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	2^901858+77689	271487	Enzo Doria	06/2016
1502	2^901372+1875301	271341	Enzo Doria	06/2016
1503	2^901146+219049	271272	Enzo Doria	02/2024
1504	(8*10^271039-77)/3	271040	Robert Price	04/2023
1505	2^899999+1144031	270927	Norman Luhn	09/2023
1506	2*10^270802-91	270803	Robert Price	02/2023
1507	23*10^270799-7	270801	Robert Price	10/2022
1508	2^899121-115033	270663	Enzo Doria	07/2015
1509	2^898900+883021	270596	Enzo Doria	12/2016
1510	2^898762-251511	270555	Enzo Doria	12/2013
1511	2^898589+47	270503	Lelio R Paula	03/2016
1512	187322*10^270343-187321	270349	Danilo Nitsche	09/2013
1513	48358*10^270343-48357	270348	Danilo Nitsche	09/2013
1514	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
1515	2^897867-3217	270285	Yves Minet	12/2016
1516	2^897849-115273	270280	Enzo Doria	07/2015
1517	2^897367+26289	270135	Enzo Doria	03/2024
1518	2^896616-114179	269909	Enzo Doria	12/2014
1519	(12648^66049-1)/(12648^257-1)	269881	Ryan Propper	11/2023
1520	(10^(2134811+1)+610^134811-1)/3	269623	Robert Price	08/2024
1521	(22*10^269517-19)/3	269518	Robert Price	07/2023
1522	10^(2134739+1)-710^134739-1	269479	Robert Price	07/2023
1523	2^894928+583561	269401	Enzo Doria	04/2017
1524	2^894673-39343	269324	Enzo Doria	08/2015
1525	2^893836+23221	269072	Enzo Doria	10/2023
1526	2^892718+29539	268735	Enzo Doria	03/2024
1527	2^892660+213901	268718	Enzo Doria	10/2023
1528	F(1285607)	268676	Henri Lifchitz	11/2008
1529	2^892234+22189	268590	Enzo Doria	09/2023
1530	2^892151+24863	268565	Enzo Doria	11/2023
1531	2^892112+187663	268553	Enzo Doria	08/2016
1532	(266*10^268407-17)/3	268409	Robert Price	02/2023
1533	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
1534	2^890957-69583	268205	Enzo Doria	12/2015
1535	32841!^2+32840!^2+...+2!^2+1!^2	268128	Serge Batalov	07/2017
1536	2^890122-351401	267954	Enzo Doria	07/2015
1537	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
1538	2^888852+229051	267572	Enzo Doria	11/2024
1539	(85^138647+1)/86	267507	Paul Bourdelais	07/2019
1540	(1005^89087-1)/1004	267451	Jinyuan Wang	01/2024
1541	(485^99523-1)/484	267291	Michael Stocker	05/2020
1542	2^886324+77791	266811	Enzo Doria	06/2016
1543	7*10^266731+87	266732	Robert Price	11/2022
1544	2^886040+213901	266725	Enzo Doria	10/2023
1545	2^885242+217909	266485	Enzo Doria	01/2024
1546	2^884738+26809	266333	Enzo Doria	12/2023
1547	2^884714+1880527	266326	Enzo Doria	10/2016
1548	7*10^266024-47	266025	Robert Price	08/2023
1549	11^255426+255426^11	265999	Serge Batalov	05/2014
1550	2^883462-343421	265949	Enzo Doria	07/2015
1551	2^883442+1875019	265943	Enzo Doria	06/2016
1552	2^883333-291583	265910	Enzo Doria	07/2015
1553	2^883132+30421	265850	Enzo Doria	03/2024
1554	10^265566+3593037	265567	Paul Bourdelais	08/2023
1555	(2*10^265321-17)/3	265321	Serge Batalov	11/2022
1556	(16*10^265052-91)/3	265053	Robert Price	11/2022
1557	2^880411+1882673	265031	Enzo Doria	12/2016
1558	2^880101+228917	264937	Enzo Doria	11/2024
1559	(14*10^264791-11)/3	264792	Robert Price	08/2022
1560	2^879530-2788031	264765	Enzo Doria	12/2015
1561	2^879292+25171	264694	Enzo Doria	11/2023
1562	(2*10^264539+61)/9	264539	Serge Batalov	11/2022
1563	2^878118+2793079	264340	Enzo Doria	02/2016
1564	(2^878073-7)/5	264326	Stefano Morozzi	08/2022
1565	(37^168527-1)/36	264283	Paul Bourdelais	08/2019
1566	5^377865+3^377865-1	264117	Jon Grantham	08/2023
1567	(19*10^263971+131)/3	263972	Robert Price	08/2023
1568	2^876202-17	263764	Stefano Morozzi	07/2022
1569	(14*10^263720-11)/3	263721	Robert Price	08/2022
1570	2^875748-461129	263627	Enzo Doria	07/2015
1571	2^875518-15	263558	Stefano Morozzi	07/2022
1572	(29*10^263523-17)/3	263524	Robert Price	01/2023
1573	2^875181-2789923	263456	Enzo Doria	12/2015
1574	2^875101-350083	263432	Enzo Doria	08/2015
1575	2^874684+1883587	263307	Enzo Doria	01/2017
1576	2^874616+1872211	263286	Enzo Doria	05/2016
1577	2^874566+30049	263271	Enzo Doria	03/2024
1578	3^551491+16	263129	Robert Price	04/2020
1579	2^874073+2792957	263123	Enzo Doria	02/2016
1580	(7*10^263006-19)/3	263007	Robert Price	10/2023
1581	2^873628+1878751	262989	Enzo Doria	08/2016
1582	2^873497+20837	262949	Enzo Doria	08/2023
1583	2^873288-269	262886	Yves Minet	01/2015
1584	(2*10^262874+7)/9	262874	Rytis Slatkevicius	01/2023
1585	(28*10^262655-43)/3	262656	Robert Price	04/2023
1586	(2*10^262603-11)/9	262603	Serge Batalov	11/2022
1587	2^871991-4207	262496	Yves Minet	03/2021
1588	(23*10^262324+7)/3	262325	Robert Price	05/2023
1589	2^871146-3173	262242	Yves Minet	07/2016
1590	(10^(2131020+1)+6310^131020-1)/9	262041	Robert Price	08/2024
1591	2^869601-163	261776	Yves Minet	01/2015
1592	(2*10^261704+61)/9	261704	Serge Batalov	11/2022
1593	2^869326+282859	261694	Enzo Doria	11/2016
1594	2^869035-114181	261606	Enzo Doria	12/2014
1595	2^868817+26777	261540	Enzo Doria	12/2023
1596	3^547850+9000004	261391	Enzo Doria	10/2023
1597	4*10^261248+91	261249	Robert Price	11/2022
1598	55083^55083+1282^1282	261150	Henri Lifchitz	10/2024
1599	2^866908+34891	260966	Enzo Doria	07/2024
1600	2^865715+80303	260607	Enzo Doria	07/2016
1601	2^865474+23209	260534	Enzo Doria	10/2023
1602	2^865238+214759	260463	Enzo Doria	11/2023
1603	2^865048+1882411	260406	Enzo Doria	12/2016
1604	2^864899-113871	260361	Enzo Doria	10/2014
1605	(16*10^260256-91)/3	260257	Robert Price	11/2022
1606	(7*10^260198-61)/9	260198	Erik Branger	11/2011
1607	2^864298-2788421	260180	Enzo Doria	12/2015
1608	2^864039-2791357	260102	Enzo Doria	01/2016
1609	2^863621-113833	259976	Enzo Doria	10/2014
1610	10^259945-11	259945	Mischa Rodermond	04/2023
1611	2^863433+34877	259920	Enzo Doria	07/2024
1612	(28*10^259897+113)/3	259898	Robert Price	06/2023
1613	2^862837+75767	259740	Enzo Doria	05/2016
1614	2^862637-31	259680	Jorge Menendez	05/2019
1615	2^862088+1874941	259515	Enzo Doria	06/2016
1616	2^861987-134557	259484	Hans Havermann	10/2018
1617	(14*10^259431-143)/3	259432	Robert Price	05/2023
1618	2^861516-1854029	259343	Enzo Doria	09/2015
1619	2^860975-1853977	259180	Enzo Doria	09/2015
1620	3^543128+16	259138	Robert Price	04/2020
1621	2^860625-1858843	259074	Enzo Doria	10/2015
1622	2^860110+77689	258919	Enzo Doria	05/2016
1623	2^859600+1880371	258766	Enzo Doria	10/2016
1624	2^859433+494711	258716	Makoto Morimoto	10/2013
1626	(2^859433-44)/(2^2*3)	258715	Makoto Morimoto	08/2019
1625	(2^859431-11)/3	258715	Stefano Morozzi	08/2022
1627	(13*10^258710-43)/3	258711	Robert Price	08/2023
1628	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
1629	2^859240+1875271	258658	Enzo Doria	06/2016
1630	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
1631	2^858812+30421	258529	Enzo Doria	03/2024
1632	(23*10^258494-47)/3	258495	Robert Price	09/2023
1633	(144^119671+1)/145	258292	Paul Bourdelais	08/2019
1634	2^857608+105	258166	Stefano Morozzi	05/2021
1635	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
1636	2^857016-633113	257988	Enzo Doria	12/2013
1637	2^855732-113969	257602	Enzo Doria	10/2014
1638	(5*10^257431+91)/3	257432	Robert Price	08/2023
1639	2^853682-3911	256984	Enzo Doria	05/2014
1640	11^246668-90	256879	Enzo Doria	12/2012
1641	2^853181+30287	256834	Enzo Doria	03/2024
1642	5*2^852698+3	256689	Jon Grantham	07/2023
1643	(23*10^256654+7)/3	256655	Robert Price	05/2023
1644	2^851904-113939	256449	Enzo Doria	10/2014
1645	2^851725-851725^2	256395	Henri Lifchitz	03/2019
1646	11^246167-90	256357	Enzo Doria	12/2012
1647	(85*10^256301-1)/3	256303	Robert Price	12/2022
1648	(10^256187+7)/63443/148782853	256175	Alfred Reich	10/2021
1649	2^850700-569049	256087	Enzo Doria	11/2013
1650	2^850675+153	256079	Stefano Morozzi	05/2021
1651	21^193601-20^193601	255983	Jean-Louis Charton	02/2015
1652	(37^163193+1)/38	255918	Paul Bourdelais	07/2019
1653	(14*10^255805-83)/3	255806	Robert Price	11/2022
1654	2^849316+25861	255670	Enzo Doria	12/2023
1655	2^849177-114025	255628	Enzo Doria	12/2014
1656	2*10^255442-21	255443	Robert Price	08/2023
1657	2^848502-3173	255425	Yves Minet	07/2016
1658	2^848178-140291	255328	Enzo Doria	01/2014
1659	7*10^255167+87	255168	Robert Price	11/2022
1660	2^847622-2441	255160	Yves Minet	02/2016
1661	2^847291+182843	255061	Enzo Doria	11/2016
1662	2^847174+1879429	255025	Enzo Doria	09/2016
1663	2^846881+215837	254937	Enzo Doria	12/2023
1664	24*29^174239+13361	254809	Curtis Bright	04/2015
1665	22*10^254639+7	254641	Robert Price	10/2022
1666	2^845633-933075	254561	Paul Bourdelais	11/2021
1667	2^845610-1868591	254554	Enzo Doria	04/2016
1668	2^845484+81931	254517	Enzo Doria	08/2016
1669	2^845402-114761	254492	Enzo Doria	05/2015
1670	98*10^254173-9	254175	Robert Price	05/2023
1671	2^844334-2792441	254170	Enzo Doria	02/2016
1672	2*10^254162+69	254163	Robert Price	08/2023
1673	(4*10^254107+11)/3	254108	Tyler Busby	02/2023
1674	11^243796-90	253888	Enzo Doria	12/2012
1675	(10^253891+7)/44777/79843/16940711	253875	Alfred Reich	10/2021
1676	30^171733-29^171733	253671	Jean-Louis Charton	10/2018
1677	2^842325+25907	253566	Enzo Doria	11/2023
1678	2^842209+1876037	253531	Enzo Doria	07/2016
1679	2^842123-59197	253505	Enzo Doria	10/2015
1680	(8*10^253313-53)/9	253313	Serge Batalov	11/2022
1681	(28*10^253210+191)/3	253211	Robert Price	07/2023
1682	2^840797-3	253106	Paul Bourdelais	06/2019
1683	2^840716-2969	253081	Yves Minet	05/2016
1684	2^840358-462491	252973	Enzo Doria	08/2015
1685	2^840310+1878379	252959	Enzo Doria	08/2016
1686	2^840203-21	252927	Stefano Morozzi	07/2022
1687	11^242579-60	252620	Enzo Doria	10/2012
1688	45^152659+2	252378	Robert Price	09/2015
1689	(95^127583+1)/96	252322	Paul Bourdelais	07/2019
1690	7*10^252209-17	252210	Robert Price	12/2022
1691	2^837725+1869377	252181	Enzo Doria	05/2016
1692	2^837536-311039	252124	Enzo Doria	06/2015
1693	21^190632-2	252058	Robert Price	07/2015
1694	2^837242+1873297	252035	Enzo Doria	06/2016
1695	2^836995+226575	251961	Enzo Doria	10/2024
1696	2^836656-2787929	251859	Enzo Doria	11/2015
1697	2^836548+219061	251827	Enzo Doria	02/2024
1698	2^836380+1875541	251776	Enzo Doria	07/2016
1699	(359^98327-1)/358	251233	Alexander Zhirkov	11/2017
1700	tau(41^28288)	250924	Nik Lygeros / Olivier Rozier	10/2013
1701	(28*10^250655+113)/3	250656	Robert Price	06/2023
1702	2^832511-461197	250611	Enzo Doria	07/2015
1703	2^832505+1881137	250609	Enzo Doria	11/2016
1704	2^832363+583295	250567	Enzo Doria	12/2016
1705	2^832244-403635	250531	Enzo Doria	01/2014
1706	(14*10^250336-41)/9	250337	Serge Batalov	01/2023
1707	2^831528+24811	250315	Enzo Doria	11/2023
1708	2^831157+1880657	250204	Enzo Doria	11/2016
1709	2^831088-7200899	250183	Enzo Doria	01/2015
1710	2^830956-1349	250143	Yves Minet	07/2015
1711	2^830699+220583	250066	Enzo Doria	03/2024
1712	2^830037+282317	249867	Enzo Doria	09/2016
1713	2^829589-113653	249732	Enzo Doria	09/2014
1714	(4*10^249550-7)/3	249551	Serge Batalov	01/2023
1715	(103*10^249399+17)/3	249401	Robert Price	04/2023
1716	2^828281-3193	249338	Yves Minet	08/2016
1717	(2^828140-19)/3	249295	Stefano Morozzi	08/2022
1718	2^828064-2785619	249273	Enzo Doria	10/2015
1719	2^827602+60409	249134	Enzo Doria	03/2016
1720	2^827306+212419	249044	Enzo Doria	09/2023
1721	10^249010+348861	249011	Patrick De Geest	04/2016
1722	10^249010-21	249010	Serge Batalov	12/2014
1723	2^826733+1882907	248872	Enzo Doria	12/2016
1724	2^825800+22441	248591	Enzo Doria	10/2023
1725	2^825682+1876549	248556	Enzo Doria	07/2016
1726	2^824991-114121	248348	Enzo Doria	12/2014
1727	2^824642-362727	248242	Enzo Doria	12/2013
1728	2^824565-114265	248219	Enzo Doria	01/2015
1729	2^824325-25	248147	Boyan Hu	12/2024
1730	(73*10^248145-1)/9	248146	Robert Price	01/2015
1731	2^823321+219407	247845	Enzo Doria	02/2024
1732	(2^823337+1)/(3*362268281)	247841	Gord Palameta	08/2018
1733	(13*10^247793-43)/3	247794	Robert Price	08/2023
1734	(2^822971-1)/6583769/28211445881/21255852651726486149207	247700	Robert Kinser	09/2016
1735	2^822296+76501	247536	Enzo Doria	05/2016
1736	2^821590-114167	247324	Enzo Doria	12/2014
1737	2^821512-2790659	247300	Enzo Doria	12/2015
1738	(21996^57121-1)/(21996^239-1)	247002	Ryan Propper	11/2023
1739	2^820356+7	246952	Jon Grantham	08/2023
1740	2^820077+382847	246868	Enzo Doria	11/2016
1741	2^820008+81	246848	Henri Lifchitz	01/2025
1742	2^820001+81269	246845	Enzo Doria	07/2016
1743	2^819463-59197	246683	Enzo Doria	10/2015
1744	2^819296+80581	246633	Enzo Doria	07/2016
1745	2^818764+21573	246473	Enzo Doria	11/2023
1746	2^817852+215491	246198	Enzo Doria	11/2023
1747	2^817160-350369	245990	Enzo Doria	06/2015
1748	2^816039-19	245653	Stefano Morozzi	07/2022
1749	2^816029+219407	245650	Enzo Doria	02/2024
1750	(71*10^245558-17)/9	245559	Serge Batalov	01/2023

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Probable Primes Top 10000

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