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	39^105456+2	167788	Robert Price	04/2015
1502	(28^115877-1)/27	167691	Paul Bourdelais	12/2017
1503	10^167639+121911	167640	Patrick De Geest	07/2018
1504	10^167639-8001	167639	Robert Price	03/2018
1505	2^556504-462059	167525	Enzo Doria	07/2015
1506	(88*10^167522-637)/9	167523	Robert Price	11/2020
1507	5*10^167510+9	167511	Robert Price	08/2015
1508	7*10^167437-93	167438	Robert Price	08/2020
1509	2^555343+1874333	167175	Enzo Doria	06/2016
1510	2^555210-461261	167135	Enzo Doria	07/2015
1511	9*10^166996+59	166997	Robert Price	01/2020
1512	2^554372+1880527	166883	Enzo Doria	11/2016
1513	2^554299+72173	166861	Enzo Doria	04/2016
1514	(185*10^166837+7)/3	166839	Robert Price	03/2020
1515	2^554037-2797063	166782	Enzo Doria	03/2016
1516	(49*10^166721-139)/9	166722	Robert Price	03/2019
1517	2*10^166646+69	166647	Robert Price	06/2020
1518	2^553484-29819	166616	Enzo Doria	08/2015
1519	(188*10^166611+7)/3	166613	Robert Price	03/2020
1520	2^553383-2784217	166585	Enzo Doria	10/2015
1521	2^553069+76427	166491	Enzo Doria	05/2016
1522	2*10^166458+51	166459	Robert Price	05/2018
1523	589^60089-588^60089	166454	Jean-Louis Charton	09/2012
1524	11^159756-2424	166369	Mike Oakes	06/2010
1525	2^552649-361275	166364	Enzo Doria	05/2014
1526	2^552628-113669	166358	Enzo Doria	09/2014
1527	10^166324+550603	166325	Patrick De Geest	07/2018
1528	10^166324-801	166324	Robert Price	02/2018
1529	(85*10^166297-1)/3	166299	Robert Price	02/2020
1530	8*10^166227+87	166228	Robert Price	10/2019
1531	2^552137+1879397	166210	Enzo Doria	09/2016
1532	(23^121949-1)/22	166061	Paul Bourdelais	10/2017
1533	2^551542+19249	166031	Payam Samidoost	08/2002
1534	2^551535-23821	166029	Enzo Doria	08/2013
1535	2^551507-23557	166021	Enzo Doria	08/2013
1536	7*10^165916-3	165917	Robert Price	08/2015
1537	(29*10^165796+67)/3	165797	Robert Price	12/2019
1538	81^86837-80^86837	165728	Robert Price	01/2015
1539	(71*10^165663-539)/9	165664	Robert Price	07/2019
1540	2^550270-69551	165648	Enzo Doria	12/2015
1541	(202*10^165569-13)/9	165571	Robert Price	01/2020
1542	2^550000-23625	165567	Enzo Doria	08/2013
1543	2^549675-1852057	165469	Enzo Doria	08/2015
1544	-tau(103^14938)	165374	Nik Lygeros / Olivier Rozier	10/2013
1545	(28*10^165358-1)/9	165359	Serge Batalov	10/2014
1547	2^549278+1879669	165350	Enzo Doria	09/2016
1546	(7*10^165350-439)/9	165350	Robert Price	02/2018
1548	2^549252-351269	165342	Enzo Doria	06/2015
1549	(14*10^165282+73)/3	165283	Robert Price	12/2018
1550	2^549049+2797607	165281	Enzo Doria	04/2016
1551	(7*10^165239+107)/3	165240	Robert Price	02/2018
1552	(44^100511-1)/43	165184	Paul Bourdelais	11/2017
1553	(7*10^165134+107)/3	165135	Robert Price	02/2018
1554	(23*10^165060-83)/3	165061	Robert Price	08/2019
1555	(76*10^164984+77)/9	164985	Robert Price	10/2019
1556	9*10^164791-89	164792	Robert Price	04/2020
1557	2^547178-1856501	164717	Enzo Doria	10/2015
1558	11^158160-60	164707	Enzo Doria	07/2012
1559	(26*10^164643-167)/3	164644	Robert Price	10/2019
1560	2^546398-59201	164483	Enzo Doria	10/2015
1561	2^546332-114893	164463	Enzo Doria	05/2015
1562	2^545958+1876189	164350	Enzo Doria	07/2016
1563	2^545878-49841	164326	Enzo Doria	10/2015
1564	(10^164284+77)/3	164284	Robert Price	01/2018
1565	2^545668-4019	164263	Yves Minet	04/2017
1566	10^164216-50000000001	164216	Robert Price	12/2020
1567	(1353^238539617^9)/10^247183	164151	Hans Havermann	07/2017
1568	(16*10^164122+197)/3	164123	Robert Price	04/2019
1569	2^545185+76757	164118	Enzo Doria	05/2016
1570	2^545076-114329	164085	Enzo Doria	01/2015
1571	(2*10^164043-143)/3	164043	Robert Price	03/2018
1572	(29^112153+1)/30	164011	Lelio R Paula	03/2017
1573	2^544757+1874777	163989	Enzo Doria	06/2016
1574	2^544444-457199	163894	Enzo Doria	01/2015
1575	2^544264-343529	163840	Enzo Doria	07/2015
1576	7*10^163780+9	163781	Robert Price	09/2015
1577	2^543989+2793047	163758	Enzo Doria	02/2016
1578	(28*10^163709+113)/3	163710	Robert Price	03/2020
1579	2^542870-69551	163421	Enzo Doria	12/2015
1580	2^542395+72533	163278	Enzo Doria	04/2016
1581	2^542072-3683	163180	Yves Minet	03/2017
1582	2^541779-1867357	163092	Enzo Doria	04/2016
1583	8*10^162924+9	162925	Robert Price	12/2015
1584	2^540905+81557	162829	Enzo Doria	08/2016
1585	2^540628-2939	162746	Yves Minet	09/2014
1586	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
1587	(203*10^162689+1)/3	162691	Robert Price	03/2020
1588	3*10^162620-59	162621	Robert Price	09/2018
1589	3^340694-112960	162553	Enzo Doria	07/2014
1590	2^539807-114081	162499	Enzo Doria	12/2014
1591	2^539654-114893	162453	Enzo Doria	05/2015
1592	9*10^162449-71	162450	Robert Price	11/2020
1593	2^539617-1851583	162441	Enzo Doria	08/2015
1594	(91*10^162410+11)/3	162412	Robert Price	02/2020
1595	2^539346+81049	162360	Enzo Doria	07/2016
1596	2^539220-115499	162322	Enzo Doria	07/2015
1597	2^539217-113713	162321	Enzo Doria	09/2014
1598	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
1599	4*10^162263-39	162264	Robert Price	09/2020
1600	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
1601	(10^162138+11)/3	162138	Serge Batalov	07/2015
1602	2^538473-112723	162097	Enzo Doria	06/2014
1603	2^538157+79337	162002	Enzo Doria	06/2016
1604	2^538136-114749	161996	Enzo Doria	05/2015
1605	2^538104+1531	161986	Lelio R Paula	01/2013
1606	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
1607	2^537815-22737	161899	Enzo Doria	07/2013
1608	2^537804-39839	161896	Enzo Doria	09/2015
1609	(754*10^161816-7)/9	161818	Robert Price	05/2020
1610	2^537458-59201	161791	Enzo Doria	10/2015
1611	2*10^161766+51	161767	Robert Price	05/2018
1612	(7*10^161760+131)/3	161761	Robert Price	06/2020
1613	2^537209-49849	161717	Enzo Doria	10/2015
1614	(58*10^161691+329)/9	161692	Robert Price	05/2019
1615	2^536937+1879397	161635	Enzo Doria	09/2016
1616	34*10^161593-9	161595	Robert Price	06/2020
1617	(31*10^161582-1)/3	161584	Robert Price	02/2020
1618	2^536569-22881	161524	Enzo Doria	07/2013
1619	10^161253+573493	161254	Patrick De Geest	07/2018
1620	10^161253-8001	161253	Robert Price	03/2018
1621	97*10^161247-3	161249	Robert Price	05/2020
1622	7*10^161192-9	161193	Robert Price	10/2015
1623	2^535269-113803	161133	Enzo Doria	09/2014
1624	2^535205-23295	161113	Enzo Doria	08/2013
1625	(89^82609+1)/90	161036	Paul Bourdelais	10/2017
1626	2^534359-23229	160859	Enzo Doria	08/2013
1627	8*10^160782+53	160783	Robert Price	08/2020
1628	67^88037-66^88037	160763	Robert Price	10/2013
1629	(88*10^160761-637)/9	160762	Robert Price	11/2020
1630	2^533948-1852559	160735	Enzo Doria	08/2015
1631	2^533665-23335	160650	Enzo Doria	08/2013
1632	(19*10^160619+77)/3	160620	Robert Price	05/2019
1633	3^336353-2^336353	160482	Mike Oakes	10/2007
1634	(91*10^160249+11)/3	160251	Robert Price	02/2020
1635	2^532253+1868417	160225	Enzo Doria	04/2016
1636	2^532108-291989	160181	Enzo Doria	07/2015
1637	(26*10^160166-131)/3	160167	Robert Price	10/2019
1638	(17*10^160143+67)/3	160144	Robert Price	01/2019
1639	(19*10^159921-49)/3	159922	Robert Price	05/2019
1640	2^531110-1853771	159881	Enzo Doria	09/2015
1641	(275^65536+53^65536)/2	159864	Kellen Shenton	11/2020
1642	2^530992-1845299	159845	Enzo Doria	07/2015
1643	(136*10^159736-1)/9	159738	Serge Batalov	12/2014
1644	2^530417-113833	159672	Enzo Doria	09/2014
1645	2^530406-69701	159669	Enzo Doria	02/2016
1646	5*10^159656+41	159657	Robert Price	03/2019
1647	7^188858-188858^7	159604	Norbert Schneider	05/2018
1648	(24^115597-1)/23	159547	Paul Bourdelais	09/2017
1649	(17*10^159438-377)/9	159439	Robert Price	03/2018
1650	(203*10^159381+1)/3	159383	Robert Price	03/2020
1651	89*10^159258-9	159260	Robert Price	05/2020
1652	2^528944-461315	159229	Enzo Doria	07/2015
1653	(13*10^159147+161)/3	159148	Robert Price	11/2018
1654	2^528620-113879	159131	Enzo Doria	10/2014
1655	2^528000-23307	158944	Enzo Doria	08/2013
1656	(29*10^158909+61)/9	158910	Robert Price	08/2018
1657	2^527817+1876817	158889	Enzo Doria	07/2016
1658	2^527774-49451	158876	Enzo Doria	10/2015
1659	2^527745-291553	158868	Enzo Doria	07/2015
1660	(91*10^158862+11)/3	158864	Robert Price	02/2020
1661	2^527644-1856999	158837	Enzo Doria	10/2015
1662	(37200^37199-37198^37199)/(2^37199)	158822	Henri Lifchitz	06/2013
1663	2^527573-1863253	158816	Enzo Doria	12/2015
1664	2^527553-23401	158810	Enzo Doria	08/2013
1665	10^158755-50001	158755	Robert Price	08/2020
1666	11^152420-210	158730	Enzo Doria	09/2012
1667	(13*10^158694+401)/9	158695	Robert Price	01/2018
1668	2^527052-69059	158659	Enzo Doria	11/2015
1669	2^526849-113233	158598	Enzo Doria	07/2014
1670	(2^526763-lucasV(1,2,526763)+1)/2	158572	Mike Oakes	11/2016
1671	(299*10^158544-17)/3	158546	Robert Price	04/2020
1672	2^526658-3551	158540	Yves Minet	03/2017
1673	7*10^158465-11	158466	Robert Price	06/2019
1674	2^526375-23115	158455	Enzo Doria	08/2013
1675	(77*10^158407-293)/9	158408	Robert Price	09/2019
1676	2^526028-112793	158351	Enzo Doria	07/2014
1677	(229*10^158339-1)/3	158341	Robert Price	07/2020
1678	2^525690-9221	158249	Lelio R Paula	01/2013
1679	2*10^158242-7	158243	Robert Price	10/2015
1680	2^525667-525667^2	158242	Henri Lifchitz	12/2017
1681	2^525186-1857431	158097	Enzo Doria	10/2015
1682	2^524515-23245	157895	Enzo Doria	08/2013
1683	2^524499-109087	157890	Enzo Doria	04/2014
1684	2^18067*(2^506221+1)-1	157827	Makoto Morimoto	05/2014
1686	2^524288+189093	157827	Makoto Morimoto	01/2016
1685	2^524288-164073	157827	Matthias Baur	03/2020
1687	(2^(2^19)-9333)/(1923463121331973)	157814	Makoto Morimoto	09/2017
1688	(10^157792+359)/9	157792	Serge Batalov	12/2014
1689	2^523924+1876591	157717	Enzo Doria	07/2016
1690	(17*10^157705+67)/3	157706	Robert Price	01/2019
1691	(46^94841+1)/47	157696	Robert Price	01/2014
1692	2^523774+77839	157672	Enzo Doria	05/2016
1693	2^523587+2799143	157616	Enzo Doria	04/2016
1694	2^523371+1872113	157551	Enzo Doria	05/2016
1695	(8*10^157368+49)/3	157369	Robert Price	05/2020
1696	(82*10^157319+449)/9	157320	Robert Price	11/2019
1697	2^522535-351457	157299	Enzo Doria	07/2015
1698	2^522226+2799079	157206	Enzo Doria	04/2016
1699	2^522134-1849451	157178	Enzo Doria	08/2015
1700	9*10^157152+71	157153	Robert Price	08/2020
1701	4*10^157150+93	157151	Robert Price	08/2018
1702	2^521401-29593	156958	Enzo Doria	08/2015
1703	7*10^156956+87	156957	Robert Price	07/2019
1704	2^521348-23397	156942	Enzo Doria	08/2013
1705	(98^78797+1)/99	156901	Paul Bourdelais	12/2017
1706	65^86522+64	156857	Lelio R Paula	04/2016
1707	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
1708	2^520977-1858183	156830	Enzo Doria	10/2015
1709	(8*10^156718-101)/3	156719	Robert Price	08/2018
1710	2^520314-1849481	156631	Enzo Doria	08/2015
1711	(13*10^156522+89)/3	156523	Robert Price	09/2018
1712	(2^(6*86654+1)-5)/3	156513	Kevin Acres	12/2013
1713	3*10^156435-97	156436	Robert Price	07/2018
1714	(8*10^156371-77)/3	156372	Robert Price	07/2018
1715	53^90679-52^90679	156356	Robert Price	01/2013
1716	2^519106-59141	156267	Enzo Doria	10/2015
1717	2^519053+6077	156251	Enzo Doria	02/2016
1718	2^518968-1860989	156225	Enzo Doria	11/2015
1719	(25*10^156221-7)/9	156222	Robert Price	05/2018
1720	2^518931-2782297	156214	Enzo Doria	09/2015
1721	2^518608-2939	156117	Yves Minet	09/2014
1722	10*27^109005+697	156027	Curtis Bright	05/2015
1723	2^517967-113485	155924	Enzo Doria	08/2014
1724	(103*10^155904+17)/3	155906	Robert Price	08/2020
1725	4*10^155853-39	155854	Robert Price	09/2020
1726	2^517698+4429	155843	Lelio R Paula	01/2013
1727	2^517543-113257	155796	Enzo Doria	07/2014
1728	(14*10^155740-143)/3	155741	Robert Price	11/2018
1729	31^104309-30^104309	155563	Henri Lifchitz	08/2013
1730	2^516742-39851	155555	Enzo Doria	09/2015
1731	(19*10^155504+131)/3	155505	Robert Price	06/2020
1732	7*10^155496+61	155497	Robert Price	08/2019
1733	2^516440+1878421	155464	Enzo Doria	08/2016
1734	2^515863-1867237	155291	Enzo Doria	03/2016
1735	2^515786-461861	155268	Enzo Doria	07/2015
1736	2^515644-113247	155225	Enzo Doria	07/2014
1737	(7*10^155203+107)/3	155204	Robert Price	02/2018
1738	10^155163-40001	155163	Robert Price	01/2021
1739	(17*10^155133-89)/9	155134	Robert Price	07/2018
1740	2^515227-114997	155099	Enzo Doria	06/2015
1742	EPrime(155025)	155025	Eric W. Weisstein	10/2010
1741	(14*10^155024-221)/9	155025	Robert Price	04/2018
1743	(4*10^155022+173)/3	155023	Robert Price	02/2018
1744	(266*10^154897+1)/3	154899	Robert Price	04/2020
1745	(115*10^154869-1)/3	154871	Serge Batalov	12/2014
1746	(86*10^154853-221)/9	154854	Robert Price	09/2019
1747	2^514361+78167	154839	Enzo Doria	05/2016
1748	2^514281-115033	154815	Enzo Doria	06/2015
1749	2^514194-3311	154788	Yves Minet	12/2014
1750	(14*10^154773+37)/3	154774	Robert Price	12/2018

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PRP Records

Probable Primes Top 10000

(277034 PRPs in the top)