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	3*10^171391+59	171392	Robert Price	08/2018
1502	(13*10^171306-37)/3	171307	Robert Price	01/2019
1503	8*10^171296+87	171297	Robert Price	10/2019
1504	(55^98419-1)/54	171284	Paul Bourdelais	12/2017
1505	(29*10^171275+67)/3	171276	Robert Price	12/2019
1506	2^568642+1876129	171179	Enzo Doria	07/2016
1507	(19*10^170970+131)/3	170971	Robert Price	06/2020
1508	(46*10^170932+143)/9	170933	Robert Price	01/2019
1509	(79*10^170901-1)/3	170903	Robert Price	02/2020
1510	(58*10^170842+221)/9	170843	Robert Price	02/2017
1511	3*10^170800+73	170801	Robert Price	08/2018
1512	11^164009-270	170798	Enzo Doria	10/2012
1513	2*10^170767+41	170768	Robert Price	05/2018
1514	3^357706-112358	170670	Enzo Doria	07/2014
1515	TheodorusPrime(170657)	170657	Eric W. Weisstein	08/2013
1516	2^566871+1876163	170646	Enzo Doria	07/2016
1517	(10657#+(404267#)/(10657#))/(1675379)	170624	Makoto Morimoto	10/2017
1518	2^566496+7	170533	Donovan Johnson	07/2006
1519	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
1520	7*10^170348+33	170349	Robert Price	06/2020
1521	2^565183-352021	170138	Enzo Doria	07/2015
1522	2^565143-114457	170125	Enzo Doria	02/2015
1523	2^564976-49869	170075	Enzo Doria	10/2015
1524	(7*10^169944+23)/3	169945	Robert Price	06/2020
1525	2^564526-351401	169940	Enzo Doria	07/2015
1526	4*10^169759+19	169760	Robert Price	10/2018
1527	21^128327-20^128327	169677	Jean-Louis Charton	11/2014
1528	(4*10^169559+83)/3	169560	Robert Price	02/2018
1529	(194*10^169461-17)/3	169463	Robert Price	09/2020
1530	2^562749+2793047	169405	Enzo Doria	02/2016
1531	(154*10^169337-1)/9	169339	Serge Batalov	12/2014
1532	(56*10^169311+691)/9	169312	Robert Price	05/2019
1533	2^562369-29503	169290	Enzo Doria	08/2015
1534	(17*10^169283+19)/9	169284	Robert Price	03/2021
1535	(22*10^169019+383)/9	169020	Robert Price	05/2018
1536	5*10^168807+87	168808	Robert Price	02/2019
1537	2^560405-39943	168699	Enzo Doria	09/2015
1538	89*10^168614-7	168616	Robert Price	04/2020
1539	(23*10^168608-83)/3	168609	Robert Price	08/2019
1540	(94*10^168541+11)/3	168543	Robert Price	04/2020
1541	2^559686-350471	168483	Enzo Doria	06/2015
1542	2^559672-1855889	168479	Enzo Doria	09/2015
1543	(5*10^168379-473)/9	168379	Robert Price	01/2018
1544	2^559000-59939	168276	Enzo Doria	11/2015
1545	(16*10^168181+41)/3	168182	Robert Price	03/2019
1546	(19*10^168173+77)/3	168174	Robert Price	05/2019
1547	2^558640-114149	168168	Enzo Doria	12/2014
1548	2^558498-1849277	168125	Enzo Doria	08/2015
1549	2^558476-1850249	168119	Enzo Doria	08/2015
1550	(7*10^168067+71)/3	168068	Robert Price	05/2018
1551	2^558150-1852211	168020	Enzo Doria	08/2015
1552	2^558125-113661	168013	Enzo Doria	09/2014
1553	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
1554	(13*10^167911+179)/3	167912	Robert Price	11/2018
1555	(26*10^167861-167)/3	167862	Robert Price	10/2019
1556	39^105456+2	167788	Robert Price	04/2015
1557	(28^115877-1)/27	167691	Paul Bourdelais	12/2017
1558	10^167639+121911	167640	Patrick De Geest	07/2018
1559	10^167639-8001	167639	Robert Price	03/2018
1560	2^556504-462059	167525	Enzo Doria	07/2015
1561	(88*10^167522-637)/9	167523	Robert Price	11/2020
1562	5*10^167510+9	167511	Robert Price	08/2015
1563	7*10^167437-93	167438	Robert Price	08/2020
1564	11^160663+6	167314	Paul Bourdelais	02/2021
1565	2^555343+1874333	167175	Enzo Doria	06/2016
1566	2^555210-461261	167135	Enzo Doria	07/2015
1567	9*10^166996+59	166997	Robert Price	01/2020
1568	(68*10^166976-329)/9	166977	Robert Price	03/2021
1569	2^554372+1880527	166883	Enzo Doria	11/2016
1570	2^554299+72173	166861	Enzo Doria	04/2016
1571	(185*10^166837+7)/3	166839	Robert Price	03/2020
1572	2^554037-2797063	166782	Enzo Doria	03/2016
1573	(49*10^166721-139)/9	166722	Robert Price	03/2019
1574	2*10^166646+69	166647	Robert Price	06/2020
1575	2^553484-29819	166616	Enzo Doria	08/2015
1576	(188*10^166611+7)/3	166613	Robert Price	03/2020
1577	2^553383-2784217	166585	Enzo Doria	10/2015
1578	2^553069+76427	166491	Enzo Doria	05/2016
1579	2*10^166458+51	166459	Robert Price	05/2018
1580	589^60089-588^60089	166454	Jean-Louis Charton	09/2012
1581	11^159756-2424	166369	Mike Oakes	06/2010
1582	2^552649-361275	166364	Enzo Doria	05/2014
1583	2^552628-113669	166358	Enzo Doria	09/2014
1584	10^166324+550603	166325	Patrick De Geest	07/2018
1585	10^166324-801	166324	Robert Price	02/2018
1586	(85*10^166297-1)/3	166299	Robert Price	02/2020
1587	8*10^166227+87	166228	Robert Price	10/2019
1588	2^552137+1879397	166210	Enzo Doria	09/2016
1589	(103*10^166126+11)/3	166128	Robert Price	01/2021
1590	(23^121949-1)/22	166061	Paul Bourdelais	10/2017
1591	2^551542+19249	166031	Payam Samidoost	08/2002
1592	2^551535-23821	166029	Enzo Doria	08/2013
1593	2^551507-23557	166021	Enzo Doria	08/2013
1594	7*10^165916-3	165917	Robert Price	08/2015
1595	(29*10^165796+67)/3	165797	Robert Price	12/2019
1596	81^86837-80^86837	165728	Robert Price	01/2015
1597	(71*10^165663-539)/9	165664	Robert Price	07/2019
1598	2^550270-69551	165648	Enzo Doria	12/2015
1599	(202*10^165569-13)/9	165571	Robert Price	01/2020
1600	2^550000-23625	165567	Enzo Doria	08/2013
1601	2^549675-1852057	165469	Enzo Doria	08/2015
1602	-tau(103^14938)	165374	Nik Lygeros / Olivier Rozier	10/2013
1603	(28*10^165358-1)/9	165359	Serge Batalov	10/2014
1604	2^549278+1879669	165350	Enzo Doria	09/2016
1605	(7*10^165350-439)/9	165350	Robert Price	02/2018
1606	2^549252-351269	165342	Enzo Doria	06/2015
1607	67*10^165327-9	165329	Robert Price	03/2021
1608	(14*10^165282+73)/3	165283	Robert Price	12/2018
1609	2^549049+2797607	165281	Enzo Doria	04/2016
1610	(7*10^165239+107)/3	165240	Robert Price	02/2018
1611	(44^100511-1)/43	165184	Paul Bourdelais	11/2017
1612	(7*10^165134+107)/3	165135	Robert Price	02/2018
1613	(23*10^165060-83)/3	165061	Robert Price	08/2019
1614	(76*10^164984+77)/9	164985	Robert Price	10/2019
1615	9*10^164791-89	164792	Robert Price	04/2020
1616	2^547178-1856501	164717	Enzo Doria	10/2015
1617	11^158160-60	164707	Enzo Doria	07/2012
1618	(26*10^164643-167)/3	164644	Robert Price	10/2019
1619	2^546398-59201	164483	Enzo Doria	10/2015
1620	2^546332-114893	164463	Enzo Doria	05/2015
1621	2^545958+1876189	164350	Enzo Doria	07/2016
1622	2^545878-49841	164326	Enzo Doria	10/2015
1623	(10^164284+77)/3	164284	Robert Price	01/2018
1624	2^545668-4019	164263	Yves Minet	04/2017
1625	10^164216-50000000001	164216	Robert Price	12/2020
1626	(1353^238539617^9)/10^247183	164151	Hans Havermann	07/2017
1627	(16*10^164122+197)/3	164123	Robert Price	04/2019
1628	2^545185+76757	164118	Enzo Doria	05/2016
1629	2^545076-114329	164085	Enzo Doria	01/2015
1630	(2*10^164043-143)/3	164043	Robert Price	03/2018
1631	(29^112153+1)/30	164011	Lelio R Paula	03/2017
1632	2^544757+1874777	163989	Enzo Doria	06/2016
1633	2^544444-457199	163894	Enzo Doria	01/2015
1634	2^544264-343529	163840	Enzo Doria	07/2015
1635	7*10^163780+9	163781	Robert Price	09/2015
1636	2^543989+2793047	163758	Enzo Doria	02/2016
1637	(28*10^163709+113)/3	163710	Robert Price	03/2020
1638	(68*10^163521-329)/9	163522	Robert Price	03/2021
1639	2^542870-69551	163421	Enzo Doria	12/2015
1640	2^542395+72533	163278	Enzo Doria	04/2016
1641	2^542072-3683	163180	Yves Minet	03/2017
1642	2^541779-1867357	163092	Enzo Doria	04/2016
1643	8*10^162924+9	162925	Robert Price	12/2015
1644	2^540905+81557	162829	Enzo Doria	08/2016
1645	2^540628-2939	162746	Yves Minet	09/2014
1646	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
1647	(203*10^162689+1)/3	162691	Robert Price	03/2020
1648	3*10^162620-59	162621	Robert Price	09/2018
1649	3^340694-112960	162553	Enzo Doria	07/2014
1650	2^539807-114081	162499	Enzo Doria	12/2014
1651	2^539654-114893	162453	Enzo Doria	05/2015
1652	9*10^162449-71	162450	Robert Price	11/2020
1653	2^539617-1851583	162441	Enzo Doria	08/2015
1654	(91*10^162410+11)/3	162412	Robert Price	02/2020
1655	2^539346+81049	162360	Enzo Doria	07/2016
1656	2^539220-115499	162322	Enzo Doria	07/2015
1657	2^539217-113713	162321	Enzo Doria	09/2014
1658	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
1659	4*10^162263-39	162264	Robert Price	09/2020
1660	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
1661	(10^162138+11)/3	162138	Serge Batalov	07/2015
1662	2^538473-112723	162097	Enzo Doria	06/2014
1663	2^538157+79337	162002	Enzo Doria	06/2016
1664	2^538136-114749	161996	Enzo Doria	05/2015
1665	2^538104+1531	161986	Lelio R Paula	01/2013
1666	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
1667	2^537815-22737	161899	Enzo Doria	07/2013
1668	2^537804-39839	161896	Enzo Doria	09/2015
1669	(754*10^161816-7)/9	161818	Robert Price	05/2020
1670	2^537458-59201	161791	Enzo Doria	10/2015
1671	2*10^161766+51	161767	Robert Price	05/2018
1672	(7*10^161760+131)/3	161761	Robert Price	06/2020
1673	2^537209-49849	161717	Enzo Doria	10/2015
1674	(58*10^161691+329)/9	161692	Robert Price	05/2019
1675	2^536937+1879397	161635	Enzo Doria	09/2016
1676	34*10^161593-9	161595	Robert Price	06/2020
1677	(31*10^161582-1)/3	161584	Robert Price	02/2020
1678	2^536569-22881	161524	Enzo Doria	07/2013
1679	10^161253+573493	161254	Patrick De Geest	07/2018
1680	10^161253-8001	161253	Robert Price	03/2018
1681	97*10^161247-3	161249	Robert Price	05/2020
1682	7*10^161192-9	161193	Robert Price	10/2015
1683	2^535269-113803	161133	Enzo Doria	09/2014
1684	2^535205-23295	161113	Enzo Doria	08/2013
1685	(89^82609+1)/90	161036	Paul Bourdelais	10/2017
1686	2^534359-23229	160859	Enzo Doria	08/2013
1687	8*10^160782+53	160783	Robert Price	08/2020
1688	67^88037-66^88037	160763	Robert Price	10/2013
1689	(88*10^160761-637)/9	160762	Robert Price	11/2020
1690	2^533948-1852559	160735	Enzo Doria	08/2015
1691	2^533665-23335	160650	Enzo Doria	08/2013
1692	(19*10^160619+77)/3	160620	Robert Price	05/2019
1693	3^336353-2^336353	160482	Mike Oakes	10/2007
1694	(91*10^160249+11)/3	160251	Robert Price	02/2020
1695	2^532253+1868417	160225	Enzo Doria	04/2016
1696	2^532108-291989	160181	Enzo Doria	07/2015
1697	(28*10^160171-79)/3	160172	Robert Price	02/2021
1698	(26*10^160166-131)/3	160167	Robert Price	10/2019
1699	(17*10^160143+67)/3	160144	Robert Price	01/2019
1700	(19*10^159921-49)/3	159922	Robert Price	05/2019
1701	2^531110-1853771	159881	Enzo Doria	09/2015
1702	(275^65536+53^65536)/2	159864	Kellen Shenton	11/2020
1703	2^530992-1845299	159845	Enzo Doria	07/2015
1704	(136*10^159736-1)/9	159738	Serge Batalov	12/2014
1705	2^530417-113833	159672	Enzo Doria	09/2014
1706	2^530406-69701	159669	Enzo Doria	02/2016
1707	5*10^159656+41	159657	Robert Price	03/2019
1708	7^188858-188858^7	159604	Norbert Schneider	05/2018
1709	(24^115597-1)/23	159547	Paul Bourdelais	09/2017
1710	(17*10^159438-377)/9	159439	Robert Price	03/2018
1711	(203*10^159381+1)/3	159383	Robert Price	03/2020
1712	89*10^159258-9	159260	Robert Price	05/2020
1713	2^528944-461315	159229	Enzo Doria	07/2015
1714	(13*10^159147+161)/3	159148	Robert Price	11/2018
1715	2^528620-113879	159131	Enzo Doria	10/2014
1716	2^528000-23307	158944	Enzo Doria	08/2013
1717	(29*10^158909+61)/9	158910	Robert Price	08/2018
1718	2^527817+1876817	158889	Enzo Doria	07/2016
1719	2^527774-49451	158876	Enzo Doria	10/2015
1720	2^527745-291553	158868	Enzo Doria	07/2015
1721	(91*10^158862+11)/3	158864	Robert Price	02/2020
1722	2^527644-1856999	158837	Enzo Doria	10/2015
1723	(37200^37199-37198^37199)/(2^37199)	158822	Henri Lifchitz	06/2013
1724	2^527573-1863253	158816	Enzo Doria	12/2015
1725	2^527553-23401	158810	Enzo Doria	08/2013
1726	10^158755-50001	158755	Robert Price	08/2020
1727	11^152420-210	158730	Enzo Doria	09/2012
1728	(13*10^158694+401)/9	158695	Robert Price	01/2018
1729	2^527052-69059	158659	Enzo Doria	11/2015
1730	2^526849-113233	158598	Enzo Doria	07/2014
1731	(2^526763-lucasV(1,2,526763)+1)/2	158572	Mike Oakes	11/2016
1732	(299*10^158544-17)/3	158546	Robert Price	04/2020
1733	2^526658-3551	158540	Yves Minet	03/2017
1734	7*10^158465-11	158466	Robert Price	06/2019
1735	2^526375-23115	158455	Enzo Doria	08/2013
1736	(77*10^158407-293)/9	158408	Robert Price	09/2019
1737	2^526028-112793	158351	Enzo Doria	07/2014
1738	(229*10^158339-1)/3	158341	Robert Price	07/2020
1739	2^525690-9221	158249	Lelio R Paula	01/2013
1740	2*10^158242-7	158243	Robert Price	10/2015
1741	2^525667-525667^2	158242	Henri Lifchitz	12/2017
1742	2^525186-1857431	158097	Enzo Doria	10/2015
1743	2^524515-23245	157895	Enzo Doria	08/2013
1744	2^524499-109087	157890	Enzo Doria	04/2014
1745	2^18067*(2^506221+1)-1	157827	Makoto Morimoto	05/2014
1747	2^524288+189093	157827	Makoto Morimoto	01/2016
1746	2^524288-164073	157827	Matthias Baur	03/2020
1748	(2^(2^19)-9333)/(1923463121331973)	157814	Makoto Morimoto	09/2017
1749	(10^157792+359)/9	157792	Serge Batalov	12/2014
1750	2^523924+1876591	157717	Enzo Doria	07/2016

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Probable Primes Top 10000

(280932 PRPs in the top)