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	(16*10^265052-91)/3	265053	Robert Price	11/2022
1502	2^880411+1882673	265031	Enzo Doria	12/2016
1503	2^880101+228917	264937	Enzo Doria	11/2024
1504	(14*10^264791-11)/3	264792	Robert Price	08/2022
1505	2^879530-2788031	264765	Enzo Doria	12/2015
1506	2^879292+25171	264694	Enzo Doria	11/2023
1507	(2*10^264539+61)/9	264539	Serge Batalov	11/2022
1508	2^878118+2793079	264340	Enzo Doria	02/2016
1509	(2^878073-7)/5	264326	Stefano Morozzi	08/2022
1510	(37^168527-1)/36	264283	Paul Bourdelais	08/2019
1511	5^377865+3^377865-1	264117	Jon Grantham	08/2023
1512	(19*10^263971+131)/3	263972	Robert Price	08/2023
1513	2^876202-17	263764	Stefano Morozzi	07/2022
1514	(14*10^263720-11)/3	263721	Robert Price	08/2022
1515	2^875748-461129	263627	Enzo Doria	07/2015
1516	2^875518-15	263558	Stefano Morozzi	07/2022
1517	(29*10^263523-17)/3	263524	Robert Price	01/2023
1518	2^875181-2789923	263456	Enzo Doria	12/2015
1519	2^875101-350083	263432	Enzo Doria	08/2015
1520	2^874684+1883587	263307	Enzo Doria	01/2017
1521	2^874616+1872211	263286	Enzo Doria	05/2016
1522	2^874566+30049	263271	Enzo Doria	03/2024
1523	3^551491+16	263129	Robert Price	04/2020
1524	2^874073+2792957	263123	Enzo Doria	02/2016
1525	(7*10^263006-19)/3	263007	Robert Price	10/2023
1526	2^873628+1878751	262989	Enzo Doria	08/2016
1527	2^873497+20837	262949	Enzo Doria	08/2023
1528	2^873288-269	262886	Yves Minet	01/2015
1529	(2*10^262874+7)/9	262874	Rytis Slatkevicius	01/2023
1530	(28*10^262655-43)/3	262656	Robert Price	04/2023
1531	(2*10^262603-11)/9	262603	Serge Batalov	11/2022
1532	2^871991-4207	262496	Yves Minet	03/2021
1533	(23*10^262324+7)/3	262325	Robert Price	05/2023
1534	2^871146-3173	262242	Yves Minet	07/2016
1535	(10^(2131020+1)+6310^131020-1)/9	262041	Robert Price	08/2024
1536	2^869601-163	261776	Yves Minet	01/2015
1537	(2*10^261704+61)/9	261704	Serge Batalov	11/2022
1538	2^869326+282859	261694	Enzo Doria	11/2016
1539	2^869035-114181	261606	Enzo Doria	12/2014
1540	2^868817+26777	261540	Enzo Doria	12/2023
1541	3^547850+9000004	261391	Enzo Doria	10/2023
1542	4*10^261248+91	261249	Robert Price	11/2022
1543	55083^55083+1282^1282	261150	Henri Lifchitz	10/2024
1544	2^866908+34891	260966	Enzo Doria	07/2024
1545	2^865715+80303	260607	Enzo Doria	07/2016
1546	2^865474+23209	260534	Enzo Doria	10/2023
1547	2^865238+214759	260463	Enzo Doria	11/2023
1548	2^865048+1882411	260406	Enzo Doria	12/2016
1549	2^864899-113871	260361	Enzo Doria	10/2014
1550	(16*10^260256-91)/3	260257	Robert Price	11/2022
1551	(7*10^260198-61)/9	260198	Erik Branger	11/2011
1552	2^864298-2788421	260180	Enzo Doria	12/2015
1553	2^864039-2791357	260102	Enzo Doria	01/2016
1554	2^863621-113833	259976	Enzo Doria	10/2014
1555	10^259945-11	259945	Mischa Rodermond	04/2023
1556	2^863433+34877	259920	Enzo Doria	07/2024
1557	(28*10^259897+113)/3	259898	Robert Price	06/2023
1558	2^862837+75767	259740	Enzo Doria	05/2016
1559	2^862637-31	259680	Jorge Menendez	05/2019
1560	2^862088+1874941	259515	Enzo Doria	06/2016
1561	2^861987-134557	259484	Hans Havermann	10/2018
1562	(14*10^259431-143)/3	259432	Robert Price	05/2023
1563	2^861516-1854029	259343	Enzo Doria	09/2015
1564	2^860975-1853977	259180	Enzo Doria	09/2015
1565	3^543128+16	259138	Robert Price	04/2020
1566	2^860625-1858843	259074	Enzo Doria	10/2015
1567	2^860110+77689	258919	Enzo Doria	05/2016
1568	2^859600+1880371	258766	Enzo Doria	10/2016
1569	2^859433+494711	258716	Makoto Morimoto	10/2013
1571	(2^859433-44)/(2^2*3)	258715	Makoto Morimoto	08/2019
1570	(2^859431-11)/3	258715	Stefano Morozzi	08/2022
1572	(13*10^258710-43)/3	258711	Robert Price	08/2023
1573	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
1574	2^859240+1875271	258658	Enzo Doria	06/2016
1575	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
1576	2^858812+30421	258529	Enzo Doria	03/2024
1577	(23*10^258494-47)/3	258495	Robert Price	09/2023
1578	(144^119671+1)/145	258292	Paul Bourdelais	08/2019
1579	2^857608+105	258166	Stefano Morozzi	05/2021
1580	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
1581	2^857016-633113	257988	Enzo Doria	12/2013
1582	2^855732-113969	257602	Enzo Doria	10/2014
1583	(5*10^257431+91)/3	257432	Robert Price	08/2023
1584	2^853682-3911	256984	Enzo Doria	05/2014
1585	11^246668-90	256879	Enzo Doria	12/2012
1586	2^853181+30287	256834	Enzo Doria	03/2024
1587	5*2^852698+3	256689	Jon Grantham	07/2023
1588	(23*10^256654+7)/3	256655	Robert Price	05/2023
1589	2^851904-113939	256449	Enzo Doria	10/2014
1590	2^851725-851725^2	256395	Henri Lifchitz	03/2019
1591	11^246167-90	256357	Enzo Doria	12/2012
1592	(85*10^256301-1)/3	256303	Robert Price	12/2022
1593	(10^256187+7)/63443/148782853	256175	Alfred Reich	10/2021
1594	2^850700-569049	256087	Enzo Doria	11/2013
1595	2^850675+153	256079	Stefano Morozzi	05/2021
1596	21^193601-20^193601	255983	Jean-Louis Charton	02/2015
1597	(37^163193+1)/38	255918	Paul Bourdelais	07/2019
1598	(14*10^255805-83)/3	255806	Robert Price	11/2022
1599	2^849316+25861	255670	Enzo Doria	12/2023
1600	2^849177-114025	255628	Enzo Doria	12/2014
1601	2*10^255442-21	255443	Robert Price	08/2023
1602	2^848502-3173	255425	Yves Minet	07/2016
1603	2^848178-140291	255328	Enzo Doria	01/2014
1604	7*10^255167+87	255168	Robert Price	11/2022
1605	2^847622-2441	255160	Yves Minet	02/2016
1606	2^847291+182843	255061	Enzo Doria	11/2016
1607	2^847174+1879429	255025	Enzo Doria	09/2016
1608	2^846881+215837	254937	Enzo Doria	12/2023
1609	24*29^174239+13361	254809	Curtis Bright	04/2015
1610	22*10^254639+7	254641	Robert Price	10/2022
1611	2^845633-933075	254561	Paul Bourdelais	11/2021
1612	2^845610-1868591	254554	Enzo Doria	04/2016
1613	2^845484+81931	254517	Enzo Doria	08/2016
1614	2^845402-114761	254492	Enzo Doria	05/2015
1615	98*10^254173-9	254175	Robert Price	05/2023
1616	2^844334-2792441	254170	Enzo Doria	02/2016
1617	2*10^254162+69	254163	Robert Price	08/2023
1618	(4*10^254107+11)/3	254108	Tyler Busby	02/2023
1619	11^243796-90	253888	Enzo Doria	12/2012
1620	(10^253891+7)/44777/79843/16940711	253875	Alfred Reich	10/2021
1621	30^171733-29^171733	253671	Jean-Louis Charton	10/2018
1622	2^842325+25907	253566	Enzo Doria	11/2023
1623	2^842209+1876037	253531	Enzo Doria	07/2016
1624	2^842123-59197	253505	Enzo Doria	10/2015
1625	(8*10^253313-53)/9	253313	Serge Batalov	11/2022
1626	(28*10^253210+191)/3	253211	Robert Price	07/2023
1627	2^840797-3	253106	Paul Bourdelais	06/2019
1628	2^840716-2969	253081	Yves Minet	05/2016
1629	2^840358-462491	252973	Enzo Doria	08/2015
1630	2^840310+1878379	252959	Enzo Doria	08/2016
1631	2^840203-21	252927	Stefano Morozzi	07/2022
1632	11^242579-60	252620	Enzo Doria	10/2012
1633	45^152659+2	252378	Robert Price	09/2015
1634	(95^127583+1)/96	252322	Paul Bourdelais	07/2019
1635	7*10^252209-17	252210	Robert Price	12/2022
1636	2^837725+1869377	252181	Enzo Doria	05/2016
1637	2^837536-311039	252124	Enzo Doria	06/2015
1638	21^190632-2	252058	Robert Price	07/2015
1639	2^837242+1873297	252035	Enzo Doria	06/2016
1640	2^836995+226575	251961	Enzo Doria	10/2024
1641	2^836656-2787929	251859	Enzo Doria	11/2015
1642	2^836548+219061	251827	Enzo Doria	02/2024
1643	2^836380+1875541	251776	Enzo Doria	07/2016
1644	(359^98327-1)/358	251233	Alexander Zhirkov	11/2017
1645	tau(41^28288)	250924	Nik Lygeros / Olivier Rozier	10/2013
1646	(28*10^250655+113)/3	250656	Robert Price	06/2023
1647	2^832511-461197	250611	Enzo Doria	07/2015
1648	2^832505+1881137	250609	Enzo Doria	11/2016
1649	2^832363+583295	250567	Enzo Doria	12/2016
1650	2^832244-403635	250531	Enzo Doria	01/2014
1651	(14*10^250336-41)/9	250337	Serge Batalov	01/2023
1652	2^831528+24811	250315	Enzo Doria	11/2023
1653	2^831157+1880657	250204	Enzo Doria	11/2016
1654	2^831088-7200899	250183	Enzo Doria	01/2015
1655	2^830956-1349	250143	Yves Minet	07/2015
1656	2^830699+220583	250066	Enzo Doria	03/2024
1657	2^830037+282317	249867	Enzo Doria	09/2016
1658	2^829589-113653	249732	Enzo Doria	09/2014
1659	(4*10^249550-7)/3	249551	Serge Batalov	01/2023
1660	(103*10^249399+17)/3	249401	Robert Price	04/2023
1661	2^828281-3193	249338	Yves Minet	08/2016
1662	(2^828140-19)/3	249295	Stefano Morozzi	08/2022
1663	2^828064-2785619	249273	Enzo Doria	10/2015
1664	2^827602+60409	249134	Enzo Doria	03/2016
1665	2^827306+212419	249044	Enzo Doria	09/2023
1666	10^249010+348861	249011	Patrick De Geest	04/2016
1667	10^249010-21	249010	Serge Batalov	12/2014
1668	2^826733+1882907	248872	Enzo Doria	12/2016
1669	2^825800+22441	248591	Enzo Doria	10/2023
1670	2^825682+1876549	248556	Enzo Doria	07/2016
1671	2^824991-114121	248348	Enzo Doria	12/2014
1672	2^824642-362727	248242	Enzo Doria	12/2013
1673	2^824565-114265	248219	Enzo Doria	01/2015
1674	2^824325-25	248147	Boyan Hu	12/2024
1675	(73*10^248145-1)/9	248146	Robert Price	01/2015
1676	2^823321+219407	247845	Enzo Doria	02/2024
1677	(2^823337+1)/(3*362268281)	247841	Gord Palameta	08/2018
1678	(13*10^247793-43)/3	247794	Robert Price	08/2023
1679	(2^822971-1)/6583769/28211445881/21255852651726486149207	247700	Robert Kinser	09/2016
1680	2^822296+76501	247536	Enzo Doria	05/2016
1681	2^821590-114167	247324	Enzo Doria	12/2014
1682	2^821512-2790659	247300	Enzo Doria	12/2015
1683	(21996^57121-1)/(21996^239-1)	247002	Ryan Propper	11/2023
1684	2^820356+7	246952	Jon Grantham	08/2023
1685	2^820077+382847	246868	Enzo Doria	11/2016
1686	2^820008+81	246848	Henri Lifchitz	01/2025
1687	2^820001+81269	246845	Enzo Doria	07/2016
1688	2^819463-59197	246683	Enzo Doria	10/2015
1689	2^819296+80581	246633	Enzo Doria	07/2016
1690	2^818764+21573	246473	Enzo Doria	11/2023
1691	2^817852+215491	246198	Enzo Doria	11/2023
1692	2^817160-350369	245990	Enzo Doria	06/2015
1693	2^816039-19	245653	Stefano Morozzi	07/2022
1694	2^816029+219407	245650	Enzo Doria	02/2024
1695	(71*10^245558-17)/9	245559	Serge Batalov	01/2023
1696	5*3^514648+2^514648	245551	Jon Grantham	08/2023
1697	88093#+(653879#)/(88093#)	245374	Makoto Morimoto	11/2017
1698	2^815111-113857	245373	Enzo Doria	10/2014
1699	(34555^54289-1)/(34555^233-1)	245334	Ryan Propper	11/2023
1700	2^814914-4001	245314	Yves Minet	05/2017
1701	846^83761-845^83761	245200	Jean-Louis Charton	12/2012
1702	2^814356-2790449	245146	Enzo Doria	12/2015
1703	2^814276-459029	245122	Enzo Doria	04/2015
1704	2^814023+180923	245046	Enzo Doria	07/2016
1705	2^813496+216751	244887	Enzo Doria	12/2023
1706	(3^513059-2^513059)/(1026119*5430216457)	244776	Mike Oakes	03/2017
1707	3^513007+16	244767	Robert Price	04/2020
1708	(46^147197-31^147197)/15	244752	Aurel Gibier	06/2024
1709	2^811882+27289	244401	Enzo Doria	12/2023
1710	2^811842-113675	244389	Enzo Doria	09/2014
1711	2^811132-2787929	244176	Enzo Doria	11/2015
1712	2^809746-2790971	243758	Enzo Doria	01/2016
1713	(14*10^243724-197)/3	243725	Robert Price	03/2023
1714	2^808767-3295	243464	Yves Minet	12/2016
1715	2^808621-113809	243420	Enzo Doria	09/2014
1716	2^808199+29693	243293	Enzo Doria	03/2024
1717	2^807724+1879621	243150	Enzo Doria	09/2016
1718	2^807417+217787	243057	Enzo Doria	01/2024
1719	(23*10^242909+91)/3	242910	Robert Price	03/2023
1720	2^806708+20371	242844	Enzo Doria	08/2023
1721	2*10^242822-91	242823	Robert Price	02/2023
1722	20^186554-3	242713	Paul Bourdelais	12/2020
1723	2^805843-113611	242583	Enzo Doria	08/2014
1724	2^805745-459763	242554	Enzo Doria	05/2015
1725	2^805353+782687	242436	Enzo Doria	11/2016
1726	(19*10^242362-7)/3	242363	Robert Price	12/2023
1727	2^804895+29963	242298	Enzo Doria	03/2024
1728	2^804725+28229	242247	Enzo Doria	01/2024
1729	6^311257+5	242206	Paul Bourdelais	02/2021
1730	2^804277-417933	242112	Enzo Doria	01/2014
1731	2^803468-269039	241868	Enzo Doria	10/2013
1732	2^803172+80851	241779	Enzo Doria	07/2016
1733	2^803011+220073	241731	Enzo Doria	03/2024
1734	3^506233-2	241535	Robert Price	11/2013
1735	2^802025-25999	241434	Enzo Doria	10/2013
1736	(3^505823+3^252912+1)/7	241339	Serge Batalov	03/2014
1737	2^801575+25073	241299	Enzo Doria	11/2023
1738	2^801303+1872923	241217	Enzo Doria	05/2016
1739	2^801105+216977	241157	Enzo Doria	12/2023
1740	(23*10^241048-143)/3	241049	Robert Price	12/2023
1741	2^800579-1862947	240999	Enzo Doria	12/2015
1742	2^799999+16205	240824	Norman Luhn	09/2023
1743	3^504206+2	240568	Luke W. Richards	03/2018
1744	2^798973-26283	240515	Enzo Doria	10/2013
1745	2^798671-69487	240424	Enzo Doria	12/2015
1746	2^797220+79831	239988	Enzo Doria	06/2016
1747	2^796910-26001	239894	Enzo Doria	10/2013
1748	2^796598+653119	239800	Enzo Doria	12/2016
1749	2^796432-1859729	239750	Enzo Doria	11/2015
1750	2^796002-1852211	239621	Enzo Doria	08/2015

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Probable Primes Top 10000

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