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	2^501512-113669	150971	Enzo Doria	09/2014
1502	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
1503	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
1504	2^500899-500899	150786	Henri Lifchitz	04/2005
1505	2^500832+1876801	150766	Enzo Doria	07/2016
1506	(23*10^150763-59)/9	150764	Robert Price	05/2018
1507	2^500699+1884953	150726	Enzo Doria	02/2017
1508	(13*10^150675-37)/3	150676	Robert Price	01/2019
1509	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
1510	2^500337-71101	150617	Enzo Doria	04/2016
1511	4*10^150577+91	150578	Robert Price	08/2018
1512	2^500160+80071	150564	Enzo Doria	06/2016
1513	(2^500120+5)/9	150551	Lelio R Paula	12/2017
1514	(43*10^150515-421)/9	150516	Robert Price	01/2019
1515	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
1516	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
1517	2^499861-29503	150474	Enzo Doria	08/2015
1518	2^499653-113533	150411	Enzo Doria	08/2014
1519	2^499534-221	150375	Yves Minet	06/2012
1520	2^499225+49727	150282	Enzo Doria	09/2016
1521	2^499054-29261	150231	Enzo Doria	07/2015
1522	(2^498898-7)/9	150183	Lelio R Paula	10/2015
1523	3*10^150182+17	150183	Robert Price	07/2018
1524	2^498623+1866983	150101	Enzo Doria	03/2016
1525	numbpart(18140942830)	150033	Serge Batalov	04/2017
1526	10^150029+4381	150030	Patrick De Geest	05/2016
1527	10^150029-41	150029	Serge Batalov	12/2014
1528	10^150000+1158603	150001	Patrick De Geest	09/2018
1529	10^150000-245703	150000	Patrick De Geest	09/2018
1530	(38*10^149999+691)/9	150000	Robert Price	10/2018
1531	2^498238-53	149985	Lelio R Paula	12/2017
1532	5*10^149907+23	149908	Robert Price	03/2019
1533	2^497850+81049	149868	Enzo Doria	07/2016
1534	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
1535	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
1536	(2*10^149803-143)/3	149803	Robert Price	03/2018
1537	2^497434-2784191	149743	Enzo Doria	10/2015
1538	2^497068-113579	149633	Enzo Doria	08/2014
1539	2^497037+73727	149624	Enzo Doria	04/2016
1540	2^496773+77747	149544	Enzo Doria	05/2016
1541	2^496477-113485	149455	Enzo Doria	08/2014
1542	2^496270-49451	149393	Enzo Doria	10/2015
1543	2^496238-1865081	149383	Enzo Doria	01/2016
1544	2^495968-1853699	149302	Enzo Doria	09/2015
1545	2^495935-4117	149292	Yves Minet	02/2018
1546	2^495712-396765	149225	Enzo Doria	07/2013
1547	(21*2^495676-1)/4835	149211	Lelio R Paula	10/2015
1548	2^495420+1880701	149137	Enzo Doria	10/2016
1549	2^495337-1847293	149112	Enzo Doria	07/2015
1550	(2^495193-7)/5	149068	Lelio R Paula	10/2015
1551	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
1552	47^89113-46^89113	149006	Robert Price	10/2012
1553	2^494916+87855	148985	Lelio R Paula	01/2016
1554	6*10^148982+73	148983	Robert Price	04/2019
1555	2^494586-2791991	148886	Enzo Doria	02/2016
1556	8*10^148860-3	148861	Ray Chandler	04/2011
1557	2^494333-286183	148810	Enzo Doria	06/2015
1558	2^494144-264119	148753	Enzo Doria	05/2014
1559	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
1560	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
1561	2^493636+82081	148600	Enzo Doria	09/2016
1562	((((((((((((((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
1563	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
1564	(2*10^148460-23)/3	148460	Robert Price	04/2018
1565	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
1566	5^211959-12874	148153	Enzo Doria	05/2014
1567	(16*10^148071+41)/3	148072	Robert Price	03/2019
1568	187^65175-2	148068	Lelio R Paula	11/2017
1569	2^491851+1871453	148062	Enzo Doria	05/2016
1570	2^491521-1865323	147963	Enzo Doria	02/2016
1571	(2^491476+7)/71	147948	Lelio R Paula	10/2015
1572	2^491391-7807	147924	Lelio R Paula	01/2013
1573	2^491370-113297	147918	Enzo Doria	07/2014
1574	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
1575	(17*10^147890+79)/3	147891	Robert Price	04/2019
1576	2^490660-17	147704	Lelio R Paula	12/2017
1577	2^490550+1179439	147671	Enzo Doria	06/2016
1578	(23*10^147649-59)/9	147650	Robert Price	05/2018
1579	2^490303+2793653	147596	Enzo Doria	03/2016
1580	199^64181-2	147543	Lelio R Paula	11/2017
1581	2^489871-286987	147466	Enzo Doria	07/2015
1582	2^489864-351899	147464	Enzo Doria	07/2015
1583	175^65724-2	147422	Lelio R Paula	11/2017
1584	2^489712+1874851	147419	Enzo Doria	06/2016
1585	63^81896-2	147359	Lelio R Paula	10/2017
1586	(11*10^147313-107)/3	147314	Robert Price	09/2018
1587	2^489305-59815	147296	Enzo Doria	10/2015
1588	(2^489280-7)/6381	147285	Lelio R Paula	09/2015
1589	2^489125+80357	147242	Enzo Doria	06/2016
1590	2^488648-112799	147098	Enzo Doria	07/2014
1591	2^488627-350317	147092	Enzo Doria	06/2015
1592	(2^488441-1)/(61543567*30051203516986199)	147012	Dario Alpern	12/2014
1593	2^488280-2165	146987	Yves Minet	07/2014
1594	2^488278+45	146987	Lelio R Paula	12/2017
1595	2^487927-39	146881	Lelio R Paula	12/2017
1596	(7*10^146860-13)/3	146861	Robert Price	07/2018
1597	2^487726-1863341	146821	Enzo Doria	12/2015
1598	(22*10^146661-19)/3	146662	Robert Price	04/2019
1599	2^487121-39523	146639	Enzo Doria	09/2015
1600	(7*2^486967+1)/39	146591	Lelio R Paula	09/2015
1601	2^486893-79	146570	Yves Minet	09/2017
1602	2^486840+1879141	146554	Enzo Doria	08/2016
1603	2^486774-87	146534	Lelio R Paula	12/2017
1604	96^73877-95^73877	146445	Robert Price	10/2015
1605	(52^85259+1)/53	146304	Paul Bourdelais	09/2017
1606	179^64935+2	146290	Lelio R Paula	10/2017
1607	(19*10^146181-49)/3	146182	Robert Price	05/2019
1608	2^485531-114621	146160	Enzo Doria	05/2015
1609	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
1610	2^485389+81887	146117	Enzo Doria	08/2016
1611	(10^146063+71)/9	146063	Serge Batalov	07/2015
1612	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
1613	(22*10^146029+257)/9	146030	Robert Price	06/2018
1614	2^484743+1872923	145923	Enzo Doria	05/2016
1615	2^484341+1879157	145802	Enzo Doria	08/2016
1616	2^484271-51	145781	Lelio R Paula	11/2017
1617	70^78989-69^78989	145743	Robert Price	01/2014
1618	51^85334+2	145714	Robert Price	07/2015
1619	2^483886-1857101	145665	Enzo Doria	10/2015
1620	2^483563-1863457	145567	Enzo Doria	12/2015
1621	2^483516-1861409	145553	Enzo Doria	11/2015
1622	2^483384-115019	145514	Enzo Doria	06/2015
1623	(19*10^145499-61)/3	145500	Robert Price	05/2019
1624	2^483302-3221	145489	Lelio R Paula	12/2012
1625	2^483046+1874029	145412	Enzo Doria	06/2016
1626	2^482991-2789317	145395	Enzo Doria	12/2015
1627	2^482978-2789711	145391	Enzo Doria	12/2015
1628	2^482966-2789711	145388	Enzo Doria	12/2015
1629	2^482817-1858843	145343	Enzo Doria	10/2015
1630	2^482751-113635	145323	Enzo Doria	08/2014
1631	2^482705-459763	145309	Enzo Doria	05/2015
1632	(4^241306+11)/3	145281	Robert Price	03/2017
1633	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
1634	53^84239-52^84239	145252	Robert Price	01/2013
1635	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
1636	2^482087+72623	145123	Enzo Doria	04/2016
1637	2^482016-286565	145102	Enzo Doria	07/2015
1638	2^481840+15	145049	Robert Price	09/2015
1639	2^481801-481801	145037	Henri Lifchitz	03/2005
1640	2^481775+1869083	145029	Enzo Doria	05/2016
1641	29^99167+2	145022	Ray Chandler	08/2011
1642	2^481663+1875653	144996	Enzo Doria	07/2016
1643	2^481149-459073	144841	Enzo Doria	05/2015
1644	2^481045-113215	144809	Enzo Doria	07/2014
1645	(64*10^144797+287)/9	144798	Robert Price	04/2019
1646	2^480859-113695	144753	Enzo Doria	09/2014
1647	2^480766-2787191	144725	Enzo Doria	11/2015
1648	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
1649	2^480678+1874239	144699	Enzo Doria	06/2016
1650	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
1651	L(692147)	144651	Henri Lifchitz	10/2008
1652	2^480417+35	144620	Robert Price	11/2015
1653	2^480296-59879	144584	Enzo Doria	10/2015
1654	2^479844+3	144448	Donovan Johnson	06/2006
1655	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
1656	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015
1657	2^479348-2792219	144299	Enzo Doria	02/2016
1658	3^302389-6242	144277	Enzo Doria	05/2014
1659	2*10^144220-3	144221	Robert Price	07/2015
1660	2^478904-109109	144165	Enzo Doria	04/2014
1661	2^478337-115333	143994	Enzo Doria	07/2015
1662	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
1663	88^74047-87^74047	143984	Robert Price	05/2015
1664	(19*10^143963+467)/9	143964	Robert Price	02/2018
1665	(71^77761+1)/72	143954	Paul Bourdelais	09/2017
1666	2^478088+27	143919	Robert Price	11/2015
1667	2^477475-22071	143735	Enzo Doria	07/2013
1668	2^477417-22123	143717	Enzo Doria	07/2013
1669	2^477359-3577	143700	Yves Minet	03/2017
1670	(14*10^143662-71)/3	143663	Robert Price	12/2018
1671	2^476936-396765	143573	Enzo Doria	07/2013
1672	2^476888-2791229	143558	Enzo Doria	01/2016
1673	2^476868-1859939	143552	Enzo Doria	11/2015
1674	755^49878+49878^755	143547	Norbert Schneider	04/2019
1675	2^476558-113627	143459	Enzo Doria	08/2014
1676	2^476478-45	143435	Lelio R Paula	11/2017
1677	(2^475854+9)/73	143245	Lelio R Paula	08/2015
1678	2^475813-113239	143234	Enzo Doria	07/2014
1679	2^475624-114059	143178	Enzo Doria	11/2014
1680	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
1681	2^475480-2786129	143134	Enzo Doria	10/2015
1682	(19*10^143129-43)/3	143130	Robert Price	05/2019
1683	(14*10^143097+73)/3	143098	Robert Price	12/2018
1684	2^475299-111937	143080	Enzo Doria	05/2014
1685	2^475160-2797859	143038	Enzo Doria	04/2016
1686	(2^475069+3)/395	143008	Lelio R Paula	08/2015
1687	2^475027-461437	142998	Enzo Doria	07/2015
1688	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
1689	(8*10^142932+43)/3	142933	Robert Price	06/2018
1690	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
1691	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
1692	2^474417-59923	142814	Enzo Doria	10/2015
1693	4*10^142810-21	142811	Robert Price	09/2018
1694	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
1695	2^474053+2897	142705	Lelio R Paula	08/2012
1696	(10^142699+359)/9	142699	Serge Batalov	12/2014
1697	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
1698	2^473740-1856639	142610	Enzo Doria	09/2015
1699	2^473617-114223	142573	Enzo Doria	12/2014
1700	2^473257+1873217	142465	Enzo Doria	06/2016
1701	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
1702	(14*10^142440+61)/3	142441	Robert Price	12/2018
1703	(10^142425+359)/9	142425	Serge Batalov	12/2014
1704	2^473101+773027	142418	Enzo Doria	05/2016
1705	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
1706	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
1707	2^472634-109511	142278	Enzo Doria	04/2014
1708	(48^84589+1)/49	142213	Robert Price	01/2014
1709	2^472258+7	142164	Lelio R Paula	08/2015
1710	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
1711	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
1712	(16*10^142058+197)/3	142059	Robert Price	04/2019
1713	2^471792+1880881	142024	Enzo Doria	11/2016
1714	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
1715	(4*10^141926-79)/3	141927	Robert Price	02/2018
1716	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
1717	(14*10^141853+37)/3	141854	Robert Price	12/2018
1718	(41*10^141836-59)/9	141837	Robert Price	10/2018
1719	4*5^202913-9	141831	Lelio R Paula	04/2015
1720	2*7^167812-3	141818	Lelio R Paula	12/2014
1721	2^471043+35	141799	Robert Price	11/2015
1722	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
1723	(11*10^141718-131)/3	141719	Robert Price	09/2018
1724	2^470692+76771	141693	Enzo Doria	05/2016
1725	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
1726	2^470305-459373	141576	Enzo Doria	05/2015
1727	2^470183+72623	141540	Enzo Doria	04/2016
1728	2^470173-16465	141537	Enzo Doria	04/2013
1729	2^469974-1841	141477	Enzo Doria	05/2014
1730	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
1731	2*10^141448+63	141449	Robert Price	05/2018
1732	2^469824+43	141432	Lelio R Paula	09/2017
1733	2*10^141407-27	141408	Robert Price	05/2018
1734	2^469630-59711	141373	Enzo Doria	10/2015
1735	(25*10^141366-331)/9	141367	Robert Price	08/2018
1736	(2^469564-3)/611	141351	Lelio R Paula	08/2015
1737	197^61601+2	141342	Lelio R Paula	08/2017
1738	2^469372-112949	141296	Enzo Doria	07/2014
1740	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
1739	143^65536+106^65536	141253	Serge Batalov	03/2018
1741	2^469198+782569	141243	Enzo Doria	10/2016
1742	2^469076-2786939	141206	Enzo Doria	11/2015
1743	2^468804+1874941	141125	Enzo Doria	06/2016
1744	2^468787+81353	141119	Enzo Doria	08/2016
1745	2^468595-350407	141062	Enzo Doria	06/2015
1746	2^468564+87855	141052	Lelio R Paula	01/2016
1747	2^468551-21987	141048	Enzo Doria	07/2013
1748	2^468523-7	141040	Lelio R Paula	08/2015
1749	2^468405+87855	141004	Lelio R Paula	01/2016
1750	2^467978-113051	140876	Enzo Doria	07/2014

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