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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	21^176191-20^176191	232964	Jean-Louis Charton	01/2015
1502	2^773723+217523	232914	Enzo Doria	01/2024
1503	2^773679-113425	232901	Enzo Doria	08/2014
1504	(7*10^232620+23)/3	232621	Robert Price	05/2023
1505	10^232599+192489	232600	Patrick De Geest	12/2013
1506	10^232599-3	232599	Markus Tervooren	10/2010
1507	2^772552-458879	232562	Enzo Doria	04/2015
1508	2^772214+1874899	232460	Enzo Doria	06/2016
1509	2^771994-1862771	232394	Enzo Doria	12/2015
1510	2^771889+1876037	232362	Enzo Doria	07/2016
1511	2^771660+1866511	232293	Enzo Doria	02/2016
1512	5^332150-18188	232163	Enzo Doria	06/2014
1513	2^770623+212543	231981	Enzo Doria	09/2023
1514	3^485977-2^485977	231870	Mike Oakes	09/2009
1515	2^770082-114161	231818	Enzo Doria	01/2015
1516	2^769791+25523	231731	Enzo Doria	11/2023
1517	7^274120-2	231659	Paul Bourdelais	08/2023
1518	(20^177967+1)/21	231540	Paul Bourdelais	05/2013
1519	(4*10^231254+23)/9	231254	Serge Batalov	11/2022
1520	2^768205+22217	231253	Enzo Doria	09/2023
1521	2^767622-9221	231078	Lelio R Paula	01/2016
1522	2^767344+1880311	230994	Enzo Doria	09/2016
1523	8*10^230921-13	230922	Robert Price	08/2023
1524	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
1525	(10^230706+179)/9	230706	Serge Batalov	12/2014
1526	2^766309+1875257	230682	Enzo Doria	06/2016
1527	(26131^52441-1)/(26131^229-1)	230629	Ryan Propper	11/2023
1528	2^765635+1879883	230480	Enzo Doria	09/2016
1529	43^141090+141090	230467	Kellen Shenton	06/2023
1530	(26*10^230394-119)/3	230395	Robert Price	07/2023
1531	2^764348-113697	230092	Enzo Doria	09/2014
1532	2^764131+78863	230027	Enzo Doria	05/2016
1533	2^763701+60197	229897	Enzo Doria	03/2016
1534	4*10^229836+21	229837	Robert Price	12/2022
1535	2^763362+27799	229795	Enzo Doria	01/2024
1536	2^762841-25905	229639	Enzo Doria	10/2013
1537	2^762659+212633	229584	Enzo Doria	09/2023
1538	77*10^229211+3	229213	Robert Price	11/2023
1539	2^761117-113569	229120	Enzo Doria	08/2014
1540	(29022^51529-1)/(29022^227-1)	228947	Ryan Propper	11/2023
1541	(98^114859+1)/99	228709	Paul Bourdelais	12/2018
1542	5*3^479067-2^479067	228574	Jon Grantham	08/2023
1543	2^758645+216011	228375	Enzo Doria	12/2023
1544	(2^758231+1)/(32714694297653973236839266867)	228223	Gord Palameta	12/2018
1545	(298*10^228177-7)/3	228179	Robert Price	02/2023
1546	2^757985-2790013	228177	Enzo Doria	12/2015
1547	34*10^228129-9	228131	Robert Price	05/2023
1548	2^757038-1862081	227892	Enzo Doria	12/2015
1549	2^756839+95849	227832	Makoto Morimoto	10/2013
1551	(2^756839+6989)/756091	227826	Makoto Morimoto	09/2016
1550	(2^756839-50211)/(137*3203)	227826	Makoto Morimoto	08/2019
1552	2^756773-112723	227812	Enzo Doria	07/2014
1553	524309#+616367	227431	Makoto Morimoto	02/2016
1554	2^755097-114193	227307	Enzo Doria	12/2014
1555	7*10^227178+39	227179	Robert Price	01/2023
1556	9*10^227153-89	227154	Robert Price	02/2023
1557	2^754473-2791513	227120	Enzo Doria	01/2016
1558	2^754376+25	227090	Stefano Morozzi	05/2021
1559	2^754138+213289	227019	Enzo Doria	09/2023
1560	2^754038+25	226989	Stefano Morozzi	05/2021
1561	2^753263+217133	226755	Enzo Doria	12/2023
1562	7*10^226479-9	226480	Robert Price	02/2023
1563	2^751426-764321	226202	Enzo Doria	12/2013
1564	(18^180181-1)/17	226176	Andy Steward	04/2007
1565	2^750740-3	225996	Paul Bourdelais	03/2012
1566	2^750725+60227	225991	Enzo Doria	02/2016
1567	2^750525-113743	225931	Enzo Doria	09/2014
1568	(2^750151-1)/(4299340426317590093831289397764574647511836143783478715117383638888678527263)	225744	Dario Alpern	10/2014
1569	2^749444-1861889	225606	Enzo Doria	12/2015
1570	tau(311^16452)	225560	Nik Lygeros / Olivier Rozier / LR team	10/2013
1571	2^749096+1876861	225501	Enzo Doria	07/2016
1572	2^748895+26213	225440	Enzo Doria	12/2023
1573	(519643#+43033)/(2318712706283)	225379	Makoto Morimoto	08/2019
1574	2^748657+79607	225369	Enzo Doria	06/2016
1575	(2^746920-11)/5	224845	Stefano Morozzi	08/2022
1576	2^746653-291583	224765	Enzo Doria	07/2015
1577	2^746461-114043	224708	Enzo Doria	11/2014
1578	2^746302+25	224660	Stefano Morozzi	05/2021
1579	(202*10^224545-1)/3	224547	Robert Price	06/2023
1580	(19*10^224533-37)/9	224534	Alfred Reich	12/2023
1581	2^745674+213949	224471	Enzo Doria	10/2023
1582	2^745098-350471	224297	Enzo Doria	06/2015
1583	2^745039-4897	224280	Yves Minet	03/2021
1584	23*10^224232-7	224234	Robert Price	10/2022
1585	(154*10^224061-1)/9	224063	Serge Batalov	12/2014
1586	2^744211-1845787	224030	Enzo Doria	07/2015
1587	2^743592-134579	223844	Hans Havermann	10/2018
1588	2^742452+3	223501	Paul Bourdelais	06/2019
1589	234178^9+9^234178	223463	Anatoly F. Selevich	07/2011
1590	2^741651-461197	223260	Enzo Doria	07/2015
1591	10^223236-1001	223236	Robert Price	10/2022
1592	2^741362-1845251	223173	Enzo Doria	07/2015
1593	3^467546-5*2^467546	223077	Jon Grantham	08/2023
1594	2^740455-1863877	222900	Enzo Doria	12/2015
1595	2^740274+217519	222845	Enzo Doria	01/2024
1596	(14*10^222718-41)/9	222719	Serge Batalov	01/2023
1597	2^739636-2792219	222653	Enzo Doria	02/2016
1598	11^213654-180	222498	Enzo Doria	01/2013
1599	2^738957-1859743	222449	Enzo Doria	11/2015
1600	4*10^222253-21	222254	Robert Price	12/2022
1601	2^737825+57	222108	Stefano Morozzi	05/2021
1602	(54^128189+1)/55	222073	Paul Bourdelais	11/2018
1603	2^737166+220099	221910	Enzo Doria	03/2024
1604	(10^221654+179)/9	221654	Serge Batalov	12/2014
1605	2^736281+79817	221643	Enzo Doria	06/2016
1606	10^221631+247617	221632	Patrick De Geest	10/2013
1607	10^221631-9	221631	Alexander Gramolin	02/2011
1608	10^221628+7	221629	Alfred Reich	04/2021
1609	2^735970-1839821	221550	Enzo Doria	06/2015
1610	2^735367+60293	221368	Enzo Doria	03/2016
1611	77*10^221343+3	221345	Robert Price	11/2023
1612	(241^92821-1)/240	221099	Anonymous	04/2024
1613	(202*10^221092-1)/3	221094	Robert Price	06/2023
1614	(29^151153+1)/30	221045	Paul Bourdelais	09/2017
1615	2^734228+24751	221025	Enzo Doria	10/2023
1616	2^733264-2784089	220735	Enzo Doria	10/2015
1617	2^733114-24555	220690	Enzo Doria	09/2013
1618	2^731891-636259	220322	Enzo Doria	12/2013
1619	98*10^220185-9	220187	Robert Price	05/2023
1620	418319^39164+418318	220161	Alfred Reich	11/2023
1621	2^731124-25539	220091	Enzo Doria	09/2013
1622	2^730972-462029	220045	Enzo Doria	07/2015
1623	2^730833+1868627	220003	Enzo Doria	04/2016
1624	2^730645-2787133	219947	Enzo Doria	11/2015
1625	2^730547-25581	219917	Enzo Doria	09/2013
1626	(113*13^197420-5)/12	219916	Anonymous	11/2022
1627	(13^197420*113-5)/12	219916	Eric Chen	10/2023
1628	2^730460+82291	219891	Enzo Doria	09/2016
1629	(5*10^219847-101)/3	219848	Robert Price	08/2023
1630	(2^730339+1)/(3278390620037943469324347)	219831	Gord Palameta	12/2018
1631	L(1051849)	219824	Renaud Lifchitz	03/2009
1632	3*2^730149+5	219798	Jon Grantham	07/2023
1633	8*10^219740-3	219741	Serge Batalov	01/2023
1634	11^210961-240	219694	Enzo Doria	01/2013
1635	(26*10^219639-77)/3	219640	Robert Price	03/2023
1636	2^729611-113437	219635	Enzo Doria	08/2014
1637	7^259710-2	219481	Paul Bourdelais	01/2021
1638	F(1049897)	219416	Henri Lifchitz	10/2008
1639	(1488^69151-1)/1487	219386	Alexander Zhirkov	02/2023
1640	2^728604+1879321	219332	Enzo Doria	10/2016
1641	33^144412+2	219292	Robert Price	04/2015
1642	2^728277-183313	219234	Hans Havermann	10/2018
1643	2^727998-1862711	219150	Enzo Doria	12/2015
1644	(29*10^219124+91)/3	219125	Robert Price	12/2022
1645	2^727729-114073	219069	Enzo Doria	12/2014
1646	2^727496-1851809	218999	Enzo Doria	08/2015
1647	2^727025+25907	218857	Enzo Doria	12/2023
1648	2^726591+2793143	218726	Enzo Doria	02/2016
1649	(7*10^218644+17)/3	218645	Robert Price	06/2023
1650	2^725534-2791931	218408	Enzo Doria	02/2016
1651	Phi(220531,10)/2686456812680882641	217774	Makoto Kamada	10/2020
1652	2^722184+1877821	217400	Enzo Doria	08/2016
1653	(109*10^217360-1)/9	217362	Serge Batalov	12/2014
1654	2^721721-4453	217260	Yves Minet	03/2021
1655	10^216950+49	216951	Robert Price	02/2023
1656	281*499979#/46410-2702372	216849	Robert Smith	08/2016
1657	281*499979#/46410+2400766	216849	Robert Smith	08/2016
1658	tau(311^15786)	216429	Nik Lygeros / Olivier Rozier / LR team	10/2013
1659	2^718756-114107	216368	Enzo Doria	12/2014
1660	2^717672+121	216041	Stefano Morozzi	05/2021
1661	2^717305+80327	215931	Enzo Doria	07/2016
1662	2^717069-59773	215860	Enzo Doria	10/2015
1663	10^215802+33	215803	Robert Price	08/2023
1664	30^146021-29^146021	215691	Jean-Louis Charton	09/2018
1665	277^88301-276^88301	215674	Jean-Louis Charton	06/2012
1666	2^716428+215011	215667	Enzo Doria	11/2023
1667	(13*10^215592-43)/3	215593	Robert Price	08/2023
1668	227^91413-40	215372	Enzo Doria	04/2015
1669	(2^715008-21)/5	215239	Stefano Morozzi	08/2022
1670	2^714717+782897	215152	Enzo Doria	11/2016
1671	tau(373^15186)	214796	Nik Lygeros / Olivier Rozier / LR team	10/2013
1672	2^713241+1879157	214707	Enzo Doria	08/2016
1673	(23*10^214633+91)/3	214634	Robert Price	03/2023
1674	11^206081-10^206081	214612	Jean-Louis Charton	10/2011
1675	2^712801-69553	214575	Enzo Doria	01/2016
1676	2^712603-25357	214515	Enzo Doria	09/2013
1677	2^711721-1846723	214250	Enzo Doria	07/2015
1678	2^710730-396765	213952	Enzo Doria	09/2013
1679	(19*10^213934-37)/9	213935	Alfred Reich	12/2023
1680	(19*10^213730-37)/9	213731	Alfred Reich	12/2023
1681	(713^74897-1)/712	213685	Jinyuan Wang	08/2023
1682	2^709773+25907	213663	Enzo Doria	12/2023
1683	2^708468-114329	213271	Enzo Doria	02/2015
1684	2^708293+27557	213218	Enzo Doria	01/2024
1685	2^707277+28997	212912	Enzo Doria	02/2024
1686	(163*10^212779-1)/9	212781	Serge Batalov	12/2014
1687	2^706838-69041	212780	Enzo Doria	11/2015
1688	2^705653+25907	212423	Enzo Doria	12/2023
1689	22*10^212339+7	212341	Robert Price	10/2022
1690	2^704577-113871	212099	Enzo Doria	10/2014
1691	(2^704548-19)/3	212090	Stefano Morozzi	08/2022
1692	2^704110-2792441	211959	Enzo Doria	02/2016
1693	2^704084+28531	211951	Enzo Doria	02/2024
1694	2^703943-1862947	211908	Enzo Doria	12/2015
1695	(60^119083+1)/61	211746	Paul Bourdelais	10/2018
1696	(184*10^211682-1)/3	211684	Robert Price	12/2022
1697	(10^211610-91)/9	211610	Serge Batalov	12/2014
1698	227^89797+2	211565	Lelio R Paula	08/2012
1699	2^702194-3	211382	Paul Bourdelais	03/2012
1700	2^702064+1874911	211343	Enzo Doria	07/2016
1701	2^701968-113873	211314	Enzo Doria	10/2014
1702	(14*10^211262-41)/9	211263	Serge Batalov	01/2023
1703	2^701713-113779	211237	Enzo Doria	09/2014
1704	2^701616-216803	211208	Enzo Doria	01/2024
1705	2^701449-25201	211158	Enzo Doria	09/2013
1706	2^701403-2786977	211144	Enzo Doria	11/2015
1707	2^701189-25423	211079	Enzo Doria	09/2013
1708	2^701162-459161	211071	Enzo Doria	05/2015
1709	2^700793+219407	210960	Enzo Doria	03/2024
1710	(24^152783-1)/23	210872	Paul Bourdelais	04/2018
1711	2^700400+9385	210842	Lelio R Paula	01/2014
1712	2^700304-17	210813	Stefano Morozzi	07/2022
1713	2^700131+1874693	210761	Enzo Doria	06/2016
1714	(2^700095+225414)/2	210750	Stefano Morozzi	04/2020
1715	(2^700090+278254)/2	210748	Stefano Morozzi	04/2020
1716	(2^700075+303666)/2	210744	Stefano Morozzi	04/2020
1717	(2^700073+75882)/2	210743	Stefano Morozzi	04/2020
1718	(2^700074+328890)/2	210743	Stefano Morozzi	04/2020
1719	(2^700052+79162)/2	210737	Stefano Morozzi	04/2020
1720	(2^700052+304458)/2	210737	Stefano Morozzi	04/2020
1721	(2^700048+376578)/2	210736	Stefano Morozzi	04/2020
1722	11^202357-1140	210734	Enzo Doria	12/2012
1723	(2^700021+25874)/2	210728	Stefano Morozzi	04/2020
1724	(2^700018+377518)/2	210727	Stefano Morozzi	04/2020
1725	2^699999+300729	210721	Norman Luhn	09/2023
1726	(238*10^210712-1)/3	210714	Robert Price	09/2023
1727	2^699740+25	210643	Stefano Morozzi	05/2021
1728	(23*10^210525-143)/3	210526	Robert Price	12/2023
1729	2^698929-2788423	210399	Enzo Doria	11/2015
1730	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
1731	2^698316+1878601	210215	Enzo Doria	08/2016
1732	34*10^210097-9	210099	Robert Price	05/2023
1733	(19*10^210011-49)/3	210012	Robert Price	06/2023
1734	6*10^209846-91	209847	Robert Price	05/2023
1735	2^697036+1878751	209829	Enzo Doria	08/2016
1736	2^696813+28607	209762	Enzo Doria	02/2024
1737	(238*10^209715-1)/3	209717	Robert Price	09/2023
1738	6^269407+5	209640	Paul Bourdelais	02/2021
1739	(2^696343-1)/11141489/36009913139329	209600	Tony Prest / Never Odd Or Even	02/2014
1740	2^696254-115151	209594	Enzo Doria	06/2015
1741	(35^135623+1)/36	209410	Paul Bourdelais	07/2018
1742	7*10^209161+39	209162	Robert Price	01/2023
1743	2^694633+1887257	209106	Enzo Doria	05/2017
1744	fibonacci(999790)-4	208944	Jon Grantham	08/2023
1745	2^693959+180923	208903	Enzo Doria	07/2016
1746	(2^693747-11)/3	208839	Stefano Morozzi	08/2022
1747	2^693462-1847561	208753	Enzo Doria	07/2015
1748	2^690890-59981	207979	Enzo Doria	11/2015
1749	(38^131591+1)/39	207884	Paul Bourdelais	07/2018
1750	3*2^690484+5	207857	Jon Grantham	07/2023

Find by discoverer :

PRP Records

Probable Primes Top 10000

(295107 PRPs in the top)