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	(2^399549+1062)/2	120276	Stefano Morozzi	09/2020
6502	2^399526-1861721	120270	Enzo Doria	11/2015
6503	12199^29430-29430^12199	120261	Norbert Schneider	08/2025
6504	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
6505	32016^5687+5687^32016	120217	Hans Havermann	01/2021
6506	(205*10^120212-1)/3	120214	Robert Price	11/2021
6507	13302^29149-29149^13302	120209	Norbert Schneider	08/2025
6508	2^399322-2798111	120208	Enzo Doria	04/2016
6509	30438^8867+8867^30438	120163	Hans Havermann	02/2021
6510	3^251841-5*2^251841	120159	Jon Grantham	08/2023
6512	72^64693-71^64693	120157	Robert Price	03/2014
6511	(17*10^120156-161)/9	120157	Robert Price	02/2021
6513	Phi(81997,-5#)	120150	Henri Lifchitz	12/2025
6514	2^399111-28489	120145	Enzo Doria	08/2015
6515	2958^34607-34607^2958	120121	Norbert Schneider	04/2025
6516	(2^399014+1318)/2	120115	Stefano Morozzi	02/2021
6517	30254^9333+9333^30254	120110	Hans Havermann	02/2021
6518	2^398972+6561	120103	Henri Lifchitz	10/2024
6519	30882^7745+7745^30882	120101	Hans Havermann	02/2021
6520	23687^27452-27452^23687	120090	Norbert Schneider	08/2025
6522	2^398877+105	120074	Donovan Johnson	01/2006
6521	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
6523	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
6524	U(686581)/4280145953	120067	Serge Batalov	07/2024
6525	16651^28442-28442^16651	120067	Norbert Schneider	07/2025
6526	12284^29359-29359^12284	120059	Norbert Schneider	06/2025
6527	3207^34240-34240^3207	120049	Norbert Schneider	04/2025
6528	2^398710+57	120024	Lelio R Paula	04/2013
6529	(2^398698+1138)/2	120020	Stefano Morozzi	09/2020
6530	2^398691-115057	120018	Enzo Doria	06/2015
6531	12134^29385-29385^12134	120009	Norbert Schneider	06/2025
6532	6089^31710-31710^6089	120008	Norbert Schneider	05/2025
6533	L(574219)	120005	Renaud Lifchitz	03/2004
6534	2^398571+60413	119982	Yves Minet	03/2011
6535	28623^15538+15538^28623	119971	Hans Havermann	02/2021
6536	p(24179)#/2-64	119949	Robert Price	04/2017
6537	2^398448+1872001	119945	Enzo Doria	05/2016
6538	(10^119946*19-91)/6093	119944	Alfred Reich	10/2023
6539	(19*10^119946-91)/9/677	119944	Alfred Reich	11/2023
6540	(191*10^119941-17)/3	119943	Robert Price	11/2021
6541	634^42803+42803^634	119938	Norbert Schneider	07/2019
6542	31083^7220+7220^31083	119935	Hans Havermann	01/2021
6543	(68*10^119931-11)/3	119933	Robert Price	01/2020
6544	8*10^119930-3	119931	Ray Chandler	04/2011
6545	(2^398398+774)/2	119930	Stefano Morozzi	09/2020
6546	(10^119880+179)/9	119880	Serge Batalov	12/2014
6547	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
6548	(10^119836+77)/3	119836	Robert Price	01/2018
6549	26681^27074-27074^26681	119835	Frank Doornink	03/2024
6550	28179^17870+17870^28179	119821	Hans Havermann	02/2021
6551	2^398029+1872527	119819	Enzo Doria	05/2016
6552	33142^4119+4119^33142	119802	Hans Havermann	01/2021
6553	2^397897-113541	119779	Enzo Doria	08/2014
6554	28636^15171+15171^28636	119728	Hans Havermann	02/2021
6555	87^61730-61730^87	119727	Norman Luhn	09/2024
6556	(10556^29929-1)/(10556^173-1)	119724	Ryan Propper	11/2023
6557	(2^397696+1042)/2	119719	Stefano Morozzi	09/2020
6559	(19*10^119716+101)/3	119717	Robert Price	09/2019
6558	29563^11208+11208^29563	119717	Hans Havermann	02/2021
6560	458^44991-44991^458	119715	Norman Luhn	09/2024
6561	2^397655-933075	119707	Paul Bourdelais	06/2021
6562	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
6563	28243^17308+17308^28243	119701	Hans Havermann	02/2021
6564	77*10^119688+3	119690	Robert Price	06/2020
6565	586*25^85601+3717	119668	Eric Chen	10/2023
6566	(2^397504+1698)/2	119661	Stefano Morozzi	09/2020
6567	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
6568	2^397426+73849	119638	Enzo Doria	04/2016
6569	8*10^119509+29	119510	Robert Price	11/2021
6570	2^396933-112723	119489	Enzo Doria	06/2014
6571	11^114738-150	119488	Enzo Doria	10/2012
6572	(4*10^119474+149)/9	119474	Robert Price	04/2018
6573	26964^26964-13^13	119472	Henri Lifchitz	08/2024
6574	11^114702+10	119450	Alfred Reich	04/2026
6575	2^396790-21	119446	Lelio R Paula	04/2013
6576	32061^5300+5300^32061	119405	Hans Havermann	01/2021
6577	(2^396633-7)/5	119398	Lelio R Paula	04/2014
6578	27382^22913+22913^27382	119388	Hans Havermann	03/2021
6579	(2^396577+2522)/2	119382	Stefano Morozzi	09/2020
6580	(2^396492+2230)/2	119356	Stefano Morozzi	01/2021
6581	(47*10^119354+259)/9	119355	Robert Price	03/2022
6583	105^59050+104	119352	Norbert Schneider	11/2016
6582	126^56824-125	119352	Norbert Schneider	12/2018
6584	2^396469+111546435	119350	Paul Bourdelais	10/2021
6585	139^55690-138	119345	Norbert Schneider	04/2019
6586	Phi(66220,p(66220))	119337	Henri Lifchitz	12/2025
6587	Phi(132889,-9)	119334	Henri Lifchitz	12/2025
6588	790^41179+41179^790	119322	Norbert Schneider	04/2019
6589	2^396374+73729	119321	Enzo Doria	04/2016
6591	88*10^119295+3	119297	Robert Price	05/2020
6590	21*29^81575+129664	119297	Eric Chen	06/2025
6592	2^396258-459491	119286	Enzo Doria	05/2015
6593	(2^396248+3126)/2	119283	Stefano Morozzi	09/2020
6594	2^396128-396128-1	119247	Karsten Bonath	06/2018
6595	(893*10^119228+7)/9	119230	Robert Price	06/2021
6596	(31*10^119229+257)/9	119230	Robert Price	12/2021
6597	(28*10^119206-67)/3	119207	Robert Price	10/2020
6598	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
6599	11^114458+6	119196	Paul Bourdelais	02/2021
6600	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
6601	(2^395902+202)/2	119179	Stefano Morozzi	09/2020
6602	(2^395825+582)/2	119155	Stefano Morozzi	09/2020
6603	(2^395733+1130)/2	119128	Stefano Morozzi	09/2020
6604	(23^119099)%(10^119099)	119099	Henri Lifchitz	05/2025
6605	29548^10725+10725^29548	119091	Hans Havermann	02/2021
6606	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
6608	(30^80599+1)/31	119054	Robert Price	07/2013
6607	Phi(80599,-5#)	119054	Henri Lifchitz	12/2025
6609	(232*10^119047+17)/3	119049	Robert Price	04/2021
6610	(43*10^119024-403)/9	119025	Robert Price	01/2019
6611	(4*10^119021+47)/3	119022	Robert Price	01/2022
6612	fibonacci(569433)+3	119005	Jon Grantham	08/2023
6613	26603^26888-26888^26603	118978	Norbert Schneider	07/2021
6614	912^40193-40193^912	118972	Norman Luhn	09/2024
6615	681^41992-41992^681	118970	Norman Luhn	09/2024
6616	6*10^118964+43	118965	Robert Price	07/2020
6617	(8*10^118960+49)/3	118961	Robert Price	05/2020
6618	31253^6402+6402^31253	118959	Hans Havermann	02/2021
6619	(194*10^118925-17)/3	118927	Robert Price	09/2020
6620	2^395062-109121	118926	Enzo Doria	04/2014
6621	2^395055-4627	118924	Yves Minet	05/2019
6622	(2^395054+702)/2	118923	Stefano Morozzi	09/2020
6623	2^395018-224141	118913	Harrison Mesh	06/2022
6624	(2^395011+2526)/2	118910	Stefano Morozzi	09/2020
6625	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
6626	25771^26948-26948^25771	118872	Frank Doornink	02/2024
6627	374^46201-46201^374	118870	Norman Luhn	09/2024
6628	(2^394858+1018)/2	118864	Stefano Morozzi	09/2020
6629	(77*10^118862-149)/9	118863	Robert Price	03/2022
6630	(16*10^118852+77)/3	118853	Robert Price	03/2019
6631	fibonacci(568658)-2	118843	Jon Grantham	08/2023
6632	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
6633	10^118772+163599	118773	Patrick De Geest	02/2021
6635	10^118772-40000000001	118772	Robert Price	09/2020
6634	10^118772-207603	118772	Patrick De Geest	02/2021
6636	26842^26577+26577^26842	118763	Hans Havermann	02/2021
6637	(2^394513+2034)/2	118760	Stefano Morozzi	09/2020
6638	(2^394473+2774)/2	118748	Stefano Morozzi	02/2021
6639	27949^17710+17710^27949	118734	Hans Havermann	02/2021
6640	2^394266+71389	118686	Enzo Doria	04/2016
6641	(10^118681-3^118681)/7	118681	Jon Grantham	08/2023
6642	2^394215-51261	118671	Tony Prest / Never Odd Or Even	04/2018
6643	(2^394215-48793)/5/5	118670	Tony Prest / Never Odd Or Even	04/2018
6644	(2^394215-17063)/3/3/5	118669	Tony Prest / Never Odd Or Even	04/2018
6645	(2^394215-24393)/5/5/5/5/5	118668	Tony Prest / Never Odd Or Even	04/2018
6646	(2^394215-35885)/3/71/173	118666	Tony Prest / Never Odd Or Even	04/2018
6647	(2^394215-47925)/353/2269	118665	Tony Prest / Never Odd Or Even	04/2018
6648	29201^11568+11568^29201	118652	Hans Havermann	02/2021
6649	(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673	118650	Tony Prest / Never Odd Or Even	04/2018
6650	(2^394131+2214)/2	118645	Stefano Morozzi	09/2020
6651	(17*10^118635+13)/3	118636	Robert Price	01/2019
6652	5^169727+2	118635	Lelio R Paula	08/2013
6653	2^394034-3	118617	M. Frind & P. Underwood	09/2002
6654	(7*10^118607+179)/3	118608	Robert Price	09/2018
6655	3^248572-6242	118599	Enzo Doria	05/2014
6656	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
6657	(49*10^118576-319)/9	118577	Robert Price	10/2021
6658	7^140303-6	118570	Robert Price	11/2014
6659	(2^393864+2686)/2	118565	Stefano Morozzi	09/2020
6660	(2^393862+3150)/2	118564	Stefano Morozzi	09/2020
6661	(2^393849+3762)/2	118561	Stefano Morozzi	01/2021
6662	(529*10^118554-7)/9	118556	Robert Price	08/2021
6663	26712^26777-26777^26712	118534	Norbert Schneider	07/2021
6664	(2^393661+2666)/2	118504	Stefano Morozzi	09/2020
6665	(2^393650+1614)/2	118501	Stefano Morozzi	09/2020
6666	27655^19264+19264^27655	118495	Hans Havermann	02/2021
6667	10^118485+469413	118486	Patrick De Geest	05/2021
6668	10^118485-50001	118485	Robert Price	08/2020
6669	(2^393528+1030)/2	118464	Stefano Morozzi	09/2020
6670	2^393427+75683	118434	Enzo Doria	04/2016
6671	2^393376-114749	118418	Enzo Doria	04/2015
6672	(65*10^118417+493)/9	118418	Robert Price	08/2021
6673	30960^6671+6671^30960	118397	Hans Havermann	02/2021
6674	(2^393234+2010)/2	118375	Stefano Morozzi	09/2020
6675	(2^393205+3030)/2	118367	Stefano Morozzi	09/2020
6676	(2^393191+2174)/2	118362	Stefano Morozzi	09/2020
6677	2^393180+73	118359	Lelio R Paula	04/2013
6678	3*2^393125+5	118343	Jon Grantham	07/2023
6679	27546^19771+19771^27546	118339	Hans Havermann	02/2021
6680	822^40595-40595^822	118330	Norman Luhn	09/2024
6681	p(23881)#/2+256	118328	Robert Price	05/2017
6682	(10^118324+359)/9	118324	Serge Batalov	12/2014
6683	(2^393048+570)/2	118319	Stefano Morozzi	09/2020
6684	p(23879)#/2+64	118317	Robert Price	03/2017
6685	2^393033+20147	118315	Enzo Doria	08/2023
6686	8*10^118308+59	118309	Robert Price	11/2021
6687	Phi(186197,5)	118308	Henri Lifchitz	12/2025
6688	9*10^118282+29	118283	Robert Price	03/2022
6689	(9*35^76602+12877)/34	118279	Eric Chen	05/2025
6690	(238*10^118265-1)/3	118267	Robert Price	04/2020
6692	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
6691	(2^392707+1710)/2	118217	Stefano Morozzi	09/2020
6693	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
6694	Phi(89679,-100)	118192	Henri Lifchitz	12/2025
6695	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
6696	(2^392567+2750)/2	118175	Stefano Morozzi	01/2021
6697	55*10^118172+3	118174	Robert Price	07/2022
6698	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
6699	27185^22222+22222^27185	118168	Hans Havermann	01/2021
6700	2^392516-29219	118160	Enzo Doria	07/2015
6701	66*10^118155+7	118157	Robert Price	07/2020
6702	Phi(177231,10)	118152	Maksym Voznyy	09/2015
6703	2^392413-112123	118129	Enzo Doria	06/2014
6704	27491^19798+19798^27491	118119	Hans Havermann	02/2021
6705	(49*10^118109-319)/9	118110	Robert Price	10/2021
6706	(2^392342+5)/27	118106	Lelio R Paula	04/2014
6707	(2^392333+1782)/2	118104	Stefano Morozzi	01/2021
6708	2^392300-1841429	118095	Enzo Doria	06/2015
6709	3*2^392260-5	118083	Jon Grantham	07/2023
6710	2^392220+75241	118070	Enzo Doria	04/2016
6711	27836^17409+17409^27836	118047	Hans Havermann	02/2021
6712	(13^118026)%(10^118026)	118026	Henri Lifchitz	05/2025
6713	10^118009+664447	118010	Patrick De Geest	07/2018
6714	10^118009-20001	118009	Robert Price	01/2018
6715	(14*10^117991+61)/3	117992	Robert Price	12/2018
6716	2^391933+5897	117984	Yves Minet	02/2011
6717	2^391912-1849259	117978	Enzo Doria	08/2015
6718	(2*34^77029+1043)/11	117968	Eric Chen	08/2023
6719	5*2^391836-3	117956	Jon Grantham	07/2023
6720	28357^14440+14440^28357	117953	Hans Havermann	02/2021
6721	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
6722	85^61124-61124^85	117934	Norman Luhn	09/2024
6723	(7*10^117930-79)/9	117930	Robert Price	01/2021
6724	27531^19168+19168^27531	117904	Hans Havermann	02/2021
6725	(46*10^117902+683)/9	117903	Robert Price	03/2019
6726	26349^26668-26668^26349	117893	Frank Doornink	03/2024
6727	27670^18189+18189^27670	117869	Hans Havermann	02/2021
6728	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
6729	(56*10^117856+583)/9	117857	Robert Price	08/2021
6730	32169^4606+4606^32169	117846	Hans Havermann	02/2021
6731	(71*10^117803-143)/9	117804	Robert Price	10/2021
6732	2^391324+90901	117801	Yves Minet	02/2011
6733	2^391301-1859923	117794	Enzo Doria	03/2016
6734	2^391261-4131	117782	Yves Minet	02/2018
6735	(2^391211+554)/2	117766	Stefano Morozzi	09/2020
6736	816^40445-40445^816	117764	Norman Luhn	09/2024
6737	38434^1157+1157^38434	117737	Hans Havermann	01/2021
6738	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
6739	(85*10^117719+473)/9	117720	Robert Price	01/2020
6740	(2^391049+582)/2	117718	Stefano Morozzi	09/2020
6741	(21*23^86445-197)/22	117715	Eric Chen	08/2023
6742	31083^6122+6122^31083	117709	Hans Havermann	02/2021
6743	2^390960+1880881	117691	Enzo Doria	11/2016
6744	(71*10^117685+91)/9	117686	Robert Price	04/2022
6746	2^390897-1860553	117672	Enzo Doria	11/2015
6745	(61*10^117671+47)/9	117672	Robert Price	07/2022
6747	2^390889-115003	117670	Enzo Doria	06/2015
6748	12^109010+35	117642	Riley Fisher	08/2023
6749	2^390779-30337	117637	Paul Bourdelais	02/2012
6750	(2^390735+378)/2	117623	Stefano Morozzi	02/2021

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