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	(76*10^164984+77)/9	164985	Robert Price	10/2019
1502	9*10^164791-89	164792	Robert Price	04/2020
1503	2^547178-1856501	164717	Enzo Doria	10/2015
1504	11^158160-60	164707	Enzo Doria	07/2012
1505	(26*10^164643-167)/3	164644	Robert Price	10/2019
1506	2^546398-59201	164483	Enzo Doria	10/2015
1507	2^546332-114893	164463	Enzo Doria	05/2015
1508	2^545958+1876189	164350	Enzo Doria	07/2016
1509	2^545878-49841	164326	Enzo Doria	10/2015
1510	(10^164284+77)/3	164284	Robert Price	01/2018
1511	2^545668-4019	164263	Yves Minet	04/2017
1512	(1353^238539617^9)/10^247183	164151	Hans Havermann	07/2017
1513	(16*10^164122+197)/3	164123	Robert Price	04/2019
1514	2^545185+76757	164118	Enzo Doria	05/2016
1515	2^545076-114329	164085	Enzo Doria	01/2015
1516	(2*10^164043-143)/3	164043	Robert Price	03/2018
1517	(29^112153+1)/30	164011	Lelio R Paula	03/2017
1518	2^544757+1874777	163989	Enzo Doria	06/2016
1519	2^544444-457199	163894	Enzo Doria	01/2015
1520	2^544264-343529	163840	Enzo Doria	07/2015
1521	7*10^163780+9	163781	Robert Price	09/2015
1522	2^543989+2793047	163758	Enzo Doria	02/2016
1523	(28*10^163709+113)/3	163710	Robert Price	03/2020
1524	2^542870-69551	163421	Enzo Doria	12/2015
1525	2^542395+72533	163278	Enzo Doria	04/2016
1526	2^542072-3683	163180	Yves Minet	03/2017
1527	2^541779-1867357	163092	Enzo Doria	04/2016
1528	8*10^162924+9	162925	Robert Price	12/2015
1529	2^540905+81557	162829	Enzo Doria	08/2016
1530	2^540628-2939	162746	Yves Minet	09/2014
1531	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
1532	(203*10^162689+1)/3	162691	Robert Price	03/2020
1533	3*10^162620-59	162621	Robert Price	09/2018
1534	3^340694-112960	162553	Enzo Doria	07/2014
1535	2^539807-114081	162499	Enzo Doria	12/2014
1536	2^539654-114893	162453	Enzo Doria	05/2015
1537	2^539617-1851583	162441	Enzo Doria	08/2015
1538	(91*10^162410+11)/3	162412	Robert Price	02/2020
1539	2^539346+81049	162360	Enzo Doria	07/2016
1540	2^539220-115499	162322	Enzo Doria	07/2015
1541	2^539217-113713	162321	Enzo Doria	09/2014
1542	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
1543	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
1544	(10^162138+11)/3	162138	Serge Batalov	07/2015
1545	2^538473-112723	162097	Enzo Doria	06/2014
1546	2^538157+79337	162002	Enzo Doria	06/2016
1547	2^538136-114749	161996	Enzo Doria	05/2015
1548	2^538104+1531	161986	Lelio R Paula	01/2013
1549	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
1550	2^537815-22737	161899	Enzo Doria	07/2013
1551	2^537804-39839	161896	Enzo Doria	09/2015
1552	(754*10^161816-7)/9	161818	Robert Price	05/2020
1553	2^537458-59201	161791	Enzo Doria	10/2015
1554	2*10^161766+51	161767	Robert Price	05/2018
1555	(7*10^161760+131)/3	161761	Robert Price	06/2020
1556	2^537209-49849	161717	Enzo Doria	10/2015
1557	(58*10^161691+329)/9	161692	Robert Price	05/2019
1558	2^536937+1879397	161635	Enzo Doria	09/2016
1559	34*10^161593-9	161595	Robert Price	06/2020
1560	(31*10^161582-1)/3	161584	Robert Price	02/2020
1561	2^536569-22881	161524	Enzo Doria	07/2013
1562	10^161253+573493	161254	Patrick De Geest	07/2018
1563	10^161253-8001	161253	Robert Price	03/2018
1564	97*10^161247-3	161249	Robert Price	05/2020
1565	7*10^161192-9	161193	Robert Price	10/2015
1566	2^535269-113803	161133	Enzo Doria	09/2014
1567	2^535205-23295	161113	Enzo Doria	08/2013
1568	(89^82609+1)/90	161036	Paul Bourdelais	10/2017
1569	2^534359-23229	160859	Enzo Doria	08/2013
1570	8*10^160782+53	160783	Robert Price	08/2020
1571	67^88037-66^88037	160763	Robert Price	10/2013
1572	2^533948-1852559	160735	Enzo Doria	08/2015
1573	2^533665-23335	160650	Enzo Doria	08/2013
1574	(19*10^160619+77)/3	160620	Robert Price	05/2019
1575	3^336353-2^336353	160482	Mike Oakes	10/2007
1576	(91*10^160249+11)/3	160251	Robert Price	02/2020
1577	2^532253+1868417	160225	Enzo Doria	04/2016
1578	2^532108-291989	160181	Enzo Doria	07/2015
1579	(26*10^160166-131)/3	160167	Robert Price	10/2019
1580	(17*10^160143+67)/3	160144	Robert Price	01/2019
1581	(19*10^159921-49)/3	159922	Robert Price	05/2019
1582	2^531110-1853771	159881	Enzo Doria	09/2015
1583	2^530992-1845299	159845	Enzo Doria	07/2015
1584	(136*10^159736-1)/9	159738	Serge Batalov	12/2014
1585	2^530417-113833	159672	Enzo Doria	09/2014
1586	2^530406-69701	159669	Enzo Doria	02/2016
1587	5*10^159656+41	159657	Robert Price	03/2019
1588	7^188858-188858^7	159604	Norbert Schneider	05/2018
1589	(24^115597-1)/23	159547	Paul Bourdelais	09/2017
1590	(17*10^159438-377)/9	159439	Robert Price	03/2018
1591	(203*10^159381+1)/3	159383	Robert Price	03/2020
1592	89*10^159258-9	159260	Robert Price	05/2020
1593	2^528944-461315	159229	Enzo Doria	07/2015
1594	(13*10^159147+161)/3	159148	Robert Price	11/2018
1595	2^528620-113879	159131	Enzo Doria	10/2014
1596	2^528000-23307	158944	Enzo Doria	08/2013
1597	(29*10^158909+61)/9	158910	Robert Price	08/2018
1598	2^527817+1876817	158889	Enzo Doria	07/2016
1599	2^527774-49451	158876	Enzo Doria	10/2015
1600	2^527745-291553	158868	Enzo Doria	07/2015
1601	(91*10^158862+11)/3	158864	Robert Price	02/2020
1602	2^527644-1856999	158837	Enzo Doria	10/2015
1603	(37200^37199-37198^37199)/(2^37199)	158822	Henri Lifchitz	06/2013
1604	2^527573-1863253	158816	Enzo Doria	12/2015
1605	2^527553-23401	158810	Enzo Doria	08/2013
1606	10^158755-50001	158755	Robert Price	08/2020
1607	11^152420-210	158730	Enzo Doria	09/2012
1608	(13*10^158694+401)/9	158695	Robert Price	01/2018
1609	2^527052-69059	158659	Enzo Doria	11/2015
1610	2^526849-113233	158598	Enzo Doria	07/2014
1611	(2^526763-lucasV(1,2,526763)+1)/2	158572	Mike Oakes	11/2016
1612	(299*10^158544-17)/3	158546	Robert Price	04/2020
1613	2^526658-3551	158540	Yves Minet	03/2017
1614	7*10^158465-11	158466	Robert Price	06/2019
1615	2^526375-23115	158455	Enzo Doria	08/2013
1616	(77*10^158407-293)/9	158408	Robert Price	09/2019
1617	2^526028-112793	158351	Enzo Doria	07/2014
1618	(229*10^158339-1)/3	158341	Robert Price	07/2020
1619	2^525690-9221	158249	Lelio R Paula	01/2013
1620	2*10^158242-7	158243	Robert Price	10/2015
1621	2^525667-525667^2	158242	Henri Lifchitz	12/2017
1622	2^525186-1857431	158097	Enzo Doria	10/2015
1623	2^524515-23245	157895	Enzo Doria	08/2013
1624	2^524499-109087	157890	Enzo Doria	04/2014
1625	2^18067*(2^506221+1)-1	157827	Makoto Morimoto	05/2014
1627	2^524288+189093	157827	Makoto Morimoto	01/2016
1626	2^524288-164073	157827	Matthias Baur	03/2020
1628	(2^(2^19)-9333)/(1923463121331973)	157814	Makoto Morimoto	09/2017
1629	(10^157792+359)/9	157792	Serge Batalov	12/2014
1630	2^523924+1876591	157717	Enzo Doria	07/2016
1631	(17*10^157705+67)/3	157706	Robert Price	01/2019
1632	(46^94841+1)/47	157696	Robert Price	01/2014
1633	2^523774+77839	157672	Enzo Doria	05/2016
1634	2^523587+2799143	157616	Enzo Doria	04/2016
1635	2^523371+1872113	157551	Enzo Doria	05/2016
1636	(8*10^157368+49)/3	157369	Robert Price	05/2020
1637	(82*10^157319+449)/9	157320	Robert Price	11/2019
1638	2^522535-351457	157299	Enzo Doria	07/2015
1639	2^522226+2799079	157206	Enzo Doria	04/2016
1640	2^522134-1849451	157178	Enzo Doria	08/2015
1641	9*10^157152+71	157153	Robert Price	08/2020
1642	4*10^157150+93	157151	Robert Price	08/2018
1643	2^521401-29593	156958	Enzo Doria	08/2015
1644	7*10^156956+87	156957	Robert Price	07/2019
1645	2^521348-23397	156942	Enzo Doria	08/2013
1646	(98^78797+1)/99	156901	Paul Bourdelais	12/2017
1647	65^86522+64	156857	Lelio R Paula	04/2016
1648	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
1649	2^520977-1858183	156830	Enzo Doria	10/2015
1650	(8*10^156718-101)/3	156719	Robert Price	08/2018
1651	2^520314-1849481	156631	Enzo Doria	08/2015
1652	(13*10^156522+89)/3	156523	Robert Price	09/2018
1653	(2^(6*86654+1)-5)/3	156513	Kevin Acres	12/2013
1654	3*10^156435-97	156436	Robert Price	07/2018
1655	(8*10^156371-77)/3	156372	Robert Price	07/2018
1656	53^90679-52^90679	156356	Robert Price	01/2013
1657	2^519106-59141	156267	Enzo Doria	10/2015
1658	2^519053+6077	156251	Enzo Doria	02/2016
1659	2^518968-1860989	156225	Enzo Doria	11/2015
1660	(25*10^156221-7)/9	156222	Robert Price	05/2018
1661	2^518931-2782297	156214	Enzo Doria	09/2015
1662	2^518608-2939	156117	Yves Minet	09/2014
1663	10*27^109005+697	156027	Curtis Bright	05/2015
1664	2^517967-113485	155924	Enzo Doria	08/2014
1665	(103*10^155904+17)/3	155906	Robert Price	08/2020
1666	2^517698+4429	155843	Lelio R Paula	01/2013
1667	2^517543-113257	155796	Enzo Doria	07/2014
1668	(14*10^155740-143)/3	155741	Robert Price	11/2018
1669	31^104309-30^104309	155563	Henri Lifchitz	08/2013
1670	2^516742-39851	155555	Enzo Doria	09/2015
1671	(19*10^155504+131)/3	155505	Robert Price	06/2020
1672	7*10^155496+61	155497	Robert Price	08/2019
1673	2^516440+1878421	155464	Enzo Doria	08/2016
1674	2^515863-1867237	155291	Enzo Doria	03/2016
1675	2^515786-461861	155268	Enzo Doria	07/2015
1676	2^515644-113247	155225	Enzo Doria	07/2014
1677	(7*10^155203+107)/3	155204	Robert Price	02/2018
1678	(17*10^155133-89)/9	155134	Robert Price	07/2018
1679	2^515227-114997	155099	Enzo Doria	06/2015
1681	EPrime(155025)	155025	Eric W. Weisstein	10/2010
1680	(14*10^155024-221)/9	155025	Robert Price	04/2018
1682	(4*10^155022+173)/3	155023	Robert Price	02/2018
1683	(266*10^154897+1)/3	154899	Robert Price	04/2020
1684	(115*10^154869-1)/3	154871	Serge Batalov	12/2014
1685	(86*10^154853-221)/9	154854	Robert Price	09/2019
1686	2^514361+78167	154839	Enzo Doria	05/2016
1687	2^514281-115033	154815	Enzo Doria	06/2015
1688	2^514194-3311	154788	Yves Minet	12/2014
1689	(14*10^154773+37)/3	154774	Robert Price	12/2018
1690	6*10^154742-31	154743	Robert Price	07/2020
1691	2^513437+1879337	154560	Enzo Doria	09/2016
1692	2^513306-113201	154521	Enzo Doria	07/2014
1693	(10^154494-13)/3	154494	Robert Price	12/2017
1694	2^513042-113787	154442	Enzo Doria	09/2014
1695	(151*10^154434-7)/9	154436	Robert Price	01/2020
1696	2^512628-114053	154317	Enzo Doria	11/2014
1697	2^512529-49783	154287	Enzo Doria	10/2015
1698	(355573#+6991)/(6991*2031599)	154285	Makoto Morimoto	06/2019
1699	2^512315-115297	154223	Enzo Doria	06/2015
1700	2^512168+79561	154178	Enzo Doria	06/2016
1701	4*10^154078-57	154079	Robert Price	10/2018
1702	(355049#+1859)/(111310148891*62587751)	154051	Makoto Morimoto	06/2019
1703	7*10^154038-57	154039	Robert Price	06/2020
1704	2^511658-114371	154025	Enzo Doria	02/2015
1705	(57^87719+1)/58	154022	Paul Bourdelais	11/2017
1706	2^511580-1846679	154001	Enzo Doria	07/2015
1707	2^511541-113713	153990	Enzo Doria	09/2014
1708	10^153935-1000001	153935	Robert Price	08/2020
1709	(16*10^153868-73)/3	153869	Robert Price	07/2020
1710	2^511077-112723	153850	Enzo Doria	06/2014
1711	69^83653-68^83653	153826	Robert Price	12/2013
1712	2^510963-113707	153816	Enzo Doria	09/2014
1713	(154*10^153810-1)/9	153812	Serge Batalov	12/2014
1714	(181*25^109991-75077)/8	153763	Curtis Bright	05/2015
1715	2*10^153746-3	153747	Robert Price	07/2015
1716	2^510626+1179379	153714	Enzo Doria	05/2016
1717	(7*10^153664+113)/3	153665	Robert Price	02/2018
1718	2^510420+81121	153652	Enzo Doria	07/2016
1719	(197*7^181761-1)/2	153608	Karsten Bonath	05/2017
1720	2^509894-459161	153494	Enzo Doria	05/2015
1721	2^509841+71657	153478	Enzo Doria	04/2016
1722	9*10^153446+41	153447	Robert Price	08/2020
1723	2^509533-1846723	153385	Enzo Doria	07/2015
1724	2^509468-39989	153366	Enzo Doria	09/2015
1725	70^83117-69^83117	153360	Robert Price	01/2014
1726	(112*10^153025-1)/3	153027	Serge Batalov	12/2014
1727	(19*10^153010+131)/3	153011	Robert Price	06/2020
1728	2^508174-1855151	152976	Enzo Doria	09/2015
1729	181^67757-2	152974	Lelio R Paula	12/2017
1730	2^508160-1864829	152972	Enzo Doria	01/2016
1731	2^507857-1848199	152881	Enzo Doria	07/2015
1732	2^507638-115361	152815	Enzo Doria	07/2015
1733	2^507551-114025	152789	Enzo Doria	11/2014
1734	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
1735	(22*10^152670-13)/9	152671	Robert Price	06/2018
1736	2^506451-22339	152457	Enzo Doria	07/2013
1737	2^505995-113185	152320	Enzo Doria	07/2014
1738	(4*10^152253+149)/9	152253	Robert Price	04/2018
1739	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
1740	2^505431-505431	152150	Henri Lifchitz	04/2005
1741	(203*10^152143+1)/3	152145	Robert Price	03/2020
1742	2^505053+73097	152037	Enzo Doria	04/2016
1743	22*10^151998+3	152000	Robert Price	01/2020
1744	(238*10^151979-1)/3	151981	Robert Price	04/2020
1745	(2^504793-7)/46765	151954	Lelio R Paula	12/2017
1746	350377#+797581	151937	Nicolas PALAU	08/2017
1747	2^504618-343991	151906	Enzo Doria	07/2015
1748	2^504212-461939	151783	Enzo Doria	07/2015
1749	2^504054-2231	151736	Yves Minet	10/2011
1750	(28*10^151682+191)/3	151683	Robert Price	02/2020

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PRP Records

Probable Primes Top 10000

(271000 PRPs in the top)