/2	77166	Stefano Morozzi	01/2020
8356	(2^256308+9)/10585	77153	Lelio R Paula	10/2012
8357	21^58348-2	77149	Lelio R Paula	08/2013
8358	(17*2^256291-1)/4785	77149	Lelio R Paula	02/2014
8359	(5*2^256274-1)/2141	77144	Lelio R Paula	02/2014
8360	(2^256244+2326)/2	77137	Stefano Morozzi	01/2020
8361	19^60321+82	77136	Lelio R Paula	03/2015
8362	5*2^256233-3	77135	Lelio R Paula	06/2014
8363	(2^256155+1566)/2	77111	Stefano Morozzi	01/2020
8364	3*2^256149+7	77110	Lelio R Paula	06/2014
8365	(2^256128+1890)/2	77102	Stefano Morozzi	01/2020
8366	3^161594-106	77100	Lelio R Paula	02/2015
8367	2^256114-185	77098	Lelio R Paula	03/2012
8368	8^85349-85349^8	77078	Norbert Schneider	05/2017
8369	2^256043-2786377	77077	Enzo Doria	03/2016
8370	2^255973+1869947	77056	Enzo Doria	05/2016
8371	12^71393-43	77046	Lelio R Paula	02/2015
8372	(2^255882+3630)/2	77028	Stefano Morozzi	01/2020
8373	15^65490+44	77023	Lelio R Paula	02/2015
8374	(3^161411-7)/940	77010	Lelio R Paula	10/2012
8375	lucasU(1107,1,25297)-lucasU(1107,1,25296)	77005	Mike Oakes	05/2009
8377	(570^27943-1)/569	77005	Serge Batalov	12/2016
8376	(570^27943-1)/(570-1)	77005	Michael Stocker	04/2020
8378	2^255750-75	76989	Lelio R Paula	03/2012
8379	3*6^98926-5	76980	Lelio R Paula	10/2014
8380	(2^255708+478)/2	76976	Stefano Morozzi	01/2020
8381	18^61320-1433	76974	Enzo Doria	03/2013
8382	6^98916-17093	76972	Enzo Doria	02/2013
8383	(2^255691+806)/2	76971	Stefano Morozzi	01/2020
8384	2^255659-110131	76962	Enzo Doria	04/2014
8385	69805!4-128	76956	Robert Price	11/2019
8386	12^71303+91	76949	Lelio R Paula	02/2015
8387	18^61298+59	76946	Lelio R Paula	02/2015
8388	(223^32768+1)/131074	76945	Lelio R Paula	02/2009
8389	(2^255613-5)/281517	76942	Lelio R Paula	10/2012
8390	18^61290-11	76936	Lelio R Paula	02/2015
8391	(2^255567+1286)/2	76934	Stefano Morozzi	01/2020
8393	63^42752-2	76926	Lelio R Paula	08/2013
8392	(11*2^255545-1)/117	76926	Lelio R Paula	02/2014
8394	2^255517+56387	76919	Yves Minet	02/2011
8395	(7*10^76916+89)/3	76917	Robert Price	08/2020
8396	18376^15329+15329^18376	76914	Hans Havermann	03/2020
8397	2^255499-112567	76913	Enzo Doria	06/2014
8398	2^255492+345	76911	Lelio R Paula	06/2013
8399	(2^255488+1678)/2	76910	Stefano Morozzi	01/2020
8400	10^76875+217591	76876	Patrick De Geest	05/2013
8402	10^76875-53	76875	Robert Price	05/2011
8401	11^73819-5880	76875	Enzo Doria	01/2013
8403	2^255313+18915	76857	Lelio R Paula	06/2013
8404	(2^255320-1017)/1446667	76853	Lelio R Paula	10/2012
8405	2^255296+5775	76852	Lelio R Paula	06/2013
8406	14^67052-29	76851	Lelio R Paula	02/2015
8407	(8*10^76840+43)/3	76841	Robert Price	10/2017
8408	(2^255246+1642)/2	76837	Stefano Morozzi	01/2020
8409	(2^255243+2250)/2	76836	Stefano Morozzi	01/2020
8410	(2^255240+1218)/2	76835	Stefano Morozzi	01/2020
8411	(7*10^76818-313)/9	76818	Robert Price	11/2016
8412	10^76801+69	76802	Robert Price	03/2011
8413	10^76801-80943	76801	Patrick De Geest	06/2013
8414	2^255105+57	76795	Lelio R Paula	03/2012
8415	(lucasV(1,2,510187)+2)/(3511)	76789	Mike Oakes	04/2017
8416	(2^255097-7)/20020055	76785	Lelio R Paula	10/2012
8417	(2^255063+3098)/2	76782	Stefano Morozzi	01/2020
8418	2^255055+1869353	76780	Enzo Doria	05/2016
8419	17^62396-90	76776	Lelio R Paula	03/2015
8420	18797^12130+12130^18797	76765	Hans Havermann	03/2020
8421	7^90833-60	76763	Lelio R Paula	02/2015
8422	13^68901-56	76752	Lelio R Paula	03/2015
8423	2^254961+1869917	76751	Enzo Doria	05/2016
8424	(2^254950+594)/2	76748	Stefano Morozzi	01/2020
8425	20734^5027+5027^20734	76743	Hans Havermann	03/2020
8426	9*5^109791-8	76742	Lelio R Paula	10/2014
8427	(469^28729-1)/468	76738	Serge Batalov	08/2020
8428	(2^254908+982)/2	76735	Stefano Morozzi	01/2020
8429	(2^254903+2766)/2	76734	Stefano Morozzi	01/2020
8430	(4143^21211-1)/4142	76724	Serge Batalov	08/2020
8431	82^40089+40089^82	76723	Serge Batalov	02/2012
8432	2^254861-2790013	76721	Enzo Doria	03/2016
8433	(10^278+1)*(10^115926+1)/(10^834+1)/(10^38642+1)/20459779741	76718	Makoto Kamada	03/2019
8434	10^76705+13	76706	Robert Price	01/2011
8435	10^76705-94077	76705	Patrick De Geest	06/2013
8436	(13709^18541-1)/13708	76701	Serge Batalov	08/2020
8437	(5*2^254785-1)/999	76696	Lelio R Paula	02/2014
8438	2^254758-110405	76690	Enzo Doria	05/2014
8439	(2^254721+470)/2	76679	Stefano Morozzi	01/2020
8440	2^254716-3779	76678	Yves Minet	04/2017
8441	2^254708-110507	76675	Enzo Doria	05/2014
8442	(47*10^76672+133)/9	76673	Robert Price	04/2017
8443	2^254670-112901	76664	Enzo Doria	06/2014
8444	(3^160665+7)/981350	76651	Lelio R Paula	10/2012
8445	2^254598-113183	76642	Enzo Doria	07/2014
8446	19^59932+22	76639	Lelio R Paula	01/2015
8447	77*10^76635+3	76637	Robert Price	06/2020
8448	2^254569-112213	76633	Enzo Doria	06/2014
8449	2*5^109626+9	76626	Lelio R Paula	10/2014
8450	2^254521+1872527	76619	Enzo Doria	05/2016
8451	(2^254515+2570)/2	76617	Stefano Morozzi	01/2020
8452	(76*10^76615+167)/9	76616	Robert Price	08/2016
8453	(2^254495+918)/2	76611	Stefano Morozzi	01/2020
8454	25^54799-24^54799	76606	Robert Price	07/2012
8455	(24737*2^254464+1)/9	76605	Lelio R Paula	06/2014
8456	25863^916+916^25863	76604	Hans Havermann	01/2020
8457	(2^254458+2398)/2	76600	Stefano Morozzi	01/2020
8458	(2^254434+1354)/2	76592	Stefano Morozzi	01/2020
8459	(2^254410+2842)/2	76585	Stefano Morozzi	01/2020
8460	19878^7121+7121^19878	76581	Hans Havermann	01/2020
8461	12^70961-85	76580	Lelio R Paula	02/2015
8462	18867^11452+11452^18867	76579	Hans Havermann	01/2020
8463	(2^254333+1806)/2	76562	Stefano Morozzi	01/2020
8464	7^90590-38	76558	Lelio R Paula	02/2015
8465	2^254304+5227	76554	Lelio R Paula	06/2013
8466	(76*10^76547-211)/9	76548	Robert Price	10/2017
8468	18^60979-5363	76546	Enzo Doria	03/2013
8467	(2^254278+3250)/2	76546	Stefano Morozzi	01/2020
8469	(19098^17881-1)/19097	76545	Serge Batalov	08/2020
8470	(21181*2^254264+1)/55314379	76538	Lelio R Paula	06/2014
8471	(34*10^76547-7)/9/61/94529/214807	76536	Makoto Morimoto	05/2016
8472	(7*10^76536-313)/9	76536	Robert Price	11/2016
8474	2^254239-27	76534	Lelio R Paula	03/2012
8473	2^254238-1841	76534	Yves Minet	03/2013
8475	(2^254235+3978)/2	76533	Stefano Morozzi	01/2020
8477	(10^76537-1)/9/66127969	76529	Jens K. Andersen	04/2009
8476	(2^254223+3938)/2	76529	Stefano Morozzi	01/2020
8478	2^254189-112225	76519	Enzo Doria	06/2014
8479	18^60938-1397	76494	Enzo Doria	03/2013
8481	2^254075-2788417	76485	Enzo Doria	03/2016
8480	18239^15612+15612^18239	76485	Hans Havermann	01/2020
8482	7*10^76483-23	76484	Robert Price	04/2016
8483	18471^13822+13822^18471	76481	Hans Havermann	01/2020
8484	18850^11407+11407^18850	76478	Hans Havermann	01/2020
8485	2^254042-112913	76475	Enzo Doria	06/2014
8486	14^66723-37	76474	Lelio R Paula	02/2015
8487	(2^254040+2970)/2	76474	Stefano Morozzi	01/2020
8488	2^254037-110305	76473	Enzo Doria	05/2014
8489	(2^254008+2290)/2	76464	Stefano Morozzi	01/2020
8490	15927^18196+18196^15927	76463	Norbert Schneider	12/2019
8491	(2^253979+1110)/2	76455	Stefano Morozzi	01/2020
8492	(1575^23911-1)/1574	76447	Serge Batalov	08/2020
8493	2^253931-111109	76441	Enzo Doria	05/2014
8494	2^253926-1167	76440	Lelio R Paula	05/2013
8495	(49*10^76438-13)/9	76439	Robert Price	07/2015
8496	(2^253876+1302)/2	76424	Stefano Morozzi	01/2020
8497	(21*2^253845-1)/143	76415	Lelio R Paula	02/2014
8498	10^76374+31	76375	Robert Price	03/2011
8499	10^76374-222159	76374	Patrick De Geest	05/2013
8500	(6300^20101-1)/6299	76367	Serge Batalov	08/2020

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