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	(86^103471+1)/87	200163	Paul Bourdelais	05/2018
1502	(10^(2100072+1)+3610^100072-1)/9	200145	Robert Price	09/2023
1503	103(10^100000+20110)^2-4707(10^100000+20110)+50383	200003	Robert Price	05/2017
1504	103(10^100000+33798)^2-4707(10^100000+33798)+50383	200003	Robert Price	01/2018
1505	numbpart(32235776596)	200002	Serge Batalov	04/2017
1506	(10^200001+149)/3	200001	Serge Batalov	12/2014
1507	10^200000+571791	200001	Patrick De Geest	08/2019
1508	(3^419180-621444)/3	200000	Stefano Morozzi	06/2019
1509	(3^419180-1941384)/3	200000	Stefano Morozzi	08/2019
1510	10^200000-45557	200000	Patrick De Geest	08/2019
1511	(10^200000-1)/9-10^58838	200000	Akihiko Yoshida	04/2020
1512	2593604092947240127723272^8192+2593604092947240127722755^8192	200000	Youcef Lemsafer	01/2023
1513	(2593604092947240127723019^8192+2593604092947240127723011^8192)/2	199999	Youcef Lemsafer	01/2023
1514	(2593604092947240127723087^8192+2593604092947240127722984^8192)/147457	199994	Youcef Lemsafer	01/2023
1515	(2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986	199989	Youcef Lemsafer	01/2023
1516	(2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169	199986	Youcef Lemsafer	01/2023
1517	92*10^199980-9	199982	Robert Price	12/2021
1518	(2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649	199977	Youcef Lemsafer	01/2023
1519	(85*10^199951-139)/9	199952	Robert Price	08/2021
1520	(10^199926+7)/29/373/2339	199919	Alfred Reich	08/2021
1521	23*10^199833-9	199835	Robert Price	10/2021
1522	fibonacci(956176)-4	199829	Jon Grantham	08/2023
1523	(299*10^199801-17)/3	199803	Robert Price	04/2020
1524	6*10^199788+77	199789	Robert Price	06/2020
1525	(23*10^199615+37)/3	199616	Robert Price	02/2022
1526	(17*10^199607-167)/3	199608	Robert Price	05/2022
1527	2^663020-933075	199589	Paul Bourdelais	06/2021
1528	3*2^662703-5	199494	Jon Grantham	07/2023
1529	(14*10^199447+73)/3	199448	Robert Price	12/2018
1530	(2^662424-15)/7	199409	Stefano Morozzi	08/2022
1531	2^662194+22189	199341	Enzo Doria	09/2023
1532	2^662103-29287	199313	Enzo Doria	08/2015
1533	(2*10^199283+457)/9	199283	Robert Price	01/2018
1534	(10^199248-19)/9	199248	Robert Price	01/2018
1535	(83*10^199213+529)/9	199214	Robert Price	12/2021
1536	(194*10^199146-17)/3	199148	Robert Price	09/2020
1537	(151*10^199003-1)/3	199005	Robert Price	03/2020
1538	9*10^198946-73	198947	Robert Price	01/2021
1539	45*10^198931-7	198933	Robert Price	07/2020
1540	2^660482-2891	198825	Yves Minet	05/2016
1541	2^659589-21	198557	Stefano Morozzi	07/2022
1542	2^659583+1879223	198555	Enzo Doria	08/2016
1543	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
1544	(49*10^198403+311)/9	198404	Robert Price	06/2019
1545	96*10^198376-7	198378	Robert Price	03/2021
1546	(10^198375+7)/59/1201/87589	198366	Alfred Reich	08/2021
1547	2^658828-29819	198327	Enzo Doria	08/2015
1548	2^658776-2791229	198312	Enzo Doria	01/2016
1549	(35*10^198294-377)/9	198295	Robert Price	07/2018
1550	(4*10^198268+137)/3	198269	Robert Price	03/2018
1551	2^658544-1854029	198242	Enzo Doria	09/2015
1552	(62*10^198229-233)/9	198230	Robert Price	02/2022
1553	(26*10^198200-41)/3	198201	Robert Price	02/2022
1554	(157^90239-1)/156	198154	Alexander Zhirkov	06/2016
1555	2*10^197959-37	197960	Robert Price	11/2021
1556	(232*10^197897+17)/3	197899	Robert Price	04/2021
1557	(4*10^197778+173)/3	197779	Robert Price	02/2018
1558	2^656763+211373	197706	Enzo Doria	08/2023
1559	78*10^197702-7	197704	Robert Price	10/2020
1560	(17*10^197640-23)/3	197641	Robert Price	03/2021
1561	(29*10^197629-77)/3	197630	Robert Price	02/2020
1562	2^656462+1874419	197615	Enzo Doria	06/2016
1563	(89^101363+1)/90	197595	Paul Bourdelais	11/2017
1564	2^655893-344563	197444	Enzo Doria	07/2015
1565	2^655875+71333	197439	Enzo Doria	04/2016
1566	2^655845-9	197430	Robert Price	01/2017
1567	(299*10^197426+1)/3	197428	Robert Price	04/2020
1568	2^655682-1849121	197380	Enzo Doria	08/2015
1569	4*10^197268-89	197269	Robert Price	11/2018
1570	(11*10^197198-89)/3	197199	Robert Price	05/2021
1571	2^655045-49603	197189	Enzo Doria	10/2015
1572	2^655000-2784089	197175	Enzo Doria	10/2015
1573	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
1574	(4*10^197061+41)/9	197061	Serge Batalov	11/2022
1575	(154*10^197005+17)/9	197007	Robert Price	06/2022
1576	2^654400-39719	196995	Enzo Doria	09/2015
1577	(5^281807-2^281807)/3	196975	Jon Grantham	08/2023
1578	(14*10^196965-221)/9	196966	Robert Price	04/2018
1579	2^654216-459995	196939	Enzo Doria	06/2015
1580	(17*10^196921+31)/3	196922	Robert Price	01/2019
1581	(14*10^196885-89)/3	196886	Robert Price	05/2020
1582	3*10^196881-59	196882	Robert Price	09/2018
1583	2^653851+82295	196829	Enzo Doria	09/2016
1584	(38*10^196792+691)/9	196793	Robert Price	10/2018
1585	(65*10^196768+493)/9	196769	Robert Price	08/2021
1587	2^653636-29429	196765	Enzo Doria	08/2015
1586	2^653638-11	196765	Stefano Morozzi	07/2022
1588	2^653601-69673	196754	Enzo Doria	02/2016
1589	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
1590	2^652786-1852571	196509	Enzo Doria	08/2015
1591	2^652752-1325	196498	Yves Minet	07/2015
1592	2^652470-1859141	196414	Enzo Doria	10/2015
1593	2^652307+1877483	196364	Enzo Doria	08/2016
1594	2^652293-115273	196360	Enzo Doria	06/2015
1595	(47*10^196281+403)/9	196282	Robert Price	03/2019
1596	(7*10^196125-31)/3	196126	Robert Price	12/2021
1597	33^129128+129128^33	196083	Norbert Schneider	06/2022
1598	6*10^196070+73	196071	Robert Price	04/2019
1599	2^651218-1868201	196037	Enzo Doria	04/2016
1600	2^651047-49687	195985	Enzo Doria	10/2015
1601	10^195968-700001	195968	Robert Price	08/2021
1602	fibonacci(937485)+3	195923	Jon Grantham	08/2023
1603	(29*10^195875-197)/3	195876	Robert Price	08/2021
1604	(25*10^195808-97)/9	195809	Robert Price	01/2022
1605	2^650285-2785333	195756	Enzo Doria	10/2015
1606	(10^195732+7)/18089/49605893	195721	Alfred Reich	08/2021
1607	(69^106397-1)/68	195647	Paul Bourdelais	10/2017
1608	2^649811+1877573	195613	Enzo Doria	08/2016
1609	2^649662-170531	195568	Hans Havermann	10/2018
1610	2^649586+182839	195545	Enzo Doria	11/2016
1611	2^649537-1867363	195531	Enzo Doria	04/2016
1612	2^649536-1861499	195530	Enzo Doria	12/2015
1613	(103*10^195478-1)/3	195480	Serge Batalov	12/2014
1614	2^649102-59351	195400	Enzo Doria	10/2015
1615	(2*10^195399+529)/9	195399	Robert Price	01/2018
1616	(202*10^195383-13)/9	195385	Robert Price	01/2020
1617	2^648988+1178971	195365	Enzo Doria	06/2016
1618	2^648975-114319	195361	Enzo Doria	02/2015
1619	(11*10^195350-137)/9	195351	Robert Price	01/2018
1620	2^648619-24835	195254	Enzo Doria	09/2013
1621	5*10^195250-21	195251	Robert Price	12/2021
1622	(14*10^195234-83)/3	195235	Robert Price	12/2018
1623	5*10^195221+81	195222	Robert Price	03/2019
1624	10^195143-5001	195143	Robert Price	12/2021
1625	2^648190-24737	195125	Enzo Doria	09/2013
1626	(57^111119+1)/58	195110	Paul Bourdelais	10/2017
1627	(29*10^195098-197)/3	195099	Robert Price	08/2021
1628	10^195060+89701	195061	Patrick De Geest	02/2021
1630	10^195060-40000000001	195060	Robert Price	09/2020
1629	10^195060-110337	195060	Patrick De Geest	02/2021
1631	56*10^195032-3	195034	Robert Price	03/2020
1632	11^187185-90	194934	Enzo Doria	09/2012
1633	(86*10^194818-437)/9	194819	Robert Price	03/2021
1634	2^647068+77281	194787	Enzo Doria	05/2016
1635	2*10^194716-93	194717	Robert Price	12/2021
1636	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
1637	F(931517)	194676	Henri Lifchitz	09/2008
1638	4*10^194668+49	194669	Robert Price	01/2019
1639	2^646589+1179407	194643	Enzo Doria	06/2016
1640	2^646289-114621	194553	Enzo Doria	05/2015
1641	2^646236-39659	194537	Enzo Doria	09/2015
1642	(16*10^194536+53)/3	194537	Robert Price	03/2019
1643	2^646161-59833	194514	Enzo Doria	11/2015
1644	(17*10^194502+31)/3	194503	Robert Price	01/2019
1645	(19*10^194428+287)/9	194429	Robert Price	10/2021
1646	2*10^194413+3	194414	Robert Price	07/2015
1647	2^645360-1848599	194273	Enzo Doria	08/2015
1648	22470^44641+44641^22470	194260	Norbert Schneider	08/2023
1649	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
1650	2*10^193981-43	193982	Robert Price	04/2018
1651	2^644382+75169	193979	Enzo Doria	04/2016
1652	2^644304-1861409	193955	Enzo Doria	11/2015
1653	(29*10^193950-23)/3	193951	Robert Price	03/2022
1654	5*10^193907-9	193908	Robert Price	05/2015
1655	2^644043+1876703	193877	Enzo Doria	07/2016
1656	2*10^193841-63	193842	Robert Price	01/2022
1657	2^643735+1879733	193784	Enzo Doria	09/2016
1658	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
1659	9*10^193712+71	193713	Robert Price	08/2020
1660	2^643216-286565	193628	Enzo Doria	07/2015
1661	10^193566+1126339	193567	Patrick De Geest	09/2022
1663	10^193566-10000000001	193566	Robert Price	04/2021
1662	10^193566-454041	193566	Patrick De Geest	08/2021
1664	2^642888-24965	193529	Enzo Doria	09/2013
1665	2^642448-114825	193397	Enzo Doria	05/2015
1666	2^642437-1856623	193393	Enzo Doria	10/2015
1667	2^642039-59797	193273	Enzo Doria	11/2015
1668	2^641987+39	193258	Jon Grantham	08/2023
1669	10^193230+513861	193231	Patrick De Geest	07/2018
1670	10^193230-8001	193230	Robert Price	03/2018
1671	(62*10^193225-233)/9	193226	Robert Price	02/2022
1672	2^641692-286349	193169	Enzo Doria	07/2015
1673	2^641690-24737	193168	Enzo Doria	09/2013
1674	22268^44421+44421^22268	193129	Norbert Schneider	06/2023
1675	2^641514+1876549	193115	Enzo Doria	07/2016
1676	2^640888-2785619	192927	Enzo Doria	10/2015
1677	2^640874-2783741	192923	Enzo Doria	09/2015
1678	10^192922+192207	192923	Patrick De Geest	08/2021
1679	10^192922-7001	192922	Robert Price	04/2021
1680	2^640854+25	192917	Stefano Morozzi	05/2021
1681	34*10^192868-9	192870	Robert Price	06/2020
1682	(46*10^192841+683)/9	192842	Robert Price	03/2019
1683	2^640181+467	192714	Lelio R Paula	08/2013
1684	2^639536-1850249	192520	Enzo Doria	08/2015
1685	40714<>40712<>...<>1086421357911<>...<>40711<>40713	192464	Hans Havermann	12/2019
1686	5*10^192422-43	192423	Robert Price	01/2019
1687	2^639110-2792441	192392	Enzo Doria	02/2016
1688	2^638955-29827	192345	Enzo Doria	08/2015
1689	2^638713-2784223	192272	Enzo Doria	10/2015
1690	(10^192216+7)/149	192214	Alfred Reich	07/2021
1691	2^638490-113507	192205	Enzo Doria	08/2014
1692	2^638189-39943	192115	Enzo Doria	09/2015
1693	2^638110+1877119	192091	Enzo Doria	07/2016
1694	2^638066-2785211	192078	Enzo Doria	10/2015
1695	(35*10^191973-341)/9	191974	Robert Price	08/2021
1696	(112*10^191900+17)/3	191902	Robert Price	03/2020
1697	2^637475-115309	191900	Enzo Doria	07/2015
1698	(68*10^191754-113)/9	191755	Robert Price	03/2021
1699	2^636930-11	191736	Stefano Morozzi	07/2022
1700	(47*10^191732+259)/9	191733	Robert Price	03/2022
1701	2^636661+1876577	191655	Enzo Doria	07/2016
1702	(9^200807-2^200807)/7	191618	Jon Grantham	07/2023
1703	(34^125101-1)/33	191589	Paul Bourdelais	11/2017
1704	fibonacci(916540)-2	191546	Jon Grantham	08/2023
1705	2^636177-1855123	191509	Enzo Doria	09/2015
1706	2^636158-113627	191503	Enzo Doria	08/2014
1707	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
1708	2^636035+79823	191466	Enzo Doria	06/2016
1709	2^636011-1860847	191459	Enzo Doria	11/2015
1710	2^635926-1860611	191433	Enzo Doria	11/2015
1711	3*2^635755+5	191382	Jon Grantham	07/2023
1712	3*10^191152-7	191153	Robert Price	08/2015
1713	2^634883-1865677	191119	Enzo Doria	02/2016
1714	2^634801+1871957	191095	Enzo Doria	05/2016
1715	(77*10^191080+157)/9	191081	Robert Price	05/2022
1716	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
1717	9*10^191018-41	191019	Robert Price	08/2020
1718	2^634470-59861	190995	Enzo Doria	11/2015
1719	2^634368-29519	190964	Enzo Doria	08/2015
1720	(19*10^190935+11)/3	190936	Robert Price	07/2023
1721	2^634188-350609	190910	Enzo Doria	06/2015
1722	(65*10^190899+493)/9	190900	Robert Price	08/2021
1723	(62*10^190795-413)/9	190796	Robert Price	09/2021
1724	(26*10^190789-131)/3	190790	Robert Price	10/2019
1725	(13*10^190732-61)/3	190733	Robert Price	11/2018
1726	3*2^633524+5	190711	Jon Grantham	07/2023
1727	(7*10^190683+143)/3	190684	Robert Price	03/2018
1728	2^633088-113879	190579	Enzo Doria	10/2014
1729	2^633064+1874911	190572	Enzo Doria	06/2016
1730	5*3^399402+2^399402	190564	Jon Grantham	08/2023
1731	(43*10^190547+83)/9	190548	Robert Price	11/2018
1732	99*10^190543+7	190545	Robert Price	05/2021
1733	(299*10^190533+1)/3	190535	Robert Price	04/2020
1734	(1744*10^190519-1747)/3	190522	Robert Price	12/2020
1735	2^632815-15	190497	Stefano Morozzi	07/2022
1736	2^632795-351205	190491	Enzo Doria	06/2015
1737	41171^41272+41272^41171	190454	Norbert Schneider	05/2023
1738	(16*10^190420-19)/3	190421	Robert Price	02/2019
1739	(43*10^190351+101)/9	190352	Robert Price	11/2018
1740	2^632156+78391	190298	Enzo Doria	06/2016
1741	97*10^190295-3	190297	Robert Price	05/2020
1742	2^632082-1851971	190276	Enzo Doria	08/2015
1743	2^632020+1880311	190257	Enzo Doria	09/2016
1744	(5*10^190242-77)/9	190242	Robert Price	04/2021
1745	7*10^190210+13	190211	Robert Price	03/2021
1746	2^631637-462373	190142	Enzo Doria	08/2015
1747	2*10^190126-21	190127	Robert Price	09/2020
1748	(28*10^190105+191)/3	190106	Robert Price	02/2020
1749	2*10^190093+33	190094	Robert Price	11/2021
1750	(68*10^190053-113)/9	190054	Robert Price	03/2021

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Probable Primes Top 10000

(293510 PRPs in the top)