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	2^508174-1855151	152976	Enzo Doria	09/2015
1502	181^67757-2	152974	Lelio R Paula	12/2017
1503	2^508160-1864829	152972	Enzo Doria	01/2016
1504	2^507857-1848199	152881	Enzo Doria	07/2015
1505	2^507638-115361	152815	Enzo Doria	07/2015
1506	2^507551-114025	152789	Enzo Doria	11/2014
1507	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
1508	(22*10^152670-13)/9	152671	Robert Price	06/2018
1509	2^506451-22339	152457	Enzo Doria	07/2013
1510	2^505995-113185	152320	Enzo Doria	07/2014
1511	(4*10^152253+149)/9	152253	Robert Price	04/2018
1512	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
1513	2^505431-505431	152150	Henri Lifchitz	04/2005
1514	2^505053+73097	152037	Enzo Doria	04/2016
1515	(2^504793-7)/46765	151954	Lelio R Paula	12/2017
1516	350377#+797581	151937	Nicolas PALAU	08/2017
1517	2^504618-343991	151906	Enzo Doria	07/2015
1518	2^504212-461939	151783	Enzo Doria	07/2015
1519	2^504054-2231	151736	Yves Minet	10/2011
1520	2^503361-39883	151527	Enzo Doria	09/2015
1521	2^503225+382667	151486	Enzo Doria	10/2016
1522	(26*10^151391-503)/9	151392	Robert Price	07/2018
1523	2^502769+1877567	151349	Enzo Doria	08/2016
1524	2^502576-4019	151291	Yves Minet	10/2011
1525	5*10^151257+41	151258	Robert Price	03/2019
1526	2^502290-2792501	151205	Enzo Doria	02/2016
1527	2^502181+1868417	151172	Enzo Doria	04/2016
1528	2^501781-1850503	151052	Enzo Doria	08/2015
1529	(5*10^151007+37)/3	151008	Robert Price	03/2018
1530	2^501627-991	151005	Yves Minet	02/2014
1531	2^501577-115333	150990	Enzo Doria	07/2015
1532	8*10^150975+3	150976	Robert Price	08/2015
1533	2^501512-113669	150971	Enzo Doria	09/2014
1534	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
1535	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
1536	2^500899-500899	150786	Henri Lifchitz	04/2005
1537	2^500832+1876801	150766	Enzo Doria	07/2016
1538	(23*10^150763-59)/9	150764	Robert Price	05/2018
1539	2^500699+1884953	150726	Enzo Doria	02/2017
1540	(13*10^150675-37)/3	150676	Robert Price	01/2019
1541	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
1542	2^500337-71101	150617	Enzo Doria	04/2016
1543	(74*10^150616+133)/9	150617	Robert Price	06/2019
1544	4*10^150577+91	150578	Robert Price	08/2018
1545	2^500160+80071	150564	Enzo Doria	06/2016
1546	(2^500120+5)/9	150551	Lelio R Paula	12/2017
1547	(43*10^150515-421)/9	150516	Robert Price	01/2019
1549	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
1548	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
1550	2^499861-29503	150474	Enzo Doria	08/2015
1551	2^499653-113533	150411	Enzo Doria	08/2014
1552	2^499534-221	150375	Yves Minet	06/2012
1553	2^499225+49727	150282	Enzo Doria	09/2016
1554	2^499054-29261	150231	Enzo Doria	07/2015
1555	(2^498898-7)/9	150183	Lelio R Paula	10/2015
1556	3*10^150182+17	150183	Robert Price	07/2018
1557	2^498623+1866983	150101	Enzo Doria	03/2016
1558	numbpart(18140942830)	150033	Serge Batalov	04/2017
1559	10^150029+4381	150030	Patrick De Geest	05/2016
1560	10^150029-41	150029	Serge Batalov	12/2014
1561	10^150000+1158603	150001	Patrick De Geest	09/2018
1562	10^150000-245703	150000	Patrick De Geest	09/2018
1563	(38*10^149999+691)/9	150000	Robert Price	10/2018
1564	2^498238-53	149985	Lelio R Paula	12/2017
1565	5*10^149907+23	149908	Robert Price	03/2019
1566	2^497850+81049	149868	Enzo Doria	07/2016
1567	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
1568	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
1569	(2*10^149803-143)/3	149803	Robert Price	03/2018
1570	2^497434-2784191	149743	Enzo Doria	10/2015
1571	(23*10^149655+19)/3	149656	Robert Price	07/2019
1572	2^497068-113579	149633	Enzo Doria	08/2014
1573	2^497037+73727	149624	Enzo Doria	04/2016
1574	2^496773+77747	149544	Enzo Doria	05/2016
1575	2^496477-113485	149455	Enzo Doria	08/2014
1576	2^496270-49451	149393	Enzo Doria	10/2015
1577	2^496238-1865081	149383	Enzo Doria	01/2016
1578	2^495968-1853699	149302	Enzo Doria	09/2015
1579	2^495935-4117	149292	Yves Minet	02/2018
1580	2^495712-396765	149225	Enzo Doria	07/2013
1581	(21*2^495676-1)/4835	149211	Lelio R Paula	10/2015
1582	2^495420+1880701	149137	Enzo Doria	10/2016
1583	2^495337-1847293	149112	Enzo Doria	07/2015
1584	(2^495193-7)/5	149068	Lelio R Paula	10/2015
1585	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
1586	47^89113-46^89113	149006	Robert Price	10/2012
1587	2^494916+87855	148985	Lelio R Paula	01/2016
1588	6*10^148982+73	148983	Robert Price	04/2019
1589	2^494586-2791991	148886	Enzo Doria	02/2016
1590	8*10^148860-3	148861	Ray Chandler	04/2011
1591	2^494333-286183	148810	Enzo Doria	06/2015
1592	2^494144-264119	148753	Enzo Doria	05/2014
1593	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
1594	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
1595	2^493636+82081	148600	Enzo Doria	09/2016
1596	((((((((((((((34251^2-2)^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	148593	Serge Batalov	07/2016
1597	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
1598	(2*10^148460-23)/3	148460	Robert Price	04/2018
1599	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
1600	(71*10^148306-539)/9	148307	Robert Price	07/2019
1601	5^211959-12874	148153	Enzo Doria	05/2014
1602	(16*10^148071+41)/3	148072	Robert Price	03/2019
1603	187^65175-2	148068	Lelio R Paula	11/2017
1604	2^491851+1871453	148062	Enzo Doria	05/2016
1605	(68*10^148060-257)/9	148061	Robert Price	07/2019
1606	2^491521-1865323	147963	Enzo Doria	02/2016
1607	(2^491476+7)/71	147948	Lelio R Paula	10/2015
1608	2^491391-7807	147924	Lelio R Paula	01/2013
1609	2^491370-113297	147918	Enzo Doria	07/2014
1610	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
1611	(17*10^147890+79)/3	147891	Robert Price	04/2019
1612	2^490660-17	147704	Lelio R Paula	12/2017
1613	2^490550+1179439	147671	Enzo Doria	06/2016
1614	(23*10^147649-59)/9	147650	Robert Price	05/2018
1615	2^490303+2793653	147596	Enzo Doria	03/2016
1616	199^64181-2	147543	Lelio R Paula	11/2017
1617	2^489871-286987	147466	Enzo Doria	07/2015
1618	2^489864-351899	147464	Enzo Doria	07/2015
1619	175^65724-2	147422	Lelio R Paula	11/2017
1620	2^489712+1874851	147419	Enzo Doria	06/2016
1621	63^81896-2	147359	Lelio R Paula	10/2017
1622	(11*10^147313-107)/3	147314	Robert Price	09/2018
1623	2^489305-59815	147296	Enzo Doria	10/2015
1624	(2^489280-7)/6381	147285	Lelio R Paula	09/2015
1625	2^489125+80357	147242	Enzo Doria	06/2016
1626	2^488648-112799	147098	Enzo Doria	07/2014
1627	2^488627-350317	147092	Enzo Doria	06/2015
1628	(2^488441-1)/(61543567*30051203516986199)	147012	Dario Alpern	12/2014
1629	2^488280-2165	146987	Yves Minet	07/2014
1630	2^488278+45	146987	Lelio R Paula	12/2017
1631	2^487927-39	146881	Lelio R Paula	12/2017
1632	(7*10^146860-13)/3	146861	Robert Price	07/2018
1633	2^487726-1863341	146821	Enzo Doria	12/2015
1634	(22*10^146661-19)/3	146662	Robert Price	04/2019
1635	2^487121-39523	146639	Enzo Doria	09/2015
1636	(7*2^486967+1)/39	146591	Lelio R Paula	09/2015
1637	2^486893-79	146570	Yves Minet	09/2017
1638	2^486840+1879141	146554	Enzo Doria	08/2016
1639	2^486774-87	146534	Lelio R Paula	12/2017
1640	96^73877-95^73877	146445	Robert Price	10/2015
1641	(52^85259+1)/53	146304	Paul Bourdelais	09/2017
1642	179^64935+2	146290	Lelio R Paula	10/2017
1643	(19*10^146181-49)/3	146182	Robert Price	05/2019
1644	2^485531-114621	146160	Enzo Doria	05/2015
1645	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
1646	2^485389+81887	146117	Enzo Doria	08/2016
1647	(10^146063+71)/9	146063	Serge Batalov	07/2015
1648	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
1649	(22*10^146029+257)/9	146030	Robert Price	06/2018
1650	2^484743+1872923	145923	Enzo Doria	05/2016
1651	2^484341+1879157	145802	Enzo Doria	08/2016
1652	2^484271-51	145781	Lelio R Paula	11/2017
1653	70^78989-69^78989	145743	Robert Price	01/2014
1654	51^85334+2	145714	Robert Price	07/2015
1655	2^483886-1857101	145665	Enzo Doria	10/2015
1656	2^483563-1863457	145567	Enzo Doria	12/2015
1657	2^483516-1861409	145553	Enzo Doria	11/2015
1658	2^483384-115019	145514	Enzo Doria	06/2015
1659	(19*10^145499-61)/3	145500	Robert Price	05/2019
1660	2^483302-3221	145489	Lelio R Paula	12/2012
1661	2^483046+1874029	145412	Enzo Doria	06/2016
1662	2^482991-2789317	145395	Enzo Doria	12/2015
1663	2^482978-2789711	145391	Enzo Doria	12/2015
1664	2^482966-2789711	145388	Enzo Doria	12/2015
1665	2^482817-1858843	145343	Enzo Doria	10/2015
1666	2^482751-113635	145323	Enzo Doria	08/2014
1667	2^482705-459763	145309	Enzo Doria	05/2015
1668	(4^241306+11)/3	145281	Robert Price	03/2017
1669	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
1670	53^84239-52^84239	145252	Robert Price	01/2013
1671	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
1672	2^482087+72623	145123	Enzo Doria	04/2016
1673	2^482016-286565	145102	Enzo Doria	07/2015
1674	2^481840+15	145049	Robert Price	09/2015
1675	2^481801-481801	145037	Henri Lifchitz	03/2005
1676	2^481775+1869083	145029	Enzo Doria	05/2016
1677	29^99167+2	145022	Ray Chandler	08/2011
1678	2^481663+1875653	144996	Enzo Doria	07/2016
1679	2^481149-459073	144841	Enzo Doria	05/2015
1680	2^481045-113215	144809	Enzo Doria	07/2014
1681	(64*10^144797+287)/9	144798	Robert Price	04/2019
1682	2^480859-113695	144753	Enzo Doria	09/2014
1683	2^480766-2787191	144725	Enzo Doria	11/2015
1684	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
1685	2^480678+1874239	144699	Enzo Doria	06/2016
1686	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
1687	L(692147)	144651	Henri Lifchitz	10/2008
1688	2^480417+35	144620	Robert Price	11/2015
1689	2^480296-59879	144584	Enzo Doria	10/2015
1690	2^479844+3	144448	Donovan Johnson	06/2006
1691	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
1692	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015
1693	2^479348-2792219	144299	Enzo Doria	02/2016
1694	3^302389-6242	144277	Enzo Doria	05/2014
1695	2*10^144220-3	144221	Robert Price	07/2015
1696	2^478904-109109	144165	Enzo Doria	04/2014
1697	2^478337-115333	143994	Enzo Doria	07/2015
1698	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
1699	88^74047-87^74047	143984	Robert Price	05/2015
1700	(19*10^143963+467)/9	143964	Robert Price	02/2018
1701	(71^77761+1)/72	143954	Paul Bourdelais	09/2017
1702	2^478088+27	143919	Robert Price	11/2015
1703	2^477475-22071	143735	Enzo Doria	07/2013
1704	2^477417-22123	143717	Enzo Doria	07/2013
1705	2^477359-3577	143700	Yves Minet	03/2017
1706	(14*10^143662-71)/3	143663	Robert Price	12/2018
1707	2^476936-396765	143573	Enzo Doria	07/2013
1708	2^476888-2791229	143558	Enzo Doria	01/2016
1709	2^476868-1859939	143552	Enzo Doria	11/2015
1710	755^49878+49878^755	143547	Norbert Schneider	04/2019
1711	2^476558-113627	143459	Enzo Doria	08/2014
1712	2^476478-45	143435	Lelio R Paula	11/2017
1713	(2^475854+9)/73	143245	Lelio R Paula	08/2015
1714	2^475813-113239	143234	Enzo Doria	07/2014
1715	2^475624-114059	143178	Enzo Doria	11/2014
1716	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
1717	2^475480-2786129	143134	Enzo Doria	10/2015
1718	(19*10^143129-43)/3	143130	Robert Price	05/2019
1719	(14*10^143097+73)/3	143098	Robert Price	12/2018
1720	2^475299-111937	143080	Enzo Doria	05/2014
1721	2^475160-2797859	143038	Enzo Doria	04/2016
1722	(2^475069+3)/395	143008	Lelio R Paula	08/2015
1723	2^475027-461437	142998	Enzo Doria	07/2015
1724	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
1725	(8*10^142932+43)/3	142933	Robert Price	06/2018
1726	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
1727	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
1728	2^474417-59923	142814	Enzo Doria	10/2015
1729	4*10^142810-21	142811	Robert Price	09/2018
1730	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
1731	2^474053+2897	142705	Lelio R Paula	08/2012
1732	(10^142699+359)/9	142699	Serge Batalov	12/2014
1733	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
1734	2^473740-1856639	142610	Enzo Doria	09/2015
1735	2^473617-114223	142573	Enzo Doria	12/2014
1736	2^473257+1873217	142465	Enzo Doria	06/2016
1737	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
1738	(14*10^142440+61)/3	142441	Robert Price	12/2018
1739	(10^142425+359)/9	142425	Serge Batalov	12/2014
1740	2^473101+773027	142418	Enzo Doria	05/2016
1741	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
1742	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
1743	2^472634-109511	142278	Enzo Doria	04/2014
1744	(48^84589+1)/49	142213	Robert Price	01/2014
1745	7*10^142189+87	142190	Robert Price	07/2019
1746	2^472258+7	142164	Lelio R Paula	08/2015
1747	(23*10^142105+91)/3	142106	Robert Price	08/2019
1748	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
1749	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
1750	(16*10^142058+197)/3	142059	Robert Price	04/2019

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