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	(23*10^180862-143)/3	180863	Robert Price	12/2019
1502	3*10^180852+29	180853	Robert Price	05/2018
1503	(79*10^180710-1)/3	180712	Robert Price	02/2020
1504	2^600300-1852559	180709	Enzo Doria	08/2015
1505	(2*10^180706-77)/3	180706	Robert Price	02/2021
1506	(10^180689+71)/9	180689	Serge Batalov	07/2015
1507	2^600209+76487	180681	Enzo Doria	05/2016
1508	(8*10^180536-269)/9	180536	Robert Price	09/2021
1509	2^599702-369885	180529	Enzo Doria	11/2013
1510	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
1511	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
1512	(29*10^180432-17)/3	180433	Robert Price	09/2019
1513	4*10^180360+93	180361	Robert Price	08/2018
1514	2^598942+80779	180300	Enzo Doria	07/2016
1515	(38*10^180296+403)/9	180297	Robert Price	10/2018
1516	2^598591-1844797	180194	Enzo Doria	06/2015
1517	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
1518	(29*10^180072+691)/9	180073	Robert Price	08/2021
1519	(59*10^180038+157)/9	180039	Robert Price	12/2021
1520	6*10^179970+91	179971	Robert Price	05/2019
1521	(4*10^179963-79)/3	179964	Robert Price	02/2018
1522	(403*10^179944-43)/9	179946	Robert Price	06/2021
1523	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
1524	2^597424-1859729	179843	Enzo Doria	11/2015
1525	Phi(180683,10)	179760	Maksym Voznyy	09/2015
1526	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
1527	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
1528	(29*10^179697+223)/9	179698	Robert Price	09/2018
1529	2^596884+73	179680	Stefano Morozzi	04/2021
1530	(68*10^179656+7)/3	179658	Robert Price	01/2020
1531	(10^179643+173)/3	179643	Robert Price	05/2021
1532	2^596690-461261	179622	Enzo Doria	07/2015
1533	2^596684-113939	179620	Enzo Doria	10/2014
1534	2*10^179602+63	179603	Robert Price	05/2018
1535	(25*10^179488-403)/9	179489	Robert Price	01/2021
1536	7*10^179460+99	179461	Robert Price	05/2021
1537	3^375887-112696	179344	Enzo Doria	07/2014
1538	4*10^179265-71	179266	Robert Price	12/2018
1539	2*10^179193+83	179194	Robert Price	12/2021
1540	2^595144-1850429	179157	Enzo Doria	08/2015
1541	3*10^179138+89	179139	Robert Price	10/2018
1542	(52*10^179062-133)/9	179063	Robert Price	09/2021
1543	2^594531+82253	178972	Enzo Doria	09/2016
1544	(664*10^178939-61)/9	178941	Robert Price	09/2021
1545	2^594260-2787899	178891	Enzo Doria	11/2015
1546	(29*10^178732-119)/9	178733	Robert Price	12/2021
1547	2^593631+101381	178701	Jorge Menendez	04/2018
1548	10^178695+136719	178696	Patrick De Geest	05/2016
1549	10^178695-71	178695	Serge Batalov	12/2014
1550	(2*10^178649-161)/3	178649	Robert Price	12/2020
1551	(691^62903-1)/690	178609	Michael Stocker	05/2020
1552	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
1553	2^593222-14145	178578	Jorge Menendez	10/2017
1554	7*10^178566+33	178567	Robert Price	06/2020
1555	2^593178+1867219	178565	Enzo Doria	03/2016
1556	(302*10^178369+13)/9	178371	Robert Price	02/2020
1557	(26*10^178296-113)/3	178297	Robert Price	06/2020
1558	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
1559	(13*10^178233+137)/3	178234	Robert Price	06/2021
1560	(5*10^178206+91)/3	178207	Robert Price	04/2018
1561	2^591872-291929	178172	Enzo Doria	07/2015
1562	2^591682-286871	178115	Enzo Doria	07/2015
1563	4*10^178091+9	178092	Robert Price	05/2015
1564	410747#+478483	178007	Makoto Morimoto	02/2016
1565	3*10^177872+73	177873	Robert Price	08/2018
1566	2^590762-396765	177838	Enzo Doria	08/2013
1567	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
1568	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
1569	Smr(37765)	177719	Eric W. Weisstein	12/2021
1570	(266*10^177577-11)/3	177579	Robert Price	04/2020
1571	(11*10^177466-113)/3	177467	Robert Price	10/2018
1572	3*10^177373-97	177374	Robert Price	07/2018
1573	2^589204+1881151	177369	Enzo Doria	11/2016
1574	2^589132-69479	177347	Enzo Doria	01/2016
1575	(101*10^177302-17)/3	177304	Robert Price	02/2020
1576	2^588912-113519	177281	Enzo Doria	08/2014
1577	(682*10^177266-7)/9	177268	Robert Price	08/2021
1578	15^150706+2	177245	Robert Price	06/2015
1579	2^588194-1861001	177065	Enzo Doria	11/2015
1580	5*10^177016-37	177017	Robert Price	11/2021
1581	(23*10^176964-47)/3	176965	Robert Price	09/2019
1582	(19*10^176932+521)/9	176933	Robert Price	05/2018
1583	(8*10^176908+43)/3	176909	Robert Price	06/2018
1584	(85*10^176900+203)/9	176901	Robert Price	09/2020
1585	2^587560-113699	176874	Enzo Doria	09/2014
1586	(101*10^176815-17)/3	176817	Robert Price	02/2020
1587	(25*10^176715-37)/3	176716	Robert Price	10/2019
1588	5^252763-12862	176674	Enzo Doria	05/2014
1589	2^586804+81721	176646	Enzo Doria	08/2016
1590	(10^176584+77)/3	176584	Robert Price	01/2018
1591	2^586570+1874419	176576	Enzo Doria	06/2016
1592	2^585994-3311	176402	Yves Minet	12/2014
1593	8*10^176383-81	176384	Robert Price	02/2021
1594	(23*10^176357+61)/3	176358	Robert Price	01/2022
1595	2^585832-112799	176354	Enzo Doria	07/2014
1596	(29*10^176240+49)/3	176241	Robert Price	09/2021
1597	2^585336-461039	176204	Enzo Doria	06/2015
1598	(25*10^176164+143)/3	176165	Robert Price	08/2020
1599	2^585095-1848127	176132	Enzo Doria	08/2015
1600	(5*10^176101-311)/9	176101	Robert Price	12/2021
1601	6*10^176092+77	176093	Robert Price	06/2020
1602	2^584950-115451	176088	Enzo Doria	07/2015
1603	(646*10^176044+11)/9	176046	Robert Price	10/2021
1604	2^584671-3697	176004	Yves Minet	03/2017
1605	(13*10^175965-37)/3	175966	Robert Price	01/2019
1606	2*10^175860-87	175861	Robert Price	04/2018
1607	(86*10^175774-221)/9	175775	Robert Price	09/2019
1608	9*10^175654+47	175655	Robert Price	01/2022
1609	10^175608+2971	175609	Mike Oakes	05/2010
1610	10^175608-55829	175608	Patrick De Geest	09/2013
1611	2^583051+1879793	175516	Enzo Doria	09/2016
1612	(76*10^175514+491)/9	175515	Robert Price	10/2021
1613	2^582860-23829	175459	Enzo Doria	08/2013
1614	(28*10^175417-67)/3	175418	Robert Price	10/2020
1615	2^582670-23913	175402	Enzo Doria	08/2013
1616	2^582573-29563	175372	Enzo Doria	08/2015
1617	2^582435-1862767	175331	Enzo Doria	12/2015
1618	(11*10^175250-149)/3	175251	Robert Price	09/2018
1619	(29*10^175236+31)/3	175237	Robert Price	04/2021
1620	2^582072-1848599	175222	Enzo Doria	08/2015
1621	(404267#+465)/(3^45^231)	175208	Makoto Morimoto	06/2019
1622	(5*10^175117-311)/9	175117	Robert Price	12/2021
1623	(220221^32768+1)/2	175075	Serge Batalov	03/2018
1624	2^581560+1874911	175068	Enzo Doria	06/2016
1625	(25*10^174987-97)/9	174988	Robert Price	01/2022
1626	(75^93307-1)/74	174955	Paul Bourdelais	09/2017
1627	(47*10^174790+493)/9	174791	Robert Price	03/2019
1628	2^580528-114035	174757	Enzo Doria	11/2014
1629	(19*10^174754+737)/9	174755	Robert Price	07/2018
1630	(35*10^174704-377)/9	174705	Robert Price	07/2018
1631	(49*10^174681+293)/9	174682	Robert Price	03/2021
1632	3*10^174665-97	174666	Robert Price	07/2018
1633	2^580046-459161	174612	Enzo Doria	05/2015
1634	2^579992-39779	174595	Enzo Doria	09/2015
1635	(4*10^174423+101)/3	174424	Robert Price	11/2021
1636	(2*10^174301-71)/3	174301	Robert Price	12/2017
1637	14^152048+3	174267	Paul Bourdelais	12/2020
1638	(2^578696+1)/257	174203	Lelio R Paula	09/2015
1639	2^578656-1851809	174193	Enzo Doria	08/2015
1640	2^578583-113917	174171	Enzo Doria	10/2014
1641	2^578434-83	174126	Yves Minet	07/2017
1642	15^148048-2	174118	Robert Price	06/2015
1643	5*10^174101+81	174102	Robert Price	03/2019
1644	2^578346+2794249	174100	Enzo Doria	03/2016
1645	10^173947+1372429	173948	Patrick De Geest	08/2021
1647	10^173947-500000001	173947	Robert Price	12/2020
1646	10^173947-286391	173947	Patrick De Geest	08/2021
1648	5*10^173904-13	173905	Robert Price	01/2019
1649	(8*10^173862-59)/3	173863	Robert Price	08/2021
1650	(71*10^173854-287)/9	173855	Robert Price	09/2019
1651	(43*10^173826+101)/9	173827	Robert Price	11/2018
1652	2*10^173809-87	173810	Robert Price	04/2018
1653	(L!41532)/2	173772	Serge Batalov	07/2017
1654	2^577146-49877	173739	Enzo Doria	10/2015
1655	2^576889+49727	173661	Enzo Doria	09/2016
1656	(167*10^173571-17)/3	173573	Robert Price	03/2020
1657	5*10^173534+29	173535	Robert Price	12/2020
1658	(2^576551-1)/4612409/64758208321/242584327930759	173528	Dario Alpern	06/2014
1659	4*10^173509+99	173510	Robert Price	12/2020
1660	(13*10^173467-37)/3	173468	Robert Price	01/2019
1661	2^576016-113919	173399	Enzo Doria	11/2014
1662	2^575911-1849387	173367	Enzo Doria	08/2015
1663	2^575614+9	173278	Stefano Morozzi	04/2021
1664	(16*10^173251+107)/3	173252	Robert Price	03/2019
1665	2^575196-114053	173152	Enzo Doria	11/2014
1666	7*10^173135-53	173136	Robert Price	06/2020
1667	(301*10^173047+23)/9	173049	Robert Price	06/2021
1668	2^574591-115387	172970	Enzo Doria	07/2015
1669	(202*10^172940-13)/9	172942	Robert Price	01/2020
1670	45^104608+104608^45	172940	Norbert Schneider	06/2021
1671	2^574328+81121	172890	Enzo Doria	07/2016
1672	(115*10^172862-1)/3	172864	Serge Batalov	12/2014
1673	3*10^172812+13	172813	Robert Price	07/2018
1674	4*5^247217-9	172798	Lelio R Paula	10/2015
1675	6*10^172772-31	172773	Robert Price	07/2020
1676	69061#+(467617#)/(69061#)	172766	Makoto Morimoto	10/2017
1677	(34*10^172693-547)/9	172694	Robert Price	03/2021
1678	5*10^172692+57	172693	Robert Price	12/2018
1679	2^573668-2782319	172692	Enzo Doria	09/2015
1680	2^573444-1855109	172624	Enzo Doria	09/2015
1681	(14*10^172532-29)/3	172533	Robert Price	09/2021
1682	3^361608+2	172531	Robert Price	08/2014
1683	(54^99563+1)/55	172481	Paul Bourdelais	11/2017
1684	2^572592-114893	172368	Enzo Doria	05/2015
1685	4*10^172354-39	172355	Robert Price	09/2020
1686	(11*10^172322-119)/9	172323	Robert Price	11/2021
1687	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
1688	(38^109037-1)/37	172254	Paul Bourdelais	10/2017
1689	(4*10^172241+89)/3	172242	Robert Price	08/2021
1690	3*10^172219+73	172220	Robert Price	08/2018
1691	(36^110503+1)/37	171975	Lelio R Paula	04/2017
1692	(22*10^171929-73)/3	171930	Robert Price	04/2019
1693	(49*10^171892-319)/9	171893	Robert Price	10/2021
1694	4*10^171891-63	171892	Robert Price	10/2018
1695	67*10^171882-9	171884	Robert Price	03/2021
1696	2^570980-2782289	171883	Enzo Doria	09/2015
1697	(25*10^171849-37)/3	171850	Robert Price	10/2019
1698	10^171832+387909	171833	Patrick De Geest	08/2021
1699	10^171832-10001	171832	Robert Price	02/2021
1700	(2^(12*47563+13)-9)/7	171818	Kevin Acres	11/2013
1701	(536*10^171601-23)/9	171603	Robert Price	02/2020
1702	7*10^171535-99	171536	Robert Price	06/2019
1703	(28*10^171534+101)/3	171535	Robert Price	09/2020
1704	2^569563-1854607	171456	Enzo Doria	09/2015
1705	3*10^171391+59	171392	Robert Price	08/2018
1706	(13*10^171306-37)/3	171307	Robert Price	01/2019
1707	8*10^171296+87	171297	Robert Price	10/2019
1708	(55^98419-1)/54	171284	Paul Bourdelais	12/2017
1709	(29*10^171275+67)/3	171276	Robert Price	12/2019
1710	(194*10^171193+1)/3	171195	Robert Price	01/2022
1711	2^568642+1876129	171179	Enzo Doria	07/2016
1712	4*10^171146-47	171147	Robert Price	10/2021
1713	(19*10^170970+131)/3	170971	Robert Price	06/2020
1714	(46*10^170932+143)/9	170933	Robert Price	01/2019
1715	(79*10^170901-1)/3	170903	Robert Price	02/2020
1716	(58*10^170842+221)/9	170843	Robert Price	02/2017
1717	(29*10^170830+583)/9	170831	Robert Price	06/2021
1718	3*10^170800+73	170801	Robert Price	08/2018
1719	(29*10^170799-119)/9	170800	Robert Price	12/2021
1720	11^164009-270	170798	Enzo Doria	10/2012
1721	2*10^170767+41	170768	Robert Price	05/2018
1722	3^357706-112358	170670	Enzo Doria	07/2014
1723	TheodorusPrime(170657)	170657	Eric W. Weisstein	08/2013
1724	2^566871+1876163	170646	Enzo Doria	07/2016
1725	(10657#+(404267#)/(10657#))/(1675379)	170624	Makoto Morimoto	10/2017
1726	2^566496+7	170533	Donovan Johnson	07/2006
1727	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
1728	7*10^170348+33	170349	Robert Price	06/2020
1729	2^565183-352021	170138	Enzo Doria	07/2015
1730	2^565143-114457	170125	Enzo Doria	02/2015
1731	2^564976-49869	170075	Enzo Doria	10/2015
1732	(7*10^169944+23)/3	169945	Robert Price	06/2020
1733	(37*10^169943+251)/9	169944	Robert Price	09/2021
1734	2^564526-351401	169940	Enzo Doria	07/2015
1735	4*10^169759+19	169760	Robert Price	10/2018
1736	21^128327-20^128327	169677	Jean-Louis Charton	11/2014
1737	2^563583+89	169656	Stefano Morozzi	04/2021
1738	(4*10^169559+83)/3	169560	Robert Price	02/2018
1739	(194*10^169461-17)/3	169463	Robert Price	09/2020
1740	2^562749+2793047	169405	Enzo Doria	02/2016
1741	(154*10^169337-1)/9	169339	Serge Batalov	12/2014
1742	(56*10^169311+691)/9	169312	Robert Price	05/2019
1743	2^562369-29503	169290	Enzo Doria	08/2015
1744	(17*10^169283+19)/9	169284	Robert Price	03/2021
1745	8*10^169071+59	169072	Robert Price	11/2021
1746	(10^169044+173)/3	169044	Robert Price	05/2021
1747	(22*10^169019+383)/9	169020	Robert Price	05/2018
1748	(64*10^168935+143)/9	168936	Robert Price	05/2021
1749	(22*10^168906+47)/3	168907	Robert Price	06/2021
1750	5*10^168807+87	168808	Robert Price	02/2019

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PRP Records

Probable Primes Top 10000

(288949 PRPs in the top)