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 (> 30000)	Who ?	When ?
1501	(22*10^146029+257)/9	146030	Robert Price	06/2018
1502	2^484743+1872923	145923	Enzo Doria	05/2016
1503	2^484341+1879157	145802	Enzo Doria	08/2016
1504	2^484271-51	145781	Lelio R Paula	11/2017
1505	70^78989-69^78989	145743	Robert Price	01/2014
1506	51^85334+2	145714	Robert Price	07/2015
1507	2^483886-1857101	145665	Enzo Doria	10/2015
1508	2^483563-1863457	145567	Enzo Doria	12/2015
1509	2^483516-1861409	145553	Enzo Doria	11/2015
1510	2^483384-115019	145514	Enzo Doria	06/2015
1511	2^483302-3221	145489	Lelio R Paula	12/2012
1512	2^483046+1874029	145412	Enzo Doria	06/2016
1513	2^482991-2789317	145395	Enzo Doria	12/2015
1514	2^482978-2789711	145391	Enzo Doria	12/2015
1515	2^482966-2789711	145388	Enzo Doria	12/2015
1516	2^482817-1858843	145343	Enzo Doria	10/2015
1517	2^482751-113635	145323	Enzo Doria	08/2014
1518	2^482705-459763	145309	Enzo Doria	05/2015
1519	(4^241306+11)/3	145281	Robert Price	03/2017
1520	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
1521	53^84239-52^84239	145252	Robert Price	01/2013
1522	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
1523	2^482087+72623	145123	Enzo Doria	04/2016
1524	2^482016-286565	145102	Enzo Doria	07/2015
1525	2^481840+15	145049	Robert Price	09/2015
1526	2^481801-481801	145037	Henri Lifchitz	03/2005
1527	2^481775+1869083	145029	Enzo Doria	05/2016
1528	29^99167+2	145022	Ray Chandler	08/2011
1529	2^481663+1875653	144996	Enzo Doria	07/2016
1530	2^481149-459073	144841	Enzo Doria	05/2015
1531	2^481045-113215	144809	Enzo Doria	07/2014
1532	2^480859-113695	144753	Enzo Doria	09/2014
1533	2^480766-2787191	144725	Enzo Doria	11/2015
1534	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
1535	2^480678+1874239	144699	Enzo Doria	06/2016
1536	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
1537	L(692147)	144651	Henri Lifchitz	10/2008
1538	2^480417+35	144620	Robert Price	11/2015
1539	2^480296-59879	144584	Enzo Doria	10/2015
1540	2^479844+3	144448	Donovan Johnson	06/2006
1541	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
1542	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015
1543	2^479348-2792219	144299	Enzo Doria	02/2016
1544	3^302389-6242	144277	Enzo Doria	05/2014
1545	2*10^144220-3	144221	Robert Price	07/2015
1546	2^478904-109109	144165	Enzo Doria	04/2014
1547	2^478337-115333	143994	Enzo Doria	07/2015
1548	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
1549	88^74047-87^74047	143984	Robert Price	05/2015
1550	(19*10^143963+467)/9	143964	Robert Price	02/2018
1551	(71^77761+1)/72	143954	Paul Bourdelais	09/2017
1552	2^478088+27	143919	Robert Price	11/2015
1553	2^477475-22071	143735	Enzo Doria	07/2013
1554	2^477417-22123	143717	Enzo Doria	07/2013
1555	2^477359-3577	143700	Yves Minet	03/2017
1556	2^476936-396765	143573	Enzo Doria	07/2013
1557	2^476888-2791229	143558	Enzo Doria	01/2016
1558	2^476868-1859939	143552	Enzo Doria	11/2015
1559	2^476558-113627	143459	Enzo Doria	08/2014
1560	2^476478-45	143435	Lelio R Paula	11/2017
1561	(2^475854+9)/73	143245	Lelio R Paula	08/2015
1562	2^475813-113239	143234	Enzo Doria	07/2014
1563	2^475624-114059	143178	Enzo Doria	11/2014
1564	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
1565	2^475480-2786129	143134	Enzo Doria	10/2015
1566	2^475299-111937	143080	Enzo Doria	05/2014
1567	2^475160-2797859	143038	Enzo Doria	04/2016
1568	(2^475069+3)/395	143008	Lelio R Paula	08/2015
1569	2^475027-461437	142998	Enzo Doria	07/2015
1570	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
1571	(8*10^142932+43)/3	142933	Robert Price	06/2018
1572	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
1573	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
1574	2^474417-59923	142814	Enzo Doria	10/2015
1575	4*10^142810-21	142811	Robert Price	09/2018
1576	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
1577	2^474053+2897	142705	Lelio R Paula	08/2012
1578	(10^142699+359)/9	142699	Serge Batalov	12/2014
1579	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
1580	2^473740-1856639	142610	Enzo Doria	09/2015
1581	2^473617-114223	142573	Enzo Doria	12/2014
1582	2^473257+1873217	142465	Enzo Doria	06/2016
1583	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
1584	(10^142425+359)/9	142425	Serge Batalov	12/2014
1585	2^473101+773027	142418	Enzo Doria	05/2016
1586	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
1587	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
1588	2^472634-109511	142278	Enzo Doria	04/2014
1589	(48^84589+1)/49	142213	Robert Price	01/2014
1590	2^472258+7	142164	Lelio R Paula	08/2015
1591	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
1592	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
1593	2^471792+1880881	142024	Enzo Doria	11/2016
1594	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
1595	(4*10^141926-79)/3	141927	Robert Price	02/2018
1596	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
1597	4*5^202913-9	141831	Lelio R Paula	04/2015
1598	2*7^167812-3	141818	Lelio R Paula	12/2014
1599	2^471043+35	141799	Robert Price	11/2015
1600	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
1601	(11*10^141718-131)/3	141719	Robert Price	09/2018
1602	2^470692+76771	141693	Enzo Doria	05/2016
1603	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
1604	2^470305-459373	141576	Enzo Doria	05/2015
1605	2^470183+72623	141540	Enzo Doria	04/2016
1606	2^470173-16465	141537	Enzo Doria	04/2013
1607	2^469974-1841	141477	Enzo Doria	05/2014
1608	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
1609	2*10^141448+63	141449	Robert Price	05/2018
1610	2^469824+43	141432	Lelio R Paula	09/2017
1611	2*10^141407-27	141408	Robert Price	05/2018
1612	2^469630-59711	141373	Enzo Doria	10/2015
1613	(25*10^141366-331)/9	141367	Robert Price	08/2018
1614	(2^469564-3)/611	141351	Lelio R Paula	08/2015
1615	197^61601+2	141342	Lelio R Paula	08/2017
1616	2^469372-112949	141296	Enzo Doria	07/2014
1618	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
1617	143^65536+106^65536	141253	Serge Batalov	03/2018
1619	2^469198+782569	141243	Enzo Doria	10/2016
1620	2^469076-2786939	141206	Enzo Doria	11/2015
1621	2^468804+1874941	141125	Enzo Doria	06/2016
1622	2^468787+81353	141119	Enzo Doria	08/2016
1623	2^468595-350407	141062	Enzo Doria	06/2015
1624	2^468564+87855	141052	Lelio R Paula	01/2016
1625	2^468551-21987	141048	Enzo Doria	07/2013
1626	2^468523-7	141040	Lelio R Paula	08/2015
1627	2^468405+87855	141004	Lelio R Paula	01/2016
1628	2^467978-113051	140876	Enzo Doria	07/2014
1629	2^467780-344429	140816	Enzo Doria	07/2015
1630	2^467605-1855603	140764	Enzo Doria	09/2015
1631	5*10^140744-7	140745	Robert Price	09/2015
1632	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
1633	2^467401-1850023	140702	Enzo Doria	08/2015
1634	(2^467270+78557)/23247	140658	Lelio R Paula	07/2015
1635	(29*2^467205+1)/2780517107	140635	Lelio R Paula	08/2015
1636	2^467166-1854941	140631	Enzo Doria	09/2015
1637	2^466866-1840571	140541	Enzo Doria	06/2015
1638	2^466829-459523	140530	Enzo Doria	05/2015
1639	2^466692-113213	140489	Enzo Doria	07/2014
1640	153^64265-2	140400	Lelio R Paula	11/2017
1641	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
1642	2^466181-112735	140335	Enzo Doria	07/2014
1643	(5*10^140281-119)/3	140282	Robert Price	03/2018
1644	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
1645	2^465803-114817	140221	Enzo Doria	05/2015
1646	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
1647	2^465503-112735	140131	Enzo Doria	07/2014
1648	6^179964+179964^6-1	140040	Robert Price	04/2014
1649	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
1650	2^465072-344789	140001	Enzo Doria	07/2015
1651	2^464864-17	139939	Lelio R Paula	09/2017
1652	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
1653	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
1654	3*10^139722+13	139723	Robert Price	07/2018
1655	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
1656	(18203^(2^15)+(18201)^(2^15))/2	139597	Robert Price	05/2018
1657	2^463633-2788423	139568	Enzo Doria	11/2015
1658	2^463271-109501	139459	Enzo Doria	04/2014
1659	(5*10^139457+79)/3	139458	Robert Price	03/2018
1660	2^463237-99	139449	Lelio R Paula	09/2017
1661	(7*10^139417-547)/9	139417	Robert Price	01/2018
1662	(10^139398+191)/3	139398	Robert Price	02/2018
1663	2^463019+79463	139383	Enzo Doria	06/2016
1664	3^292129-112756	139381	Enzo Doria	07/2014
1665	(15*2^462951+1)/527	139361	Lelio R Paula	08/2015
1666	2^462855-1865707	139334	Enzo Doria	02/2016
1667	2^462786-292043	139313	Enzo Doria	08/2015
1668	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
1669	2^462238-935	139148	Yves Minet	02/2014
1670	2^461228+1870441	138844	Enzo Doria	05/2016
1671	2^461204-113675	138837	Enzo Doria	08/2014
1672	(2^461139-7)/47	138815	Lelio R Paula	08/2015
1673	(17*10^138812-521)/9	138813	Robert Price	04/2018
1674	3*10^138811-11	138812	Robert Price	07/2018
1675	(17*2^460963+1)/124051613	138757	Lelio R Paula	08/2015
1676	2^460567-113541	138645	Enzo Doria	08/2014
1677	7*10^138604+3	138605	Robert Price	08/2015
1678	2^460330+69	138574	Lelio R Paula	09/2017
1679	2^460078-69581	138498	Enzo Doria	12/2015
1680	2^459768+1531	138404	Lelio R Paula	06/2012
1681	2^459343-113611	138277	Enzo Doria	08/2014
1682	2^459199+1874393	138233	Enzo Doria	06/2016
1683	2^459063-345307	138192	Enzo Doria	06/2015
1684	2*10^138162-43	138163	Robert Price	04/2018
1685	2^458927-112747	138151	Enzo Doria	06/2014
1686	2^458927-69217	138151	Enzo Doria	11/2015
1687	555555*2^458524+1513	138036	Darren Bedwell	08/2009
1688	2^458465+2^32+1	138012	T. D. Noe	06/2007
1689	2^458321-113053	137969	Enzo Doria	07/2014
1690	2^458298+79459	137962	Enzo Doria	06/2016
1691	2^458248-21815	137947	Enzo Doria	07/2013
1692	2^458194+1876549	137931	Enzo Doria	07/2016
1693	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
1694	2^457937+57	137853	Lelio R Paula	09/2017
1695	(8*10^137845+13)/3	137846	Robert Price	06/2018
1696	2^457822+105	137819	Donovan Johnson	06/2006
1697	2^457754-113711	137798	Enzo Doria	09/2014
1698	11^132315-360	137792	Enzo Doria	09/2012
1699	2^457347-37	137676	Lelio R Paula	09/2017
1700	2^457322-2786393	137668	Enzo Doria	10/2015
1701	gcd(Phi(699340,10),(10^34967+1)^3(10^34967+1+10^17484)-(10^69934+10^34967)(10^17484-1)+10^104901)	137664	Serge Batalov	04/2015
1702	2^457240-59939	137643	Enzo Doria	10/2015
1703	2^457120-21575	137607	Enzo Doria	07/2013
1704	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
1705	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
1706	2^456796-113513	137510	Enzo Doria	08/2014
1707	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
1708	2^456503-114361	137422	Enzo Doria	01/2015
1709	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
1710	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
1711	2^455922+76249	137247	Enzo Doria	05/2016
1712	14^119741-119741^14	137239	Serge Batalov	04/2016
1713	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
1715	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
1714	124^65536+57^65536	137195	Serge Batalov	03/2018
1716	2^455689+72677	137177	Enzo Doria	04/2016
1717	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
1718	(37^87421-1)/36	137093	Robert Price	03/2012
1719	2^455323-57	137066	Lelio R Paula	09/2017
1720	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
1721	2^455025-112723	136977	Enzo Doria	06/2014
1722	2^454675-1777	136871	Yves Minet	10/2011
1723	3*10^136829+29	136830	Robert Price	05/2018
1724	4*10^136813-57	136814	Robert Price	10/2018
1725	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
1726	2^454348-53	136773	Lelio R Paula	09/2017
1727	31^91680-2	136729	Lelio R Paula	05/2017
1728	2^454199-113697	136728	Enzo Doria	09/2014
1729	(13*10^136687+47)/3	136688	Robert Price	10/2018
1730	2^453935-2791357	136649	Enzo Doria	01/2016
1731	2^453906-69131	136640	Enzo Doria	11/2015
1732	2^453791+1873913	136605	Enzo Doria	06/2016
1733	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
1734	2^453503-2788297	136519	Enzo Doria	11/2015
1735	2^453267-113827	136447	Enzo Doria	09/2014
1736	2^453102+1877629	136398	Enzo Doria	08/2016
1737	L(651821)	136223	Henri Lifchitz	09/2008
1738	2^452460+77701	136205	Enzo Doria	05/2016
1739	2^452440-114755	136199	Enzo Doria	04/2015
1740	2*10^136057-43	136058	Robert Price	04/2018
1741	(2^451956-5)/181	136051	Lelio R Paula	07/2015
1742	2^451947-22165	136050	Enzo Doria	07/2013
1743	2^451787-21805	136002	Enzo Doria	07/2013
1744	2^451734-112817	135986	Enzo Doria	06/2014
1745	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
1746	2^451705-21879	135977	Enzo Doria	07/2013
1747	2^451560-112349	135934	Enzo Doria	06/2014
1748	2^451530+45	135925	Lelio R Paula	08/2017
1749	2^451450-21743	135900	Enzo Doria	07/2013
1750	2^450805+65	135706	Lelio R Paula	08/2017

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Probable Primes Top 10000

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