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	99*10^189876-7	189878	Robert Price	07/2020
1502	2^630359+1788953	189757	Enzo Doria	05/2016
1503	2^630228+1871971	189718	Enzo Doria	05/2016
1504	2^630108+781	189682	Lelio R Paula	08/2013
1505	2^629870-1867811	189610	Enzo Doria	04/2016
1506	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
1507	2^629326+2792929	189447	Enzo Doria	02/2016
1508	4*10^189401+13	189402	Robert Price	02/2021
1509	(10^189385-61)/3	189385	Serge Batalov	12/2014
1510	2^629036+1874011	189359	Enzo Doria	06/2016
1511	2^628930+80779	189327	Enzo Doria	07/2016
1512	(134*10^189309-11)/3	189311	Robert Price	01/2022
1513	2^628582+1179439	189223	Enzo Doria	06/2016
1514	(44*10^188999-503)/9	189000	Robert Price	12/2018
1515	(16*10^188823+167)/3	188824	Robert Price	06/2019
1516	(10^188796+7)/4967/71933	188788	Alfred Reich	08/2021
1517	2^627037-2785843	188757	Enzo Doria	10/2015
1518	(10^188566+7)/311640753181661	188552	Alfred Reich	04/2022
1519	(16*10^188457+161)/3	188458	Robert Price	02/2019
1520	L(901657)	188436	Renaud Lifchitz	11/2008
1521	(19*10^188375+137)/3	188376	Robert Price	03/2022
1522	2^625651+74213	188340	Enzo Doria	04/2016
1523	2^625584-460919	188320	Enzo Doria	06/2015
1524	(8*10^188308-71)/9	188308	Serge Batalov	11/2022
1525	(14*10^188218+139)/9	188219	Robert Price	11/2021
1526	(10^188164+359)/9	188164	Serge Batalov	12/2014
1527	2^624481-113611	187988	Enzo Doria	08/2014
1530	(2^624389+125582)/2	187960	Stefano Morozzi	09/2019
1528	(2^624389+166982)/2	187960	Stefano Morozzi	09/2019
1529	(2^624389+179886)/2	187960	Stefano Morozzi	09/2019
1531	(2^624387+64466)/2	187959	Stefano Morozzi	09/2019
1532	(2^624378+112990)/2	187957	Stefano Morozzi	09/2019
1533	(2^624380+161986)/2	187957	Stefano Morozzi	09/2019
1535	(2^624376+55762)/2	187956	Stefano Morozzi	09/2019
1534	(2^624377+169506)/2	187956	Stefano Morozzi	09/2019
1536	(2^624355+80178)/2	187950	Stefano Morozzi	09/2019
1537	(2^624351+61350)/2	187949	Stefano Morozzi	09/2019
1538	(2^624341+63462)/2	187946	Stefano Morozzi	09/2019
1539	(2^624344+135990)/2	187946	Stefano Morozzi	09/2019
1540	(2^624344+183898)/2	187946	Stefano Morozzi	09/2019
1542	(2^624340+126982)/2	187945	Stefano Morozzi	09/2019
1541	(2^624338+196110)/2	187945	Stefano Morozzi	09/2019
1543	(2^624337+105162)/2	187944	Stefano Morozzi	09/2019
1544	(2^624333+44594)/2	187943	Stefano Morozzi	09/2019
1545	(2^624321+88742)/2	187940	Stefano Morozzi	09/2019
1546	(2^624324+135178)/2	187940	Stefano Morozzi	09/2019
1547	(2^624317+14186)/2	187938	Stefano Morozzi	09/2019
1548	(2^624313+24450)/2	187937	Stefano Morozzi	09/2019
1549	(2^624309+184590)/2	187936	Stefano Morozzi	09/2019
1551	(2^624307+152658)/2	187935	Stefano Morozzi	09/2019
1550	(2^624307+185978)/2	187935	Stefano Morozzi	09/2019
1552	(2^624303+40814)/2	187934	Stefano Morozzi	09/2019
1553	(2^624304+99238)/2	187934	Stefano Morozzi	09/2019
1554	2^624077-112723	187866	Enzo Doria	07/2014
1555	2^624008+1874941	187846	Enzo Doria	06/2016
1556	2^623870+78679	187804	Enzo Doria	05/2016
1557	2^623714-114035	187757	Enzo Doria	11/2014
1558	2^623651-1834251	187738	Enzo Doria	07/2015
1559	(7*10^187645+53)/3	187646	Robert Price	05/2018
1560	2^623146+1879609	187586	Enzo Doria	09/2016
1561	(401*10^187512+13)/9	187514	Robert Price	09/2021
1562	(5*10^187471+91)/3	187472	Robert Price	04/2018
1563	2^622500+81931	187392	Enzo Doria	08/2016
1564	(13*10^187382-157)/9	187383	Robert Price	05/2021
1565	2^622300-1861739	187331	Enzo Doria	12/2015
1566	(22*10^187317-91)/3	187318	Robert Price	02/2022
1567	(38*10^187281+349)/9	187282	Robert Price	10/2018
1568	2^622052+76771	187257	Enzo Doria	05/2016
1569	2^622005-24091	187243	Enzo Doria	08/2013
1570	7*10^187205-57	187206	Robert Price	06/2020
1571	2^621879-351787	187205	Enzo Doria	07/2015
1572	(5*10^187168-53)/3	187169	Robert Price	09/2020
1573	(23*10^187164-143)/3	187165	Robert Price	12/2019
1574	2^621700+79411	187151	Enzo Doria	06/2016
1575	(7*10^187101+131)/3	187102	Robert Price	06/2020
1576	(2*10^187062-71)/3	187062	Robert Price	12/2017
1577	2^620929-113203	186919	Enzo Doria	07/2014
1578	10^186842+168223	186843	Patrick De Geest	07/2018
1579	10^186842-8001	186842	Robert Price	03/2018
1580	2^620347-1777	186744	Lelio R Paula	07/2013
1581	(11*10^186659+133)/9	186660	Robert Price	04/2022
1582	11^179143-4170	186559	Enzo Doria	12/2012
1583	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
1584	2*10^186517+33	186518	Robert Price	11/2021
1585	2^619297-2792353	186427	Enzo Doria	02/2016
1586	(49*10^186409+383)/9	186410	Robert Price	04/2019
1587	2^618940-460139	186320	Enzo Doria	06/2015
1588	2^618046+74179	186051	Enzo Doria	04/2016
1589	3*10^186019+11	186020	Robert Price	07/2018
1590	(16*10^185978-19)/3	185979	Robert Price	02/2019
1591	(22*10^185950-7)/3	185951	Robert Price	12/2022
1592	2*10^185930-3	185931	Robert Price	07/2015
1593	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
1594	4*10^185905+91	185906	Robert Price	08/2018
1595	(34*10^185902-601)/9	185903	Robert Price	07/2022
1596	(19*10^185873+131)/3	185874	Robert Price	06/2020
1597	(37*10^185811+377)/9	185812	Robert Price	11/2018
1598	2^617250+9385	185811	Lelio R Paula	07/2013
1599	2^617130+9	185775	Stefano Morozzi	05/2021
1600	39^116749+2	185756	Robert Price	04/2015
1601	2^616924-39719	185713	Enzo Doria	09/2015
1602	2^616712+1867621	185649	Enzo Doria	04/2016
1603	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
1604	8*10^185529-67	185530	Robert Price	08/2019
1605	4*10^185355+9	185356	Robert Price	05/2015
1606	(16*10^185347+89)/3	185348	Robert Price	03/2021
1607	2^615622+76639	185321	Enzo Doria	05/2016
1608	2^615591+1879223	185312	Enzo Doria	08/2016
1609	2^615503+1876643	185285	Enzo Doria	07/2016
1610	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
1612	(4*10^185221-91)/3	185222	Robert Price	03/2018
1611	(7*10^185221+131)/3	185222	Robert Price	06/2020
1613	(62*10^185216-413)/9	185217	Robert Price	09/2021
1614	(232*10^185180+17)/3	185182	Robert Price	04/2021
1615	56*10^185139-3	185141	Robert Price	03/2020
1616	(28*10^185105+47)/3	185106	Robert Price	02/2021
1617	2^614783-2790097	185069	Enzo Doria	12/2015
1618	2^614745-29323	185057	Enzo Doria	07/2015
1619	(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840	185052	Serge Batalov	07/2013
1620	(49*10^184993-67)/9	184994	Robert Price	03/2019
1621	(5*10^184954-191)/3	184955	Robert Price	05/2021
1622	(14*10^184950+211)/9	184951	Robert Price	04/2018
1623	2^614315+81353	184928	Enzo Doria	08/2016
1624	2^614294-1849961	184921	Enzo Doria	08/2015
1625	2^614266+1877809	184913	Enzo Doria	08/2016
1626	(185*10^184878-11)/3	184880	Robert Price	10/2020
1627	91*10^184867-9	184869	Robert Price	06/2021
1628	(85*10^184768+77)/9	184769	Robert Price	07/2022
1629	2^613715-1860727	184747	Enzo Doria	11/2015
1630	(4*10^184730+89)/3	184731	Robert Price	08/2021
1631	2*10^184723+41	184724	Robert Price	05/2018
1632	(49*10^184703+293)/9	184704	Robert Price	03/2021
1633	2^613487-349987	184678	Enzo Doria	07/2015
1634	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
1635	14^161089-161089^14	184629	Serge Batalov	05/2016
1636	2^613033-114621	184542	Enzo Doria	05/2015
1637	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
1638	2^612341-1604809	184334	Enzo Doria	05/2015
1639	(11*10^184308-161)/3	184309	Robert Price	11/2021
1640	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
1641	(14*10^184150+37)/3	184151	Robert Price	12/2018
1642	2^611731-4837	184150	Yves Minet	08/2018
1643	3*10^184124-7	184125	Robert Price	08/2015
1644	2^611628-24537	184119	Enzo Doria	08/2013
1645	3*10^184110+13	184111	Robert Price	07/2018
1646	(194*10^184093+1)/3	184095	Robert Price	01/2022
1647	2^611460+71881	184068	Enzo Doria	04/2016
1648	4*10^184004-63	184005	Robert Price	10/2018
1649	2^610982-1867301	183924	Enzo Doria	03/2016
1650	3*10^183872-49	183873	Robert Price	07/2018
1651	2^610597+1178897	183809	Enzo Doria	05/2016
1652	(8*10^183773-269)/9	183773	Robert Price	09/2021
1653	(65*10^183768-29)/9	183769	Robert Price	01/2021
1654	(17*10^183764+31)/3	183765	Robert Price	01/2019
1655	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
1656	2^610401+1277	183750	Lelio R Paula	07/2013
1657	2^610356-1849019	183736	Enzo Doria	08/2015
1658	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
1659	23*10^183710-7	183712	Robert Price	02/2020
1660	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
1661	(4*10^183659+149)/9	183659	Robert Price	04/2018
1662	(4*10^183657+41)/9	183657	Serge Batalov	11/2022
1663	7*10^183596+39	183597	Robert Price	01/2023
1664	2^609846-1834251	183582	Enzo Doria	07/2015
1665	10^183546+1547323	183547	Patrick De Geest	02/2021
1667	10^183546-800000001	183546	Robert Price	09/2020
1666	10^183546-584297	183546	Patrick De Geest	02/2021
1668	7*10^183511+39	183512	Robert Price	01/2023
1669	(23*10^183477-71)/3	183478	Robert Price	07/2020
1670	11^176176-240	183469	Enzo Doria	11/2012
1671	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
1672	6*10^183429+53	183430	Robert Price	05/2020
1673	(28*10^183403+191)/3	183404	Robert Price	02/2020
1674	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
1675	2^608965-113989	183317	Enzo Doria	10/2014
1676	A005165(43592)	183312	Serge Batalov	07/2017
1677	(61*10^183294+119)/9	183295	Robert Price	05/2019
1678	2^608814-461261	183272	Enzo Doria	06/2015
1679	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
1680	2^608541-608541^2	183190	Henri Lifchitz	02/2018
1681	2^608293+143807	183115	Enzo Doria	10/2016
1682	2^608164-462419	183076	Enzo Doria	08/2015
1683	2^607950-1862303	183012	Enzo Doria	12/2015
1684	(46*10^182896+683)/9	182897	Robert Price	03/2019
1685	(2*10^182787+73)/3	182787	Robert Price	09/2020
1686	2^607101+1871987	182756	Enzo Doria	05/2016
1687	2^606869-69175	182686	Enzo Doria	11/2015
1688	8*10^182671+71	182672	Robert Price	05/2022
1689	(23*10^182666-71)/3	182667	Robert Price	07/2020
1690	3*10^182614-11	182615	Robert Price	07/2018
1691	2^606560-357	182593	Enzo Doria	05/2014
1692	66*10^182420+7	182422	Robert Price	07/2020
1693	2^605687+1866983	182330	Enzo Doria	03/2016
1694	2^605655-114445	182321	Enzo Doria	02/2015
1695	94*10^182291-3	182293	Robert Price	05/2020
1696	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
1697	(14*10^182177-221)/9	182178	Robert Price	04/2018
1698	2^605174-112751	182176	Enzo Doria	06/2014
1699	2^604761+1874507	182052	Enzo Doria	06/2016
1700	2^604705+1871957	182035	Enzo Doria	05/2016
1701	(14*10^182000+229)/9	182001	Robert Price	03/2018
1702	(10^181996+41)/3	181996	Robert Price	12/2017
1703	(17*10^181979+91)/9	181980	Robert Price	02/2022
1704	(5*10^181950-101)/3	181951	Robert Price	04/2018
1705	2^603915+75233	181797	Enzo Doria	04/2016
1706	39470^39537+39537^39470	181723	Norbert Schneider	12/2022
1707	(10^181710+7)/563747/2019847	181698	Alfred Reich	08/2021
1708	7*10^181594-57	181595	Robert Price	06/2020
1709	8*10^181580+29	181581	Robert Price	11/2021
1710	(83*10^181544+61)/9	181545	Serge Batalov	01/2023
1711	(2*10^181457+7)/9	181457	Rytis Slatkevicius	01/2023
1712	3*10^181445+23	181446	Robert Price	03/2022
1713	(194*10^181369-11)/3	181371	Robert Price	09/2020
1714	11^174145-360	181354	Enzo Doria	10/2012
1715	2^602351-396765	181326	Enzo Doria	08/2013
1716	6*10^181306+17	181307	Robert Price	04/2019
1717	(286*10^181220-1)/3	181222	Robert Price	11/2020
1718	2^601957-113833	181208	Enzo Doria	09/2014
1719	66^99581-65^99581	181193	Robert Price	09/2013
1720	10^181182+383973	181183	Patrick De Geest	04/2016
1721	10^181182-21	181182	Serge Batalov	12/2014
1722	(797*10^181171-41)/9	181173	Robert Price	04/2022
1723	(5*10^181127-29)/3	181128	Robert Price	03/2018
1724	2^601521-29143	181076	Enzo Doria	07/2015
1725	2^601442-2797811	181053	Enzo Doria	04/2016
1726	44*10^181029+3	181031	Robert Price	04/2020
1727	5*10^180992-9	180993	Robert Price	05/2015
1728	10^180979+79477	180980	Patrick De Geest	04/2016
1729	10^180979+107739	180980	Patrick De Geest	04/2016
1730	10^180979-11	180979	Serge Batalov	12/2014
1731	2^601023-113851	180926	Enzo Doria	10/2014
1732	(23*10^180862-143)/3	180863	Robert Price	12/2019
1733	3*10^180852+29	180853	Robert Price	05/2018
1734	(277*10^180782-7)/9	180784	Robert Price	02/2022
1735	(8*10^180725-629)/9	180725	Robert Price	01/2022
1736	(79*10^180710-1)/3	180712	Robert Price	02/2020
1737	2^600300-1852559	180709	Enzo Doria	08/2015
1738	(2*10^180706-77)/3	180706	Robert Price	02/2021
1739	(10^180689+71)/9	180689	Serge Batalov	07/2015
1740	2^600209+76487	180681	Enzo Doria	05/2016
1741	(8*10^180536-269)/9	180536	Robert Price	09/2021
1742	2^599702-369885	180529	Enzo Doria	11/2013
1743	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
1744	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
1745	(29*10^180432-17)/3	180433	Robert Price	09/2019
1746	4*10^180360+93	180361	Robert Price	08/2018
1747	2^598942+80779	180300	Enzo Doria	07/2016
1748	(38*10^180296+403)/9	180297	Robert Price	10/2018
1749	(85*10^180241+77)/9	180242	Robert Price	07/2022
1750	2^598591-1844797	180194	Enzo Doria	06/2015

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