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 ?
1501	66094^39385+39385^66094	303724	Hans Havermann	01/2022
1502	69147^24574+24574^69147	303589	Hans Havermann	02/2022
1503	78390^7459+7459^78390	303580	Hans Havermann	01/2022
1504	2^1008301+1869377	303529	Enzo Doria	06/2016
1505	65008^46615+46615^65008	303492	Hans Havermann	02/2022
1506	(2^1007838+5)/3	303389	Serge Batalov	08/2015
1507	65018^46293+46293^65018	303343	Hans Havermann	01/2022
1508	6^389756+5	303290	Paul Bourdelais	02/2021
1509	71016^18649+18649^71016	303285	Hans Havermann	01/2022
1510	2^1007065+29231	303157	Enzo Doria	03/2024
1511	80160^6047+6047^80160	303129	Hans Havermann	01/2022
1512	67434^31237+31237^67434	303094	Hans Havermann	03/2022
1513	65537^42102+42102^65537	303063	Hans Havermann	02/2022
1514	71790^16553+16553^71790	302874	Hans Havermann	11/2021
1515	65208^44129+44129^65208	302874	Hans Havermann	11/2021
1516	84181^3960+3960^84181	302858	Hans Havermann	11/2021
1517	(13703^73441-1)/(13703^271-1)	302691	Ryan Propper	11/2023
1518	71956^16087+16087^71956	302682	Hans Havermann	11/2021
1519	2^1005326+383059	302634	Enzo Doria	12/2016
1520	2^1004929+1877567	302514	Enzo Doria	08/2016
1521	69341^22978+22978^69341	302418	Hans Havermann	12/2021
1522	111443^516+516^111443	302306	Hans Havermann	12/2021
1523	67638^29387+29387^67638	302218	Hans Havermann	11/2021
1524	2^1003494+1874899	302082	Enzo Doria	06/2016
1525	75189^10400+10400^75189	302037	Hans Havermann	12/2021
1526	67237^31042+31042^67237	302026	Hans Havermann	12/2021
1527	64540^47791+47791^64540	302005	Hans Havermann	11/2021
1528	2^1003046+60529	301947	Enzo Doria	04/2016
1529	83278^4209+4209^83278	301815	Hans Havermann	09/2021
1530	64431^48250+48250^64431	301763	Hans Havermann	09/2021
1531	67237^30714+30714^67237	301716	Hans Havermann	09/2021
1532	2^1002144+235861	301676	Enzo Doria	05/2025
1533	64641^46288+46288^64641	301581	Hans Havermann	09/2021
1534	71513^16482+16482^71513	301572	Hans Havermann	10/2021
1535	72017^15396+15396^72017	301565	Hans Havermann	09/2021
1536	65534^39927+39927^65534	301540	Hans Havermann	10/2021
1537	(23^221411-1)/22	301501	Paul Bourdelais	08/2020
1538	63169^59152+59152^63169	301441	Hans Havermann	09/2021
1539	75055^10348+10348^75055	301336	Hans Havermann	09/2021
1540	2^1000647+1881353	301225	Enzo Doria	11/2016
1541	83686^3961+3961^83686	301086	Hans Havermann	10/2021
1542	68529^24742+24742^68529	301078	Hans Havermann	09/2021
1543	65207^41416+41416^65207	301072	Hans Havermann	10/2021
1545	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
1544	2^999999+77151	301030	Norman Luhn	09/2023
1546	90762^2071+2071^90762	300984	Hans Havermann	06/2021
1547	63909^51142+51142^63909	300934	Hans Havermann	08/2021
1548	2^999646+1874029	300924	Enzo Doria	06/2016
1549	66280^34607+34607^66280	300856	Hans Havermann	06/2021
1550	65534^38925+38925^65534	300817	Hans Havermann	07/2021
1551	63296^56517+56517^63296	300794	Hans Havermann	06/2021
1552	110610^523+523^110610	300694	Hans Havermann	06/2021
1553	66428^33609+33609^66428	300684	Hans Havermann	06/2021
1554	74247^11210+11210^74247	300672	Hans Havermann	06/2021
1555	(59^169777-1)/58	300649	Paul Bourdelais	08/2020
1556	10^300476+3	300477	Ed Trice	10/2012
1557	10^300476-530913	300476	Patrick De Geest	03/2016
1558	66703^31960+31960^66703	300471	Hans Havermann	06/2021
1559	63722^51915+51915^63722	300468	Hans Havermann	06/2021
1560	2^998053+1879667	300444	Enzo Doria	09/2016
1561	77018^7959+7959^77018	300437	Hans Havermann	07/2021
1562	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
1563	2^997689+217787	300335	Enzo Doria	01/2024
1564	69478^20987+20987^69478	300281	Hans Havermann	07/2021
1565	64088^48393+48393^64088	300239	Hans Havermann	07/2021
1566	2^997369+237917	300238	Enzo Doria	06/2025
1567	64605^44146+44146^64605	300084	Hans Havermann	08/2021
1568	2^996845+29027	300081	Enzo Doria	02/2024
1569	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
1570	67594^27465+27465^67594	300035	Hans Havermann	06/2021
1571	10^300000+287389	300001	Patrick De Geest	10/2019
1572	10^300000-83657	300000	Patrick De Geest	10/2019
1573	70599^17756+17756^70599	300000	Hans Havermann	06/2021
1574	numbpart(72526161452)	299999	Serge Batalov	04/2017
1575	2^996182-114431	299881	Enzo Doria	02/2015
1576	3*2^996126+5	299865	Jon Grantham	07/2023
1577	2^996034-17	299837	Stefano Morozzi	07/2022
1578	2^995793+36587	299764	Enzo Doria	09/2024
1579	(19*10^299640+77)/3	299641	Robert Price	03/2023
1580	2^995214-2788361	299590	Enzo Doria	12/2015
1581	2^994791-114319	299462	Enzo Doria	01/2015
1582	2^994490-1863791	299372	Enzo Doria	01/2016
1583	(10^(2149610+1)+2710^149610-1)/9	299221	Robert Price	06/2026
1584	2^993322+1885729	299020	Enzo Doria	03/2017
1585	2^993227+230033	298992	Enzo Doria	12/2024
1586	(36395^65536+36393^65536)/2	298913	Kellen Shenton	04/2022
1587	2^992711-2788807	298836	Enzo Doria	12/2015
1588	2^992525-114199	298780	Enzo Doria	12/2014
1589	(7^353501-3^353501)/4	298743	Jon Grantham	08/2023
1590	2^992329+1884707	298721	Enzo Doria	02/2017
1591	2^992292+229801	298710	Enzo Doria	12/2024
1592	2^992052+215491	298638	Enzo Doria	11/2023
1593	2^991968-23	298613	Stefano Morozzi	07/2022
1594	2^991715-19	298536	Stefano Morozzi	07/2022
1595	2^991387+237383	298438	Enzo Doria	06/2025
1596	(10^298414+7)/191/823/56921/1334467	298398	Alfred Reich	10/2021
1597	2^989562+25	297888	Stefano Morozzi	05/2021
1598	2^988580+214051	297593	Enzo Doria	10/2023
1599	2^988537+218837	297580	Enzo Doria	03/2024
1600	(19*10^297497+77)/3	297498	Robert Price	03/2023
1601	(2*10^297488-23)/3	297488	Robert Price	10/2022
1602	2^988148+48271	297463	Enzo Doria	07/2025
1603	2^987033+46427	297127	Enzo Doria	05/2025
1604	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
1605	2^985217-114553	296580	Enzo Doria	03/2015
1606	(76^157649-1)/75	296507	Paul Bourdelais	07/2019
1607	2^984650+21529	296410	Enzo Doria	08/2023
1608	2^984131-1828009	296253	Enzo Doria	01/2015
1609	2^983620+60451	296100	Phil Moore	03/2008
1610	2^982721-2683	295829	Yves Minet	02/2016
1611	(23*10^295581+7)/3	295582	Robert Price	05/2023
1612	2^981298-2788421	295401	Enzo Doria	12/2015
1613	2^981163-2790967	295360	Enzo Doria	12/2015
1614	2^981016-15	295316	Stefano Morozzi	07/2022
1615	8*10^295160-13	295161	Robert Price	08/2023
1616	2^979594+1865839	294888	Enzo Doria	02/2016
1617	2^979502+221029	294860	Enzo Doria	03/2024
1618	2*10^294527-91	294528	Robert Price	02/2023
1619	(49363^63001-1)/(49363^251-1)	294511	Ryan Propper	11/2023
1620	10^294475+49	294476	Robert Price	02/2023
1621	2^977896+234601	294377	Enzo Doria	04/2025
1622	(11*10^294308+91)/3	294309	Robert Price	03/2023
1623	2^976760+1885021	294035	Enzo Doria	02/2017
1624	3*2^976518+5	293962	Jon Grantham	07/2023
1625	2^975798+218599	293745	Enzo Doria	01/2024
1626	2^974441+1878407	293336	Enzo Doria	08/2016
1627	2^974180+1876831	293258	Enzo Doria	07/2016
1628	2^974170+453319	293255	Enzo Doria	01/2017
1629	(211^126023-1)/210	292911	Anonymous	05/2024
1630	2^972744-114419	292826	Enzo Doria	03/2015
1631	11^281143+6	292781	Paul Bourdelais	03/2021
1632	(4*10^292619-91)/3	292620	Robert Price	12/2022
1633	E(69468)/13247122135	292549	Sergey Batalov	10/2023
1634	CopelandErdos(292447)	292447	Mark Rodenkirch	12/2015
1635	3*10^292344-97	292345	Robert Price	01/2023
1636	2^970911+1873373	292274	Enzo Doria	07/2016
1637	2^970670+383059	292201	Enzo Doria	12/2016
1638	2^970141-100363	292042	Enzo Doria	02/2014
1639	2^969945+1874717	291983	Enzo Doria	06/2016
1640	2^969384+1880701	291814	Enzo Doria	10/2016
1641	(13*10^291721-43)/3	291722	Robert Price	08/2023
1642	(3^611333-2^611333)/(99035947*87109884549431)	291659	Mike Oakes	02/2017
1643	128^138108+127	291023	Alfred Reich	06/2026
1644	10^(2145126+1)-210^145126-1	290253	Robert Price	03/2025
1645	3*2^963892+5	290161	Jon Grantham	07/2023
1646	(151*10^289877-1)/3	289879	Robert Price	07/2023
1647	2^962194+60139	289650	Enzo Doria	02/2016
1648	2^961409+44267	289413	Enzo Doria	04/2025
1649	2^959307-1861507	288781	Enzo Doria	11/2015
1650	(17*10^288692+31)/3	288693	Robert Price	04/2023
1651	14^251797-3	288592	Paul Bourdelais	12/2020
1652	(8745^73441-1)/(8745^271-1)	288419	Ryan Propper	11/2023
1653	(2*10^288371-23)/3	288371	Robert Price	10/2022
1654	(31*10^288238-1)/3	288240	Robert Price	02/2023
1655	(7^341063-2^341063)/5	288231	Jon Grantham	08/2023
1656	2^957372+283531	288198	Enzo Doria	02/2017
1657	2^957192-1864049	288144	Enzo Doria	01/2016
1658	(95774^58081-1)/(95774^241-1)	288116	Ryan Propper	11/2023
1659	2^956446+1875199	287919	Enzo Doria	06/2016
1660	2^956283+219143	287870	Enzo Doria	02/2024
1661	7*10^287854+39	287855	Robert Price	01/2023
1662	2^956082+28309	287810	Enzo Doria	02/2024
1663	(17^233689+1)/18	287542	Paul Bourdelais	09/2013
1664	2^955178+1883587	287538	Enzo Doria	12/2016
1665	2^954127-954127^2	287221	Henri Lifchitz	01/2021
1666	2^954001+1875257	287183	Enzo Doria	07/2016
1667	2*10^287175-49	287176	Robert Price	05/2023
1668	(22*10^287085-19)/3	287086	Robert Price	07/2023
1669	2^953667+38573	287083	Enzo Doria	11/2024
1670	2^953488+22411	287029	Enzo Doria	09/2023
1671	(23891^65536+1)/2	286932	Serge Batalov	03/2018
1672	5*3^601336-2^601336	286911	Jon Grantham	08/2023
1673	2^952268+1878601	286662	Enzo Doria	09/2016
1674	2^950801+81557	286220	Enzo Doria	08/2016
1675	2^949403+217523	285799	Enzo Doria	01/2024
1676	22845^65536+22844^65536	285658	Kellen Shenton	03/2021
1677	(19*10^285615+53)/9	285616	Rytis Slatkevicius	12/2024
1678	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
1679	(54^164839+1)/55	285565	Paul Bourdelais	07/2019
1680	2^948510+782569	285530	Enzo Doria	10/2016
1681	2^948374-114137	285490	Enzo Doria	01/2015
1682	2^947739+1872923	285298	Enzo Doria	06/2016
1683	2^946274+218407	284857	Enzo Doria	03/2024
1684	7*10^284751+9	284752	Robert Price	04/2023
1685	2^944561-21	284342	Stefano Morozzi	07/2022
1686	(4*10^284330-31)/9	284330	Serge Batalov	11/2022
1687	(32*10^283826-23)/9	283827	Serge Batalov	01/2023
1688	2^942533+82067	283731	Enzo Doria	09/2016
1689	2^941469+39	283411	Jon Grantham	08/2023
1690	(10^283342-31)/3	283342	Robert Price	03/2023
1691	2^940950+1874989	283255	Enzo Doria	06/2016
1692	2^940426-2786141	283097	Enzo Doria	11/2015
1693	2^940155+226973	283015	Enzo Doria	09/2024
1694	(2*10^282948-11)/9	282948	Serge Batalov	11/2022
1695	2^939881-114115	282933	Enzo Doria	12/2014
1696	(14*10^282673-143)/3	282674	Robert Price	05/2023
1697	10^282493+632551	282494	Patrick De Geest	02/2017
1699	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
1698	10^282493-132327	282493	Patrick De Geest	02/2017
1700	3^591827-2^591827	282374	Mike Oakes	08/2009
1701	Tau(509^18946)	282048	Nik Lygeros / Olivier Rozier	05/2015
1702	Sm(58628)/47409417156	282023	Youcef Lemsafer	06/2026
1703	2^936716-1835519	281980	Enzo Doria	04/2015
1704	2^936588+79411	281942	Enzo Doria	06/2016
1705	2^936047+1877423	281779	Enzo Doria	08/2016
1706	2^935713+1869377	281678	Enzo Doria	05/2016
1707	2^933082+1877059	280886	Enzo Doria	08/2016
1708	(5*10^280710+1)/3	280711	Serge Batalov	10/2014
1709	2^932443+225893	280694	Enzo Doria	08/2024
1710	2^932064+26521	280580	Enzo Doria	12/2023
1711	2^931976+25	280553	Stefano Morozzi	05/2021
1712	(42^172663+1)/43	280274	Paul Bourdelais	07/2019
1713	(10^279978+11)/3	279978	Serge Batalov	07/2015
1714	2^929524-1864829	279815	Enzo Doria	01/2016
1715	2^929329+22697	279756	Enzo Doria	09/2023
1716	2^929152+60181	279703	Enzo Doria	02/2016
1717	2^928621-2787883	279543	Enzo Doria	11/2015
1718	(2^927763+lucasV(-1,2,927763)+1)/2	279285	Mike Oakes	04/2017
1719	3*10^279271+77	279272	Robert Price	06/2024
1720	2^927429+1882277	279184	Enzo Doria	12/2016
1721	2^926766-11	278985	Stefano Morozzi	07/2022
1722	(71^150697-1)/70	278978	Paul Bourdelais	07/2019
1723	(33^183661-1)/32	278891	Paul Bourdelais	12/2018
1724	(5347*26^197061-297)/25	278839	Eric Chen	12/2025
1725	(166*10^278633-7)/3	278635	Robert Price	02/2023
1726	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
1727	2^925330-1301	278553	Yves Minet	06/2015
1728	(299*10^278546+1)/3	278548	Robert Price	01/2023
1729	2^925299+216053	278543	Enzo Doria	11/2023
1731	(21^210599+1)/22	278457	Paul Bourdelais	08/2013
1730	(79^146749-1)/6395645198026062186	278457	Paul Vanderveen	06/2025
1732	(266*10^278325+1)/3	278327	Robert Price	01/2023
1733	2^923261-69175	277930	Enzo Doria	11/2015
1734	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
1735	2^922301+57	277641	Stefano Morozzi	05/2021
1736	7*10^277478-39	277479	Robert Price	07/2023
1737	((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	277369	Serge Batalov	07/2016
1738	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
1739	2^920318+2792299	277044	Enzo Doria	02/2016
1740	(16*10^276537-31)/3	276538	Robert Price	03/2023
1741	2^918596-2786939	276525	Enzo Doria	11/2015
1742	2^917910+28369	276319	Enzo Doria	01/2024
1743	2^917328+228571	276144	Enzo Doria	11/2024
1744	(6737^72361-1)/(6737^269-1)	276002	Ryan Propper	11/2023
1745	2^916639+60563	275936	Enzo Doria	04/2016
1746	(2*10^275922+1)/3	275922	Serge Batalov	11/2022
1747	2^916385-2786383	275860	Enzo Doria	11/2015
1748	2^915928+82081	275722	Enzo Doria	09/2016
1749	(4*10^275671+11)/3	275672	Tyler Busby	02/2023
1750	2^915576-114137	275616	Enzo Doria	01/2015

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Probable Primes Top 10000

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