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	2^499225+49727	150282	Enzo Doria	09/2016
1502	2^499054-29261	150231	Enzo Doria	07/2015
1503	(2^498898-7)/9	150183	Lelio R Paula	10/2015
1504	3*10^150182+17	150183	Robert Price	07/2018
1505	2^498623+1866983	150101	Enzo Doria	03/2016
1506	numbpart(18140942830)	150033	Serge Batalov	04/2017
1507	10^150029+4381	150030	Patrick De Geest	05/2016
1508	10^150029-41	150029	Serge Batalov	12/2014
1509	10^150000+1158603	150001	Patrick De Geest	09/2018
1510	10^150000-245703	150000	Patrick De Geest	09/2018
1511	(38*10^149999+691)/9	150000	Robert Price	10/2018
1512	2^498238-53	149985	Lelio R Paula	12/2017
1513	5*10^149907+23	149908	Robert Price	03/2019
1514	2^497850+81049	149868	Enzo Doria	07/2016
1515	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
1516	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
1517	(2*10^149803-143)/3	149803	Robert Price	03/2018
1518	2^497434-2784191	149743	Enzo Doria	10/2015
1519	2^497068-113579	149633	Enzo Doria	08/2014
1520	2^497037+73727	149624	Enzo Doria	04/2016
1521	2^496773+77747	149544	Enzo Doria	05/2016
1522	2^496477-113485	149455	Enzo Doria	08/2014
1523	2^496270-49451	149393	Enzo Doria	10/2015
1524	2^496238-1865081	149383	Enzo Doria	01/2016
1525	2^495968-1853699	149302	Enzo Doria	09/2015
1526	2^495935-4117	149292	Yves Minet	02/2018
1527	2^495712-396765	149225	Enzo Doria	07/2013
1528	(21*2^495676-1)/4835	149211	Lelio R Paula	10/2015
1529	2^495420+1880701	149137	Enzo Doria	10/2016
1530	2^495337-1847293	149112	Enzo Doria	07/2015
1531	(2^495193-7)/5	149068	Lelio R Paula	10/2015
1532	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
1533	47^89113-46^89113	149006	Robert Price	10/2012
1534	2^494916+87855	148985	Lelio R Paula	01/2016
1535	6*10^148982+73	148983	Robert Price	04/2019
1536	2^494586-2791991	148886	Enzo Doria	02/2016
1537	8*10^148860-3	148861	Ray Chandler	04/2011
1538	2^494333-286183	148810	Enzo Doria	06/2015
1539	2^494144-264119	148753	Enzo Doria	05/2014
1540	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
1541	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
1542	2^493636+82081	148600	Enzo Doria	09/2016
1543	((((((((((((((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
1544	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
1545	(2*10^148460-23)/3	148460	Robert Price	04/2018
1546	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
1547	5^211959-12874	148153	Enzo Doria	05/2014
1548	(16*10^148071+41)/3	148072	Robert Price	03/2019
1549	187^65175-2	148068	Lelio R Paula	11/2017
1550	2^491851+1871453	148062	Enzo Doria	05/2016
1551	2^491521-1865323	147963	Enzo Doria	02/2016
1552	(2^491476+7)/71	147948	Lelio R Paula	10/2015
1553	2^491391-7807	147924	Lelio R Paula	01/2013
1554	2^491370-113297	147918	Enzo Doria	07/2014
1555	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
1556	(17*10^147890+79)/3	147891	Robert Price	04/2019
1557	2^490660-17	147704	Lelio R Paula	12/2017
1558	2^490550+1179439	147671	Enzo Doria	06/2016
1559	(23*10^147649-59)/9	147650	Robert Price	05/2018
1560	2^490303+2793653	147596	Enzo Doria	03/2016
1561	199^64181-2	147543	Lelio R Paula	11/2017
1562	2^489871-286987	147466	Enzo Doria	07/2015
1563	2^489864-351899	147464	Enzo Doria	07/2015
1564	175^65724-2	147422	Lelio R Paula	11/2017
1565	2^489712+1874851	147419	Enzo Doria	06/2016
1566	63^81896-2	147359	Lelio R Paula	10/2017
1567	(11*10^147313-107)/3	147314	Robert Price	09/2018
1568	2^489305-59815	147296	Enzo Doria	10/2015
1569	(2^489280-7)/6381	147285	Lelio R Paula	09/2015
1570	2^489125+80357	147242	Enzo Doria	06/2016
1571	2^488648-112799	147098	Enzo Doria	07/2014
1572	2^488627-350317	147092	Enzo Doria	06/2015
1573	(2^488441-1)/(61543567*30051203516986199)	147012	Dario Alpern	12/2014
1574	2^488280-2165	146987	Yves Minet	07/2014
1575	2^488278+45	146987	Lelio R Paula	12/2017
1576	2^487927-39	146881	Lelio R Paula	12/2017
1577	(7*10^146860-13)/3	146861	Robert Price	07/2018
1578	2^487726-1863341	146821	Enzo Doria	12/2015
1579	2^487121-39523	146639	Enzo Doria	09/2015
1580	(7*2^486967+1)/39	146591	Lelio R Paula	09/2015
1581	2^486893-79	146570	Yves Minet	09/2017
1582	2^486840+1879141	146554	Enzo Doria	08/2016
1583	2^486774-87	146534	Lelio R Paula	12/2017
1584	96^73877-95^73877	146445	Robert Price	10/2015
1585	(52^85259+1)/53	146304	Paul Bourdelais	09/2017
1586	179^64935+2	146290	Lelio R Paula	10/2017
1587	2^485531-114621	146160	Enzo Doria	05/2015
1588	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
1589	2^485389+81887	146117	Enzo Doria	08/2016
1590	(10^146063+71)/9	146063	Serge Batalov	07/2015
1591	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
1592	(22*10^146029+257)/9	146030	Robert Price	06/2018
1593	2^484743+1872923	145923	Enzo Doria	05/2016
1594	2^484341+1879157	145802	Enzo Doria	08/2016
1595	2^484271-51	145781	Lelio R Paula	11/2017
1596	70^78989-69^78989	145743	Robert Price	01/2014
1597	51^85334+2	145714	Robert Price	07/2015
1598	2^483886-1857101	145665	Enzo Doria	10/2015
1599	2^483563-1863457	145567	Enzo Doria	12/2015
1600	2^483516-1861409	145553	Enzo Doria	11/2015
1601	2^483384-115019	145514	Enzo Doria	06/2015
1602	2^483302-3221	145489	Lelio R Paula	12/2012
1603	2^483046+1874029	145412	Enzo Doria	06/2016
1604	2^482991-2789317	145395	Enzo Doria	12/2015
1605	2^482978-2789711	145391	Enzo Doria	12/2015
1606	2^482966-2789711	145388	Enzo Doria	12/2015
1607	2^482817-1858843	145343	Enzo Doria	10/2015
1608	2^482751-113635	145323	Enzo Doria	08/2014
1609	2^482705-459763	145309	Enzo Doria	05/2015
1610	(4^241306+11)/3	145281	Robert Price	03/2017
1611	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
1612	53^84239-52^84239	145252	Robert Price	01/2013
1613	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
1614	2^482087+72623	145123	Enzo Doria	04/2016
1615	2^482016-286565	145102	Enzo Doria	07/2015
1616	2^481840+15	145049	Robert Price	09/2015
1617	2^481801-481801	145037	Henri Lifchitz	03/2005
1618	2^481775+1869083	145029	Enzo Doria	05/2016
1619	29^99167+2	145022	Ray Chandler	08/2011
1620	2^481663+1875653	144996	Enzo Doria	07/2016
1621	2^481149-459073	144841	Enzo Doria	05/2015
1622	2^481045-113215	144809	Enzo Doria	07/2014
1623	(64*10^144797+287)/9	144798	Robert Price	04/2019
1624	2^480859-113695	144753	Enzo Doria	09/2014
1625	2^480766-2787191	144725	Enzo Doria	11/2015
1626	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
1627	2^480678+1874239	144699	Enzo Doria	06/2016
1628	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
1629	L(692147)	144651	Henri Lifchitz	10/2008
1630	2^480417+35	144620	Robert Price	11/2015
1631	2^480296-59879	144584	Enzo Doria	10/2015
1632	2^479844+3	144448	Donovan Johnson	06/2006
1633	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
1634	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015
1635	2^479348-2792219	144299	Enzo Doria	02/2016
1636	3^302389-6242	144277	Enzo Doria	05/2014
1637	2*10^144220-3	144221	Robert Price	07/2015
1638	2^478904-109109	144165	Enzo Doria	04/2014
1639	2^478337-115333	143994	Enzo Doria	07/2015
1640	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
1641	88^74047-87^74047	143984	Robert Price	05/2015
1642	(19*10^143963+467)/9	143964	Robert Price	02/2018
1643	(71^77761+1)/72	143954	Paul Bourdelais	09/2017
1644	2^478088+27	143919	Robert Price	11/2015
1645	2^477475-22071	143735	Enzo Doria	07/2013
1646	2^477417-22123	143717	Enzo Doria	07/2013
1647	2^477359-3577	143700	Yves Minet	03/2017
1648	(14*10^143662-71)/3	143663	Robert Price	12/2018
1649	2^476936-396765	143573	Enzo Doria	07/2013
1650	2^476888-2791229	143558	Enzo Doria	01/2016
1651	2^476868-1859939	143552	Enzo Doria	11/2015
1652	2^476558-113627	143459	Enzo Doria	08/2014
1653	2^476478-45	143435	Lelio R Paula	11/2017
1654	(2^475854+9)/73	143245	Lelio R Paula	08/2015
1655	2^475813-113239	143234	Enzo Doria	07/2014
1656	2^475624-114059	143178	Enzo Doria	11/2014
1657	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
1658	2^475480-2786129	143134	Enzo Doria	10/2015
1659	(14*10^143097+73)/3	143098	Robert Price	12/2018
1660	2^475299-111937	143080	Enzo Doria	05/2014
1661	2^475160-2797859	143038	Enzo Doria	04/2016
1662	(2^475069+3)/395	143008	Lelio R Paula	08/2015
1663	2^475027-461437	142998	Enzo Doria	07/2015
1664	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
1665	(8*10^142932+43)/3	142933	Robert Price	06/2018
1666	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
1667	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
1668	2^474417-59923	142814	Enzo Doria	10/2015
1669	4*10^142810-21	142811	Robert Price	09/2018
1670	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
1671	2^474053+2897	142705	Lelio R Paula	08/2012
1672	(10^142699+359)/9	142699	Serge Batalov	12/2014
1673	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
1674	2^473740-1856639	142610	Enzo Doria	09/2015
1675	2^473617-114223	142573	Enzo Doria	12/2014
1676	2^473257+1873217	142465	Enzo Doria	06/2016
1677	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
1678	(14*10^142440+61)/3	142441	Robert Price	12/2018
1679	(10^142425+359)/9	142425	Serge Batalov	12/2014
1680	2^473101+773027	142418	Enzo Doria	05/2016
1681	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
1682	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
1683	2^472634-109511	142278	Enzo Doria	04/2014
1684	(48^84589+1)/49	142213	Robert Price	01/2014
1685	2^472258+7	142164	Lelio R Paula	08/2015
1686	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
1687	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
1688	(16*10^142058+197)/3	142059	Robert Price	04/2019
1689	2^471792+1880881	142024	Enzo Doria	11/2016
1690	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
1691	(4*10^141926-79)/3	141927	Robert Price	02/2018
1692	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
1693	(14*10^141853+37)/3	141854	Robert Price	12/2018
1694	(41*10^141836-59)/9	141837	Robert Price	10/2018
1695	4*5^202913-9	141831	Lelio R Paula	04/2015
1696	2*7^167812-3	141818	Lelio R Paula	12/2014
1697	2^471043+35	141799	Robert Price	11/2015
1698	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
1699	(11*10^141718-131)/3	141719	Robert Price	09/2018
1700	2^470692+76771	141693	Enzo Doria	05/2016
1701	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
1702	2^470305-459373	141576	Enzo Doria	05/2015
1703	2^470183+72623	141540	Enzo Doria	04/2016
1704	2^470173-16465	141537	Enzo Doria	04/2013
1705	2^469974-1841	141477	Enzo Doria	05/2014
1706	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
1707	2*10^141448+63	141449	Robert Price	05/2018
1708	2^469824+43	141432	Lelio R Paula	09/2017
1709	2*10^141407-27	141408	Robert Price	05/2018
1710	2^469630-59711	141373	Enzo Doria	10/2015
1711	(25*10^141366-331)/9	141367	Robert Price	08/2018
1712	(2^469564-3)/611	141351	Lelio R Paula	08/2015
1713	197^61601+2	141342	Lelio R Paula	08/2017
1714	2^469372-112949	141296	Enzo Doria	07/2014
1716	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
1715	143^65536+106^65536	141253	Serge Batalov	03/2018
1717	2^469198+782569	141243	Enzo Doria	10/2016
1718	2^469076-2786939	141206	Enzo Doria	11/2015
1719	2^468804+1874941	141125	Enzo Doria	06/2016
1720	2^468787+81353	141119	Enzo Doria	08/2016
1721	2^468595-350407	141062	Enzo Doria	06/2015
1722	2^468564+87855	141052	Lelio R Paula	01/2016
1723	2^468551-21987	141048	Enzo Doria	07/2013
1724	2^468523-7	141040	Lelio R Paula	08/2015
1725	2^468405+87855	141004	Lelio R Paula	01/2016
1726	2^467978-113051	140876	Enzo Doria	07/2014
1727	2^467780-344429	140816	Enzo Doria	07/2015
1728	2^467605-1855603	140764	Enzo Doria	09/2015
1729	5*10^140744-7	140745	Robert Price	09/2015
1730	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
1731	2^467401-1850023	140702	Enzo Doria	08/2015
1732	(2^467270+78557)/23247	140658	Lelio R Paula	07/2015
1733	(29*2^467205+1)/2780517107	140635	Lelio R Paula	08/2015
1734	2^467166-1854941	140631	Enzo Doria	09/2015
1735	2^466866-1840571	140541	Enzo Doria	06/2015
1736	2^466829-459523	140530	Enzo Doria	05/2015
1737	2^466692-113213	140489	Enzo Doria	07/2014
1738	(44*10^140410-503)/9	140411	Robert Price	12/2018
1739	153^64265-2	140400	Lelio R Paula	11/2017
1740	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
1741	2^466181-112735	140335	Enzo Doria	07/2014
1742	(5*10^140281-119)/3	140282	Robert Price	03/2018
1743	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
1744	2^465803-114817	140221	Enzo Doria	05/2015
1745	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
1746	2^465503-112735	140131	Enzo Doria	07/2014
1747	6^179964+179964^6-1	140040	Robert Price	04/2014
1748	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
1749	2^465072-344789	140001	Enzo Doria	07/2015
1750	5*10^139945+81	139946	Robert Price	03/2019

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