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 ?
6501	(2^398698+1138)/2	120020	Stefano Morozzi	09/2020
6502	2^398691-115057	120018	Enzo Doria	06/2015
6503	12134^29385-29385^12134	120009	Norbert Schneider	06/2025
6504	6089^31710-31710^6089	120008	Norbert Schneider	05/2025
6505	L(574219)	120005	Renaud Lifchitz	03/2004
6506	2^398571+60413	119982	Yves Minet	03/2011
6507	28623^15538+15538^28623	119971	Hans Havermann	02/2021
6508	p(24179)#/2-64	119949	Robert Price	04/2017
6509	2^398448+1872001	119945	Enzo Doria	05/2016
6510	(10^119946*19-91)/6093	119944	Alfred Reich	10/2023
6511	(19*10^119946-91)/9/677	119944	Alfred Reich	11/2023
6512	(191*10^119941-17)/3	119943	Robert Price	11/2021
6513	634^42803+42803^634	119938	Norbert Schneider	07/2019
6514	31083^7220+7220^31083	119935	Hans Havermann	01/2021
6515	(68*10^119931-11)/3	119933	Robert Price	01/2020
6516	8*10^119930-3	119931	Ray Chandler	04/2011
6517	(2^398398+774)/2	119930	Stefano Morozzi	09/2020
6518	(10^119880+179)/9	119880	Serge Batalov	12/2014
6519	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
6520	(10^119836+77)/3	119836	Robert Price	01/2018
6521	26681^27074-27074^26681	119835	Frank Doornink	03/2024
6522	28179^17870+17870^28179	119821	Hans Havermann	02/2021
6523	2^398029+1872527	119819	Enzo Doria	05/2016
6524	33142^4119+4119^33142	119802	Hans Havermann	01/2021
6525	2^397897-113541	119779	Enzo Doria	08/2014
6526	28636^15171+15171^28636	119728	Hans Havermann	02/2021
6527	87^61730-61730^87	119727	Norman Luhn	09/2024
6528	(10556^29929-1)/(10556^173-1)	119724	Ryan Propper	11/2023
6529	(2^397696+1042)/2	119719	Stefano Morozzi	09/2020
6531	(19*10^119716+101)/3	119717	Robert Price	09/2019
6530	29563^11208+11208^29563	119717	Hans Havermann	02/2021
6532	458^44991-44991^458	119715	Norman Luhn	09/2024
6533	2^397655-933075	119707	Paul Bourdelais	06/2021
6534	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
6535	28243^17308+17308^28243	119701	Hans Havermann	02/2021
6536	77*10^119688+3	119690	Robert Price	06/2020
6537	586*25^85601+3717	119668	Eric Chen	10/2023
6538	(2^397504+1698)/2	119661	Stefano Morozzi	09/2020
6539	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
6540	2^397426+73849	119638	Enzo Doria	04/2016
6541	8*10^119509+29	119510	Robert Price	11/2021
6542	2^396933-112723	119489	Enzo Doria	06/2014
6543	11^114738-150	119488	Enzo Doria	10/2012
6544	(4*10^119474+149)/9	119474	Robert Price	04/2018
6545	26964^26964-13^13	119472	Henri Lifchitz	08/2024
6546	11^114702+10	119450	Alfred Reich	04/2026
6547	2^396790-21	119446	Lelio R Paula	04/2013
6548	32061^5300+5300^32061	119405	Hans Havermann	01/2021
6549	(2^396633-7)/5	119398	Lelio R Paula	04/2014
6550	27382^22913+22913^27382	119388	Hans Havermann	03/2021
6551	(2^396577+2522)/2	119382	Stefano Morozzi	09/2020
6552	(2^396492+2230)/2	119356	Stefano Morozzi	01/2021
6553	(47*10^119354+259)/9	119355	Robert Price	03/2022
6555	105^59050+104	119352	Norbert Schneider	11/2016
6554	126^56824-125	119352	Norbert Schneider	12/2018
6556	2^396469+111546435	119350	Paul Bourdelais	10/2021
6557	139^55690-138	119345	Norbert Schneider	04/2019
6558	Phi(66220,p(66220))	119337	Henri Lifchitz	12/2025
6559	Phi(132889,-9)	119334	Henri Lifchitz	12/2025
6560	790^41179+41179^790	119322	Norbert Schneider	04/2019
6561	2^396374+73729	119321	Enzo Doria	04/2016
6563	88*10^119295+3	119297	Robert Price	05/2020
6562	21*29^81575+129664	119297	Eric Chen	06/2025
6564	2^396258-459491	119286	Enzo Doria	05/2015
6565	(2^396248+3126)/2	119283	Stefano Morozzi	09/2020
6566	2^396128-396128-1	119247	Karsten Bonath	06/2018
6567	(893*10^119228+7)/9	119230	Robert Price	06/2021
6568	(31*10^119229+257)/9	119230	Robert Price	12/2021
6569	(28*10^119206-67)/3	119207	Robert Price	10/2020
6570	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
6571	11^114458+6	119196	Paul Bourdelais	02/2021
6572	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
6573	(2^395902+202)/2	119179	Stefano Morozzi	09/2020
6574	(2^395825+582)/2	119155	Stefano Morozzi	09/2020
6575	(2^395733+1130)/2	119128	Stefano Morozzi	09/2020
6576	(23^119099)%(10^119099)	119099	Henri Lifchitz	05/2025
6577	29548^10725+10725^29548	119091	Hans Havermann	02/2021
6578	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
6580	(30^80599+1)/31	119054	Robert Price	07/2013
6579	Phi(80599,-5#)	119054	Henri Lifchitz	12/2025
6581	(232*10^119047+17)/3	119049	Robert Price	04/2021
6582	(43*10^119024-403)/9	119025	Robert Price	01/2019
6583	(4*10^119021+47)/3	119022	Robert Price	01/2022
6584	fibonacci(569433)+3	119005	Jon Grantham	08/2023
6585	26603^26888-26888^26603	118978	Norbert Schneider	07/2021
6586	912^40193-40193^912	118972	Norman Luhn	09/2024
6587	681^41992-41992^681	118970	Norman Luhn	09/2024
6588	6*10^118964+43	118965	Robert Price	07/2020
6589	(8*10^118960+49)/3	118961	Robert Price	05/2020
6590	31253^6402+6402^31253	118959	Hans Havermann	02/2021
6591	(194*10^118925-17)/3	118927	Robert Price	09/2020
6592	2^395062-109121	118926	Enzo Doria	04/2014
6593	2^395055-4627	118924	Yves Minet	05/2019
6594	(2^395054+702)/2	118923	Stefano Morozzi	09/2020
6595	2^395018-224141	118913	Harrison Mesh	06/2022
6596	(2^395011+2526)/2	118910	Stefano Morozzi	09/2020
6597	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
6598	25771^26948-26948^25771	118872	Frank Doornink	02/2024
6599	374^46201-46201^374	118870	Norman Luhn	09/2024
6600	(2^394858+1018)/2	118864	Stefano Morozzi	09/2020
6601	(77*10^118862-149)/9	118863	Robert Price	03/2022
6602	(16*10^118852+77)/3	118853	Robert Price	03/2019
6603	fibonacci(568658)-2	118843	Jon Grantham	08/2023
6604	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
6605	10^118772+163599	118773	Patrick De Geest	02/2021
6607	10^118772-40000000001	118772	Robert Price	09/2020
6606	10^118772-207603	118772	Patrick De Geest	02/2021
6608	26842^26577+26577^26842	118763	Hans Havermann	02/2021
6609	(2^394513+2034)/2	118760	Stefano Morozzi	09/2020
6610	(2^394473+2774)/2	118748	Stefano Morozzi	02/2021
6611	27949^17710+17710^27949	118734	Hans Havermann	02/2021
6612	2^394266+71389	118686	Enzo Doria	04/2016
6613	(10^118681-3^118681)/7	118681	Jon Grantham	08/2023
6614	2^394215-51261	118671	Tony Prest / Never Odd Or Even	04/2018
6615	(2^394215-48793)/5/5	118670	Tony Prest / Never Odd Or Even	04/2018
6616	(2^394215-17063)/3/3/5	118669	Tony Prest / Never Odd Or Even	04/2018
6617	(2^394215-24393)/5/5/5/5/5	118668	Tony Prest / Never Odd Or Even	04/2018
6618	(2^394215-35885)/3/71/173	118666	Tony Prest / Never Odd Or Even	04/2018
6619	(2^394215-47925)/353/2269	118665	Tony Prest / Never Odd Or Even	04/2018
6620	29201^11568+11568^29201	118652	Hans Havermann	02/2021
6621	(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673	118650	Tony Prest / Never Odd Or Even	04/2018
6622	(2^394131+2214)/2	118645	Stefano Morozzi	09/2020
6623	(17*10^118635+13)/3	118636	Robert Price	01/2019
6624	5^169727+2	118635	Lelio R Paula	08/2013
6625	2^394034-3	118617	M. Frind & P. Underwood	09/2002
6626	(7*10^118607+179)/3	118608	Robert Price	09/2018
6627	3^248572-6242	118599	Enzo Doria	05/2014
6628	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
6629	(49*10^118576-319)/9	118577	Robert Price	10/2021
6630	7^140303-6	118570	Robert Price	11/2014
6631	(2^393864+2686)/2	118565	Stefano Morozzi	09/2020
6632	(2^393862+3150)/2	118564	Stefano Morozzi	09/2020
6633	(2^393849+3762)/2	118561	Stefano Morozzi	01/2021
6634	(529*10^118554-7)/9	118556	Robert Price	08/2021
6635	26712^26777-26777^26712	118534	Norbert Schneider	07/2021
6636	(2^393661+2666)/2	118504	Stefano Morozzi	09/2020
6637	(2^393650+1614)/2	118501	Stefano Morozzi	09/2020
6638	27655^19264+19264^27655	118495	Hans Havermann	02/2021
6639	10^118485+469413	118486	Patrick De Geest	05/2021
6640	10^118485-50001	118485	Robert Price	08/2020
6641	(2^393528+1030)/2	118464	Stefano Morozzi	09/2020
6642	2^393427+75683	118434	Enzo Doria	04/2016
6643	2^393376-114749	118418	Enzo Doria	04/2015
6644	(65*10^118417+493)/9	118418	Robert Price	08/2021
6645	30960^6671+6671^30960	118397	Hans Havermann	02/2021
6646	(2^393234+2010)/2	118375	Stefano Morozzi	09/2020
6647	(2^393205+3030)/2	118367	Stefano Morozzi	09/2020
6648	(2^393191+2174)/2	118362	Stefano Morozzi	09/2020
6649	2^393180+73	118359	Lelio R Paula	04/2013
6650	3*2^393125+5	118343	Jon Grantham	07/2023
6651	27546^19771+19771^27546	118339	Hans Havermann	02/2021
6652	822^40595-40595^822	118330	Norman Luhn	09/2024
6653	p(23881)#/2+256	118328	Robert Price	05/2017
6654	(10^118324+359)/9	118324	Serge Batalov	12/2014
6655	(2^393048+570)/2	118319	Stefano Morozzi	09/2020
6656	p(23879)#/2+64	118317	Robert Price	03/2017
6657	2^393033+20147	118315	Enzo Doria	08/2023
6658	8*10^118308+59	118309	Robert Price	11/2021
6659	Phi(186197,5)	118308	Henri Lifchitz	12/2025
6660	9*10^118282+29	118283	Robert Price	03/2022
6661	(9*35^76602+12877)/34	118279	Eric Chen	05/2025
6662	(238*10^118265-1)/3	118267	Robert Price	04/2020
6664	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
6663	(2^392707+1710)/2	118217	Stefano Morozzi	09/2020
6665	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
6666	Phi(89679,-100)	118192	Henri Lifchitz	12/2025
6667	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
6668	(2^392567+2750)/2	118175	Stefano Morozzi	01/2021
6669	55*10^118172+3	118174	Robert Price	07/2022
6670	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
6671	27185^22222+22222^27185	118168	Hans Havermann	01/2021
6672	2^392516-29219	118160	Enzo Doria	07/2015
6673	66*10^118155+7	118157	Robert Price	07/2020
6674	Phi(177231,10)	118152	Maksym Voznyy	09/2015
6675	2^392413-112123	118129	Enzo Doria	06/2014
6676	27491^19798+19798^27491	118119	Hans Havermann	02/2021
6677	(49*10^118109-319)/9	118110	Robert Price	10/2021
6678	(2^392342+5)/27	118106	Lelio R Paula	04/2014
6679	(2^392333+1782)/2	118104	Stefano Morozzi	01/2021
6680	2^392300-1841429	118095	Enzo Doria	06/2015
6681	3*2^392260-5	118083	Jon Grantham	07/2023
6682	2^392220+75241	118070	Enzo Doria	04/2016
6683	27836^17409+17409^27836	118047	Hans Havermann	02/2021
6684	(13^118026)%(10^118026)	118026	Henri Lifchitz	05/2025
6685	10^118009+664447	118010	Patrick De Geest	07/2018
6686	10^118009-20001	118009	Robert Price	01/2018
6687	(14*10^117991+61)/3	117992	Robert Price	12/2018
6688	2^391933+5897	117984	Yves Minet	02/2011
6689	2^391912-1849259	117978	Enzo Doria	08/2015
6690	(2*34^77029+1043)/11	117968	Eric Chen	08/2023
6691	5*2^391836-3	117956	Jon Grantham	07/2023
6692	28357^14440+14440^28357	117953	Hans Havermann	02/2021
6693	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
6694	85^61124-61124^85	117934	Norman Luhn	09/2024
6695	(7*10^117930-79)/9	117930	Robert Price	01/2021
6696	27531^19168+19168^27531	117904	Hans Havermann	02/2021
6697	(46*10^117902+683)/9	117903	Robert Price	03/2019
6698	26349^26668-26668^26349	117893	Frank Doornink	03/2024
6699	27670^18189+18189^27670	117869	Hans Havermann	02/2021
6700	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
6701	(56*10^117856+583)/9	117857	Robert Price	08/2021
6702	32169^4606+4606^32169	117846	Hans Havermann	02/2021
6703	(71*10^117803-143)/9	117804	Robert Price	10/2021
6704	2^391324+90901	117801	Yves Minet	02/2011
6705	2^391301-1859923	117794	Enzo Doria	03/2016
6706	2^391261-4131	117782	Yves Minet	02/2018
6707	(2^391211+554)/2	117766	Stefano Morozzi	09/2020
6708	816^40445-40445^816	117764	Norman Luhn	09/2024
6709	38434^1157+1157^38434	117737	Hans Havermann	01/2021
6710	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
6711	(85*10^117719+473)/9	117720	Robert Price	01/2020
6712	(2^391049+582)/2	117718	Stefano Morozzi	09/2020
6713	(21*23^86445-197)/22	117715	Eric Chen	08/2023
6714	31083^6122+6122^31083	117709	Hans Havermann	02/2021
6715	2^390960+1880881	117691	Enzo Doria	11/2016
6716	(71*10^117685+91)/9	117686	Robert Price	04/2022
6718	2^390897-1860553	117672	Enzo Doria	11/2015
6717	(61*10^117671+47)/9	117672	Robert Price	07/2022
6719	2^390889-115003	117670	Enzo Doria	06/2015
6720	12^109010+35	117642	Riley Fisher	08/2023
6721	2^390779-30337	117637	Paul Bourdelais	02/2012
6722	(2^390735+378)/2	117623	Stefano Morozzi	02/2021
6723	11^112916-780	117590	Enzo Doria	12/2012
6724	27641^17916+17916^27641	117564	Hans Havermann	02/2021
6725	27906^16321+16321^27906	117561	Hans Havermann	02/2021
6726	27294^20275+20275^27294	117555	Hans Havermann	02/2021
6727	(2^390473+1002)/2	117544	Stefano Morozzi	09/2020
6728	35912^1875+1875^35912	117541	Hans Havermann	02/2021
6729	(16^97613-5^97613)/11	117537	Robert Price	07/2013
6730	(2^390438+1774)/2	117534	Stefano Morozzi	01/2021
6731	(2^390418+1722)/2	117528	Stefano Morozzi	09/2020
6732	(2^390403+654)/2	117523	Stefano Morozzi	09/2020
6733	(2^390343+2246)/2	117505	Stefano Morozzi	01/2021
6734	28043^15478+15478^28043	117493	Hans Havermann	02/2021
6735	Phi(247237,3)	117487	Henri Lifchitz	12/2025
6736	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
6737	37077^1474+1474^37077	117479	Hans Havermann	01/2021
6738	31^78759-30	117459	Theodore Burton	02/2007
6739	(2^390176+1222)/2	117455	Stefano Morozzi	09/2020
6740	(2^390133+1242)/2	117442	Stefano Morozzi	09/2020
6741	(2^390013+2634)/2	117406	Stefano Morozzi	09/2020
6742	3*10^117402+61	117403	Robert Price	09/2020
6743	2^389998+37	117402	Lelio R Paula	03/2013
6744	(2^389977+314)/2	117395	Stefano Morozzi	09/2020
6745	(2^389921+342)/2	117378	Stefano Morozzi	01/2021
6746	71830^43+43^71830	117333	Hans Havermann	01/2021
6747	(2^389768+1582)/2	117332	Stefano Morozzi	09/2020
6748	33802^2951+2951^33802	117292	Hans Havermann	02/2021
6749	(2^561185)%L(561185)	117281	Henri Lifchitz	05/2025
6750	26789^23866+23866^26789	117277	Hans Havermann	02/2021

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