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	2^615622+76639	185321	Enzo Doria	05/2016
1502	2^615591+1879223	185312	Enzo Doria	08/2016
1503	2^615503+1876643	185285	Enzo Doria	07/2016
1504	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
1505	(4*10^185221-91)/3	185222	Robert Price	03/2018
1506	(7*10^185221+131)/3	185222	Robert Price	06/2020
1507	(62*10^185216-413)/9	185217	Robert Price	09/2021
1508	(232*10^185180+17)/3	185182	Robert Price	04/2021
1509	56*10^185139-3	185141	Robert Price	03/2020
1510	(28*10^185105+47)/3	185106	Robert Price	02/2021
1511	2^614783-2790097	185069	Enzo Doria	12/2015
1512	2^614745-29323	185057	Enzo Doria	07/2015
1513	(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840	185052	Serge Batalov	07/2013
1514	(49*10^184993-67)/9	184994	Robert Price	03/2019
1515	(5*10^184954-191)/3	184955	Robert Price	05/2021
1516	(14*10^184950+211)/9	184951	Robert Price	04/2018
1517	2^614315+81353	184928	Enzo Doria	08/2016
1518	2^614294-1849961	184921	Enzo Doria	08/2015
1519	2^614266+1877809	184913	Enzo Doria	08/2016
1520	(185*10^184878-11)/3	184880	Robert Price	10/2020
1521	91*10^184867-9	184869	Robert Price	06/2021
1522	(85*10^184768+77)/9	184769	Robert Price	07/2022
1523	2^613715-1860727	184747	Enzo Doria	11/2015
1524	(4*10^184730+89)/3	184731	Robert Price	08/2021
1525	2*10^184723+41	184724	Robert Price	05/2018
1526	(49*10^184703+293)/9	184704	Robert Price	03/2021
1527	2^613487-349987	184678	Enzo Doria	07/2015
1528	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
1529	14^161089-161089^14	184629	Serge Batalov	05/2016
1530	2^613033-114621	184542	Enzo Doria	05/2015
1531	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
1532	2^612341-1604809	184334	Enzo Doria	05/2015
1533	(11*10^184308-161)/3	184309	Robert Price	11/2021
1534	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
1535	(14*10^184150+37)/3	184151	Robert Price	12/2018
1536	2^611731-4837	184150	Yves Minet	08/2018
1537	3*10^184124-7	184125	Robert Price	08/2015
1538	2^611628-24537	184119	Enzo Doria	08/2013
1539	3*10^184110+13	184111	Robert Price	07/2018
1540	(194*10^184093+1)/3	184095	Robert Price	01/2022
1541	2^611460+71881	184068	Enzo Doria	04/2016
1542	4*10^184004-63	184005	Robert Price	10/2018
1543	2^610982-1867301	183924	Enzo Doria	03/2016
1544	3*10^183872-49	183873	Robert Price	07/2018
1545	2^610597+1178897	183809	Enzo Doria	05/2016
1546	(8*10^183773-269)/9	183773	Robert Price	09/2021
1547	(65*10^183768-29)/9	183769	Robert Price	01/2021
1548	(17*10^183764+31)/3	183765	Robert Price	01/2019
1549	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
1550	2^610401+1277	183750	Lelio R Paula	07/2013
1551	2^610356-1849019	183736	Enzo Doria	08/2015
1552	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
1553	23*10^183710-7	183712	Robert Price	02/2020
1554	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
1555	(4*10^183659+149)/9	183659	Robert Price	04/2018
1556	2^609846-1834251	183582	Enzo Doria	07/2015
1557	10^183546+1547323	183547	Patrick De Geest	02/2021
1559	10^183546-800000001	183546	Robert Price	09/2020
1558	10^183546-584297	183546	Patrick De Geest	02/2021
1560	(23*10^183477-71)/3	183478	Robert Price	07/2020
1561	11^176176-240	183469	Enzo Doria	11/2012
1562	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
1563	6*10^183429+53	183430	Robert Price	05/2020
1564	(28*10^183403+191)/3	183404	Robert Price	02/2020
1565	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
1566	2^608965-113989	183317	Enzo Doria	10/2014
1567	A005165(43592)	183312	Serge Batalov	07/2017
1568	(61*10^183294+119)/9	183295	Robert Price	05/2019
1569	2^608814-461261	183272	Enzo Doria	06/2015
1570	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
1571	2^608541-608541^2	183190	Henri Lifchitz	02/2018
1572	2^608293+143807	183115	Enzo Doria	10/2016
1573	2^608164-462419	183076	Enzo Doria	08/2015
1574	2^607950-1862303	183012	Enzo Doria	12/2015
1575	(46*10^182896+683)/9	182897	Robert Price	03/2019
1576	(2*10^182787+73)/3	182787	Robert Price	09/2020
1577	2^607101+1871987	182756	Enzo Doria	05/2016
1578	2^606869-69175	182686	Enzo Doria	11/2015
1579	8*10^182671+71	182672	Robert Price	05/2022
1580	(23*10^182666-71)/3	182667	Robert Price	07/2020
1581	3*10^182614-11	182615	Robert Price	07/2018
1582	2^606560-357	182593	Enzo Doria	05/2014
1583	66*10^182420+7	182422	Robert Price	07/2020
1584	2^605687+1866983	182330	Enzo Doria	03/2016
1585	2^605655-114445	182321	Enzo Doria	02/2015
1586	94*10^182291-3	182293	Robert Price	05/2020
1587	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
1588	(14*10^182177-221)/9	182178	Robert Price	04/2018
1589	2^605174-112751	182176	Enzo Doria	06/2014
1590	2^604761+1874507	182052	Enzo Doria	06/2016
1591	2^604705+1871957	182035	Enzo Doria	05/2016
1592	(14*10^182000+229)/9	182001	Robert Price	03/2018
1593	(10^181996+41)/3	181996	Robert Price	12/2017
1594	(17*10^181979+91)/9	181980	Robert Price	02/2022
1595	(5*10^181950-101)/3	181951	Robert Price	04/2018
1596	2^603915+75233	181797	Enzo Doria	04/2016
1597	(10^181710+7)/563747/2019847	181698	Alfred Reich	08/2021
1598	7*10^181594-57	181595	Robert Price	06/2020
1599	8*10^181580+29	181581	Robert Price	11/2021
1600	3*10^181445+23	181446	Robert Price	03/2022
1601	(194*10^181369-11)/3	181371	Robert Price	09/2020
1602	11^174145-360	181354	Enzo Doria	10/2012
1603	2^602351-396765	181326	Enzo Doria	08/2013
1604	6*10^181306+17	181307	Robert Price	04/2019
1605	(286*10^181220-1)/3	181222	Robert Price	11/2020
1606	2^601957-113833	181208	Enzo Doria	09/2014
1607	66^99581-65^99581	181193	Robert Price	09/2013
1608	10^181182+383973	181183	Patrick De Geest	04/2016
1609	10^181182-21	181182	Serge Batalov	12/2014
1610	(797*10^181171-41)/9	181173	Robert Price	04/2022
1611	(5*10^181127-29)/3	181128	Robert Price	03/2018
1612	2^601521-29143	181076	Enzo Doria	07/2015
1613	2^601442-2797811	181053	Enzo Doria	04/2016
1614	44*10^181029+3	181031	Robert Price	04/2020
1615	5*10^180992-9	180993	Robert Price	05/2015
1616	10^180979+79477	180980	Patrick De Geest	04/2016
1617	10^180979+107739	180980	Patrick De Geest	04/2016
1618	10^180979-11	180979	Serge Batalov	12/2014
1619	2^601023-113851	180926	Enzo Doria	10/2014
1620	(23*10^180862-143)/3	180863	Robert Price	12/2019
1621	3*10^180852+29	180853	Robert Price	05/2018
1622	(277*10^180782-7)/9	180784	Robert Price	02/2022
1623	(8*10^180725-629)/9	180725	Robert Price	01/2022
1624	(79*10^180710-1)/3	180712	Robert Price	02/2020
1625	2^600300-1852559	180709	Enzo Doria	08/2015
1626	(2*10^180706-77)/3	180706	Robert Price	02/2021
1627	(10^180689+71)/9	180689	Serge Batalov	07/2015
1628	2^600209+76487	180681	Enzo Doria	05/2016
1629	(8*10^180536-269)/9	180536	Robert Price	09/2021
1630	2^599702-369885	180529	Enzo Doria	11/2013
1631	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
1632	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
1633	(29*10^180432-17)/3	180433	Robert Price	09/2019
1634	4*10^180360+93	180361	Robert Price	08/2018
1635	2^598942+80779	180300	Enzo Doria	07/2016
1636	(38*10^180296+403)/9	180297	Robert Price	10/2018
1637	(85*10^180241+77)/9	180242	Robert Price	07/2022
1638	2^598591-1844797	180194	Enzo Doria	06/2015
1639	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
1640	(29*10^180072+691)/9	180073	Robert Price	08/2021
1641	(59*10^180038+157)/9	180039	Robert Price	12/2021
1642	95*10^180019-9	180021	Robert Price	01/2022
1643	6*10^179970+91	179971	Robert Price	05/2019
1644	(4*10^179963-79)/3	179964	Robert Price	02/2018
1645	(403*10^179944-43)/9	179946	Robert Price	06/2021
1646	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
1647	2^597424-1859729	179843	Enzo Doria	11/2015
1648	Phi(180683,10)	179760	Maksym Voznyy	09/2015
1649	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
1650	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
1651	(29*10^179697+223)/9	179698	Robert Price	09/2018
1652	2^596884+73	179680	Stefano Morozzi	04/2021
1653	(11*10^179679+13)/3	179680	Robert Price	03/2022
1654	(68*10^179656+7)/3	179658	Robert Price	01/2020
1655	(10^179643+173)/3	179643	Robert Price	05/2021
1656	2^596690-461261	179622	Enzo Doria	07/2015
1657	2^596684-113939	179620	Enzo Doria	10/2014
1658	2*10^179602+63	179603	Robert Price	05/2018
1659	(25*10^179488-403)/9	179489	Robert Price	01/2021
1660	7*10^179460+99	179461	Robert Price	05/2021
1661	3^375887-112696	179344	Enzo Doria	07/2014
1662	4*10^179265-71	179266	Robert Price	12/2018
1663	2*10^179193+83	179194	Robert Price	12/2021
1664	2^595144-1850429	179157	Enzo Doria	08/2015
1665	2^595122-5	179150	Stefano Morozzi	07/2022
1666	3*10^179138+89	179139	Robert Price	10/2018
1667	(52*10^179062-133)/9	179063	Robert Price	09/2021
1668	2^594531+82253	178972	Enzo Doria	09/2016
1669	(664*10^178939-61)/9	178941	Robert Price	09/2021
1670	2^594260-2787899	178891	Enzo Doria	11/2015
1671	(14*10^178822+67)/9	178823	Robert Price	05/2022
1672	(29*10^178732-119)/9	178733	Robert Price	12/2021
1673	2^593631+101381	178701	Jorge Menendez	04/2018
1674	10^178695+136719	178696	Patrick De Geest	05/2016
1675	10^178695-71	178695	Serge Batalov	12/2014
1676	(2*10^178649-161)/3	178649	Robert Price	12/2020
1677	(691^62903-1)/690	178609	Michael Stocker	05/2020
1678	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
1679	2^593222-14145	178578	Jorge Menendez	10/2017
1680	7*10^178566+33	178567	Robert Price	06/2020
1681	2^593178+1867219	178565	Enzo Doria	03/2016
1682	(38*10^178456+151)/9	178457	Robert Price	03/2022
1683	(302*10^178369+13)/9	178371	Robert Price	02/2020
1684	(26*10^178296-113)/3	178297	Robert Price	06/2020
1685	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
1686	(13*10^178233+137)/3	178234	Robert Price	06/2021
1687	(5*10^178206+91)/3	178207	Robert Price	04/2018
1688	2^591872-291929	178172	Enzo Doria	07/2015
1689	2^591682-286871	178115	Enzo Doria	07/2015
1690	4*10^178091+9	178092	Robert Price	05/2015
1691	410747#+478483	178007	Makoto Morimoto	02/2016
1692	3*10^177872+73	177873	Robert Price	08/2018
1693	2^590762-396765	177838	Enzo Doria	08/2013
1694	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
1695	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
1696	Smr(37765)	177719	Eric W. Weisstein	12/2021
1697	(266*10^177577-11)/3	177579	Robert Price	04/2020
1698	(11*10^177466-113)/3	177467	Robert Price	10/2018
1699	3*10^177373-97	177374	Robert Price	07/2018
1700	2^589204+1881151	177369	Enzo Doria	11/2016
1701	2^589132-69479	177347	Enzo Doria	01/2016
1702	(101*10^177302-17)/3	177304	Robert Price	02/2020
1703	2^588912-113519	177281	Enzo Doria	08/2014
1704	(682*10^177266-7)/9	177268	Robert Price	08/2021
1705	15^150706+2	177245	Robert Price	06/2015
1706	2^588194-1861001	177065	Enzo Doria	11/2015
1707	5*10^177016-37	177017	Robert Price	11/2021
1708	(23*10^176964-47)/3	176965	Robert Price	09/2019
1709	20530^41031+41031^20530	176942	Norbert Schneider	07/2022
1710	(19*10^176932+521)/9	176933	Robert Price	05/2018
1711	(8*10^176908+43)/3	176909	Robert Price	06/2018
1712	(85*10^176900+203)/9	176901	Robert Price	09/2020
1713	2^587560-113699	176874	Enzo Doria	09/2014
1714	20596^40995+40995^20596	176844	Norbert Schneider	07/2022
1715	(101*10^176815-17)/3	176817	Robert Price	02/2020
1716	(25*10^176715-37)/3	176716	Robert Price	10/2019
1717	5^252763-12862	176674	Enzo Doria	05/2014
1718	2^586804+81721	176646	Enzo Doria	08/2016
1719	(10^176584+77)/3	176584	Robert Price	01/2018
1720	2^586570+1874419	176576	Enzo Doria	06/2016
1721	(157*10^176482-1)/3	176484	Robert Price	01/2022
1722	2^585994-3311	176402	Yves Minet	12/2014
1723	8*10^176383-81	176384	Robert Price	02/2021
1724	(23*10^176357+61)/3	176358	Robert Price	01/2022
1725	2^585832-112799	176354	Enzo Doria	07/2014
1726	(29*10^176240+49)/3	176241	Robert Price	09/2021
1727	(2^585387-11)/3	176219	Stefano Morozzi	08/2022
1728	2^585336-461039	176204	Enzo Doria	06/2015
1729	(25*10^176164+143)/3	176165	Robert Price	08/2020
1730	2^585095-1848127	176132	Enzo Doria	08/2015
1731	(5*10^176101-311)/9	176101	Robert Price	12/2021
1732	6*10^176092+77	176093	Robert Price	06/2020
1733	2^584950-115451	176088	Enzo Doria	07/2015
1734	(646*10^176044+11)/9	176046	Robert Price	10/2021
1735	2^584671-3697	176004	Yves Minet	03/2017
1736	(13*10^175965-37)/3	175966	Robert Price	01/2019
1737	2*10^175860-87	175861	Robert Price	04/2018
1738	(86*10^175774-221)/9	175775	Robert Price	09/2019
1739	9*10^175654+47	175655	Robert Price	01/2022
1740	10^175608+2971	175609	Mike Oakes	05/2010
1741	10^175608-55829	175608	Patrick De Geest	09/2013
1742	2^583051+1879793	175516	Enzo Doria	09/2016
1743	(76*10^175514+491)/9	175515	Robert Price	10/2021
1744	2^582860-23829	175459	Enzo Doria	08/2013
1745	(28*10^175417-67)/3	175418	Robert Price	10/2020
1746	2^582670-23913	175402	Enzo Doria	08/2013
1747	2^582573-29563	175372	Enzo Doria	08/2015
1748	2^582435-1862767	175331	Enzo Doria	12/2015
1749	10^175295-40000001	175295	Robert Price	07/2022
1750	(11*10^175250-149)/3	175251	Robert Price	09/2018

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Probable Primes Top 10000

(291192 PRPs in the top)