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	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
6502	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
6503	282^49477-49477^282	121231	Norman Luhn	10/2024
6505	2^402715+1874223	121230	Enzo Doria	06/2016
6504	(35*10^121229-593)/9	121230	Robert Price	07/2018
6506	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
6507	291^49190-49190^291	121199	Norman Luhn	10/2024
6508	981^40512+980	121199	Alfred Reich	05/2026
6509	(10^121243)/(121243^10)	121193	Henri Lifchitz	05/2025
6510	28719^16568+16568^28719	121174	Hans Havermann	02/2021
6511	Phi(24773,-17#)	121170	Henri Lifchitz	12/2025
6512	7*10^121144+9	121145	Robert Price	09/2015
6513	27490^25467+25467^27490	121121	Hans Havermann	02/2021
6514	34575^3182+3182^34575	121106	Hans Havermann	02/2021
6515	5*10^121100-37	121101	Robert Price	11/2021
6516	F(579521)/516247738177	121101	Serge Batalov	07/2024
6517	25592^27467-27467^25592	121078	Frank Doornink	02/2024
6518	29954^10935+10935^29954	120979	Hans Havermann	02/2021
6519	33585^3992+3992^33585	120946	Hans Havermann	02/2021
6520	40296^1003+1003^40296	120941	Hans Havermann	02/2021
6521	2^401725-113251	120932	Enzo Doria	07/2014
6522	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
6523	2^401652+73711	120910	Enzo Doria	04/2016
6524	(2^401632+3)/79	120902	Lelio R Paula	04/2014
6525	40450^973+973^40450	120870	Hans Havermann	01/2021
6526	(8*10^120851-11)/3	120852	Robert Price	07/2023
6527	10^120841+88417	120842	Patrick De Geest	04/2020
6528	10^120841-123456789	120841	Robert Price	02/2020
6529	10^120841-176853	120841	Patrick De Geest	04/2020
6530	2^401406-2791331	120836	Enzo Doria	03/2016
6531	(28^83497+1)/29	120832	Robert Price	07/2013
6532	(22*10^120828+161)/3	120829	Robert Price	05/2019
6533	2^401369+1867367	120825	Enzo Doria	03/2016
6534	(5*10^120821+43)/3	120822	Robert Price	12/2021
6535	26990^27263-27263^26990	120808	Frank Doornink	03/2024
6536	(10^120782+29)/3	120782	Serge Batalov	12/2014
6537	2^401215-1657	120778	Yves Minet	07/2014
6538	2^401159+53	120761	Lelio R Paula	10/2013
6539	27782^22179+22179^27782	120739	Hans Havermann	01/2021
6540	242^50649-50649^242	120738	Norman Luhn	09/2024
6541	32974^4585+4585^32974	120730	Hans Havermann	02/2021
6542	2^401031-113047	120723	Enzo Doria	07/2014
6543	30598^8813+8813^30598	120713	Hans Havermann	02/2021
6544	(71*10^120703-287)/9	120704	Robert Price	09/2019
6545	25671^27370-27370^25671	120687	Frank Doornink	02/2024
6546	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
6547	34793^2940+2940^34793	120675	Hans Havermann	02/2021
6548	26028^27329-27329^26028	120670	Frank Doornink	03/2024
6549	(2^400846+538)/2	120667	Stefano Morozzi	09/2020
6550	(166*10^120654+11)/3	120656	Robert Price	03/2021
6551	34066^3481+3481^34066	120652	Hans Havermann	02/2021
6552	8*10^120637-27	120638	Robert Price	10/2021
6553	(2^400709+3546)/2	120626	Stefano Morozzi	09/2020
6554	(2^400700+3126)/2	120623	Stefano Morozzi	09/2020
6555	(2^400693+2634)/2	120621	Stefano Morozzi	09/2020
6556	9*10^120617-61	120618	Robert Price	06/2021
6557	(29*10^120590-71)/3	120591	Robert Price	07/2021
6558	2^400571-15	120584	Lelio R Paula	10/2013
6559	(10^120574+359)/9	120574	Serge Batalov	12/2014
6560	(8*10^120552-17)/9	120552	Serge Batalov	11/2022
6561	27431^24810+24810^27431	120550	Hans Havermann	02/2021
6562	2^400424-216413	120540	Enzo Doria	04/2013
6563	29090^13911+13911^29090	120531	Hans Havermann	02/2021
6564	(2^400346+1722)/2	120516	Stefano Morozzi	09/2020
6565	27899^20868+20868^27899	120510	Hans Havermann	02/2021
6566	33740^3729+3729^33740	120506	Hans Havermann	02/2021
6567	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
6568	17228^28437-28437^17228	120466	Norbert Schneider	08/2025
6569	1069^39770-39770^1069	120463	Norbert Schneider	05/2025
6571	2^400166+1874899	120462	Enzo Doria	06/2016
6570	(2^400165+1602)/2	120462	Stefano Morozzi	09/2020
6572	2739^35038-35038^2739	120447	Norbert Schneider	05/2025
6573	37078^1771+1771^37078	120438	Hans Havermann	02/2021
6574	(2^400084+1638)/2	120437	Stefano Morozzi	09/2020
6575	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
6576	12857^29306-29306^12857	120423	Norbert Schneider	07/2025
6577	2^399999+54173	120412	Norman Luhn	08/2023
6578	(2^399974+2790)/2	120404	Stefano Morozzi	02/2021
6579	2^399966+73759	120402	Enzo Doria	04/2016
6580	(2^399961+2306)/2	120400	Stefano Morozzi	02/2021
6581	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
6582	2^399918-95	120388	Lelio R Paula	04/2013
6583	2^399918+214009	120388	Enzo Doria	10/2023
6584	(28*10^120381-67)/3	120382	Robert Price	10/2020
6585	(49*10^120380-139)/9	120381	Robert Price	03/2019
6586	(2^399874+2194)/2	120374	Stefano Morozzi	09/2020
6587	2^399792-1849259	120350	Enzo Doria	08/2015
6588	9*10^120342-7	120343	Robert Price	09/2015
6589	(2^399751+786)/2	120337	Stefano Morozzi	09/2020
6590	(331*10^120332-7)/9	120334	Robert Price	04/2022
6591	14609^28890-28890^14609	120316	Norbert Schneider	09/2025
6592	(13*10^120306-37)/3	120307	Robert Price	01/2019
6593	(23*10^120299+37)/3	120300	Robert Price	02/2022
6594	25935^27254-27254^25935	120297	Frank Doornink	03/2024
6595	(2^399604+3070)/2	120293	Stefano Morozzi	09/2020
6596	(2^399549+1062)/2	120276	Stefano Morozzi	09/2020
6597	2^399526-1861721	120270	Enzo Doria	11/2015
6598	12199^29430-29430^12199	120261	Norbert Schneider	08/2025
6599	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
6600	32016^5687+5687^32016	120217	Hans Havermann	01/2021
6601	(205*10^120212-1)/3	120214	Robert Price	11/2021
6602	13302^29149-29149^13302	120209	Norbert Schneider	08/2025
6603	2^399322-2798111	120208	Enzo Doria	04/2016
6604	30438^8867+8867^30438	120163	Hans Havermann	02/2021
6605	3^251841-5*2^251841	120159	Jon Grantham	08/2023
6607	72^64693-71^64693	120157	Robert Price	03/2014
6606	(17*10^120156-161)/9	120157	Robert Price	02/2021
6608	Phi(81997,-5#)	120150	Henri Lifchitz	12/2025
6609	2^399111-28489	120145	Enzo Doria	08/2015
6610	2958^34607-34607^2958	120121	Norbert Schneider	04/2025
6611	(2^399014+1318)/2	120115	Stefano Morozzi	02/2021
6612	30254^9333+9333^30254	120110	Hans Havermann	02/2021
6613	2^398972+6561	120103	Henri Lifchitz	10/2024
6614	30882^7745+7745^30882	120101	Hans Havermann	02/2021
6615	23687^27452-27452^23687	120090	Norbert Schneider	08/2025
6617	2^398877+105	120074	Donovan Johnson	01/2006
6616	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
6618	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
6619	U(686581)/4280145953	120067	Serge Batalov	07/2024
6620	16651^28442-28442^16651	120067	Norbert Schneider	07/2025
6621	12284^29359-29359^12284	120059	Norbert Schneider	06/2025
6622	3207^34240-34240^3207	120049	Norbert Schneider	04/2025
6623	2^398710+57	120024	Lelio R Paula	04/2013
6624	(2^398698+1138)/2	120020	Stefano Morozzi	09/2020
6625	2^398691-115057	120018	Enzo Doria	06/2015
6626	12134^29385-29385^12134	120009	Norbert Schneider	06/2025
6627	6089^31710-31710^6089	120008	Norbert Schneider	05/2025
6628	L(574219)	120005	Renaud Lifchitz	03/2004
6629	2^398571+60413	119982	Yves Minet	03/2011
6630	28623^15538+15538^28623	119971	Hans Havermann	02/2021
6631	p(24179)#/2-64	119949	Robert Price	04/2017
6632	2^398448+1872001	119945	Enzo Doria	05/2016
6633	(10^119946*19-91)/6093	119944	Alfred Reich	10/2023
6634	(19*10^119946-91)/9/677	119944	Alfred Reich	11/2023
6635	(191*10^119941-17)/3	119943	Robert Price	11/2021
6636	634^42803+42803^634	119938	Norbert Schneider	07/2019
6637	31083^7220+7220^31083	119935	Hans Havermann	01/2021
6638	(68*10^119931-11)/3	119933	Robert Price	01/2020
6639	8*10^119930-3	119931	Ray Chandler	04/2011
6640	(2^398398+774)/2	119930	Stefano Morozzi	09/2020
6641	(10^119880+179)/9	119880	Serge Batalov	12/2014
6642	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
6643	(10^119836+77)/3	119836	Robert Price	01/2018
6644	26681^27074-27074^26681	119835	Frank Doornink	03/2024
6645	28179^17870+17870^28179	119821	Hans Havermann	02/2021
6646	2^398029+1872527	119819	Enzo Doria	05/2016
6647	33142^4119+4119^33142	119802	Hans Havermann	01/2021
6648	2^397897-113541	119779	Enzo Doria	08/2014
6649	28636^15171+15171^28636	119728	Hans Havermann	02/2021
6650	87^61730-61730^87	119727	Norman Luhn	09/2024
6651	(10556^29929-1)/(10556^173-1)	119724	Ryan Propper	11/2023
6652	(2^397696+1042)/2	119719	Stefano Morozzi	09/2020
6654	(19*10^119716+101)/3	119717	Robert Price	09/2019
6653	29563^11208+11208^29563	119717	Hans Havermann	02/2021
6655	458^44991-44991^458	119715	Norman Luhn	09/2024
6656	2^397655-933075	119707	Paul Bourdelais	06/2021
6657	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
6658	28243^17308+17308^28243	119701	Hans Havermann	02/2021
6659	77*10^119688+3	119690	Robert Price	06/2020
6660	586*25^85601+3717	119668	Eric Chen	10/2023
6661	(2^397504+1698)/2	119661	Stefano Morozzi	09/2020
6662	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
6663	2^397426+73849	119638	Enzo Doria	04/2016
6664	8*10^119509+29	119510	Robert Price	11/2021
6665	2^396933-112723	119489	Enzo Doria	06/2014
6666	11^114738-150	119488	Enzo Doria	10/2012
6667	(4*10^119474+149)/9	119474	Robert Price	04/2018
6668	26964^26964-13^13	119472	Henri Lifchitz	08/2024
6669	11^114702+10	119450	Alfred Reich	04/2026
6670	2^396790-21	119446	Lelio R Paula	04/2013
6671	32061^5300+5300^32061	119405	Hans Havermann	01/2021
6672	(2^396633-7)/5	119398	Lelio R Paula	04/2014
6673	27382^22913+22913^27382	119388	Hans Havermann	03/2021
6674	(2^396577+2522)/2	119382	Stefano Morozzi	09/2020
6675	(2^396492+2230)/2	119356	Stefano Morozzi	01/2021
6676	(47*10^119354+259)/9	119355	Robert Price	03/2022
6678	105^59050+104	119352	Norbert Schneider	11/2016
6677	126^56824-125	119352	Norbert Schneider	12/2018
6679	2^396469+111546435	119350	Paul Bourdelais	10/2021
6680	139^55690-138	119345	Norbert Schneider	04/2019
6681	Phi(66220,p(66220))	119337	Henri Lifchitz	12/2025
6682	Phi(132889,-9)	119334	Henri Lifchitz	12/2025
6683	790^41179+41179^790	119322	Norbert Schneider	04/2019
6684	2^396374+73729	119321	Enzo Doria	04/2016
6685	88*10^119295+3	119297	Robert Price	05/2020
6686	21*29^81575+129664	119297	Eric Chen	06/2025
6687	2^396258-459491	119286	Enzo Doria	05/2015
6688	(2^396248+3126)/2	119283	Stefano Morozzi	09/2020
6689	2^396128-396128-1	119247	Karsten Bonath	06/2018
6690	(893*10^119228+7)/9	119230	Robert Price	06/2021
6691	(31*10^119229+257)/9	119230	Robert Price	12/2021
6692	(28*10^119206-67)/3	119207	Robert Price	10/2020
6693	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
6694	11^114458+6	119196	Paul Bourdelais	02/2021
6695	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
6696	(2^395902+202)/2	119179	Stefano Morozzi	09/2020
6697	(2^395825+582)/2	119155	Stefano Morozzi	09/2020
6698	(2^395733+1130)/2	119128	Stefano Morozzi	09/2020
6699	(23^119099)%(10^119099)	119099	Henri Lifchitz	05/2025
6700	29548^10725+10725^29548	119091	Hans Havermann	02/2021
6701	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
6703	(30^80599+1)/31	119054	Robert Price	07/2013
6702	Phi(80599,-5#)	119054	Henri Lifchitz	12/2025
6704	(232*10^119047+17)/3	119049	Robert Price	04/2021
6705	(43*10^119024-403)/9	119025	Robert Price	01/2019
6706	(4*10^119021+47)/3	119022	Robert Price	01/2022
6707	fibonacci(569433)+3	119005	Jon Grantham	08/2023
6708	26603^26888-26888^26603	118978	Norbert Schneider	07/2021
6709	912^40193-40193^912	118972	Norman Luhn	09/2024
6710	681^41992-41992^681	118970	Norman Luhn	09/2024
6711	6*10^118964+43	118965	Robert Price	07/2020
6712	(8*10^118960+49)/3	118961	Robert Price	05/2020
6713	31253^6402+6402^31253	118959	Hans Havermann	02/2021
6714	(194*10^118925-17)/3	118927	Robert Price	09/2020
6715	2^395062-109121	118926	Enzo Doria	04/2014
6716	2^395055-4627	118924	Yves Minet	05/2019
6717	(2^395054+702)/2	118923	Stefano Morozzi	09/2020
6718	2^395018-224141	118913	Harrison Mesh	06/2022
6719	(2^395011+2526)/2	118910	Stefano Morozzi	09/2020
6720	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
6721	25771^26948-26948^25771	118872	Frank Doornink	02/2024
6722	374^46201-46201^374	118870	Norman Luhn	09/2024
6723	(2^394858+1018)/2	118864	Stefano Morozzi	09/2020
6724	(77*10^118862-149)/9	118863	Robert Price	03/2022
6725	(16*10^118852+77)/3	118853	Robert Price	03/2019
6726	fibonacci(568658)-2	118843	Jon Grantham	08/2023
6727	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
6728	10^118772+163599	118773	Patrick De Geest	02/2021
6730	10^118772-40000000001	118772	Robert Price	09/2020
6729	10^118772-207603	118772	Patrick De Geest	02/2021
6731	26842^26577+26577^26842	118763	Hans Havermann	02/2021
6732	(2^394513+2034)/2	118760	Stefano Morozzi	09/2020
6733	(2^394473+2774)/2	118748	Stefano Morozzi	02/2021
6734	27949^17710+17710^27949	118734	Hans Havermann	02/2021
6735	2^394266+71389	118686	Enzo Doria	04/2016
6736	(10^118681-3^118681)/7	118681	Jon Grantham	08/2023
6737	2^394215-51261	118671	Tony Prest / Never Odd Or Even	04/2018
6738	(2^394215-48793)/5/5	118670	Tony Prest / Never Odd Or Even	04/2018
6739	(2^394215-17063)/3/3/5	118669	Tony Prest / Never Odd Or Even	04/2018
6740	(2^394215-24393)/5/5/5/5/5	118668	Tony Prest / Never Odd Or Even	04/2018
6741	(2^394215-35885)/3/71/173	118666	Tony Prest / Never Odd Or Even	04/2018
6742	(2^394215-47925)/353/2269	118665	Tony Prest / Never Odd Or Even	04/2018
6743	29201^11568+11568^29201	118652	Hans Havermann	02/2021
6744	(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673	118650	Tony Prest / Never Odd Or Even	04/2018
6745	(2^394131+2214)/2	118645	Stefano Morozzi	09/2020
6746	(17*10^118635+13)/3	118636	Robert Price	01/2019
6747	5^169727+2	118635	Lelio R Paula	08/2013
6748	2^394034-3	118617	M. Frind & P. Underwood	09/2002
6749	(7*10^118607+179)/3	118608	Robert Price	09/2018
6750	3^248572-6242	118599	Enzo Doria	05/2014

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Probable Primes Top 10000

(303269 PRPs in the top)