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 ?
9251	2^219600+76561	66107	Enzo Doria	05/2016
9252	2^219594+255255	66105	Lelio R Paula	10/2011
9253	4*7^78210-3	66096	Lelio R Paula	09/2014
9254	(15185*2^219557-1)/63	66096	Lelio R Paula	04/2015
9255	(19*2^219499-1)/13	66076	Lelio R Paula	01/2014
9256	2^219496+66615	66075	Lelio R Paula	10/2011
9257	(F(79021)^5-F(79020)^5)/F(79019)	66057	Wayne Halsdorf	03/2012
9258	15871^14500+14500^15871	66046	Hans Havermann	08/2019
9260	(2^219414+7)/443657	66045	Lelio R Paula	04/2012
9259	(115*10^66043-1)/3	66045	Serge Batalov	12/2014
9261	10^66033+19	66034	Robert Price	01/2011
9262	10^66033-78309	66033	Patrick De Geest	05/2013
9263	(2^219350+2662)/2	66031	Stefano Morozzi	12/2019
9264	(lucasV(1,2,438701)+2)/7599419	66025	Mike Oakes	04/2017
9265	2^219304+454245	66018	Henri Lifchitz	03/2007
9266	(27*2^219293+1)/9145	66012	Lelio R Paula	08/2012
9267	(2^219278+2650)/2	66009	Stefano Morozzi	12/2019
9268	2^219273-112635	66008	Enzo Doria	06/2014
9269	17548^5771+5771^17548	66003	Hans Havermann	08/2019
9270	2^219250+25	66001	Lelio R Paula	08/2011
9271	132^31123+131	65999	Norbert Schneider	03/2015
9272	19327^2598+2598^19327	65995	Hans Havermann	08/2019
9273	18440^3789+3789^18440	65988	Hans Havermann	08/2019
9274	V(319871)	65987	Serge Batalov	03/2015
9275	(2^219193+2166)/2	65984	Stefano Morozzi	12/2019
9276	2^219189-195	65983	Lelio R Paula	08/2011
9277	(2^219167+3446)/2	65976	Stefano Morozzi	12/2019
9278	(7*2^219143-1)/55	65968	Lelio R Paula	01/2014
9279	(73^35401-1)/72	65962	Paul Bourdelais	08/2017
9280	2^219112-17009	65960	Enzo Doria	05/2013
9281	2^219093-111201	65954	Enzo Doria	05/2014
9282	2^219089-112099	65953	Enzo Doria	06/2014
9283	46714!3+81	65950	Robert Price	09/2014
9284	(11*10^65944-131)/3	65945	Robert Price	02/2017
9285	(2^219030+2394)/2	65935	Stefano Morozzi	12/2019
9286	2^219021-3553	65932	Yves Minet	03/2017
9287	Pell-LucasQ(172243)/2	65931	Eric W. Weisstein	01/2007
9288	2^218990+73519	65923	Enzo Doria	04/2016
9289	(2^218977+2634)/2	65919	Stefano Morozzi	12/2019
9290	(2^218965+2354)/2	65915	Stefano Morozzi	12/2019
9291	58^37378-57	65914	Norbert Schneider	09/2014
9293	(2^218945-7)/1675	65906	Lelio R Paula	04/2012
9292	5*10^65905+81	65906	Robert Price	08/2017
9294	3*10^65899-13	65900	Robert Price	11/2017
9295	(-lucasV(1,2,437845)-2)/1679917	65896	Mike Oakes	04/2017
9296	127^31322-2	65896	Lelio R Paula	10/2017
9297	2^218897-111889	65895	Enzo Doria	05/2014
9298	2^218896+1869451	65895	Enzo Doria	05/2016
9299	(2^218893+3570)/2	65894	Stefano Morozzi	12/2019
9300	63^36616+2	65885	Lelio R Paula	05/2013
9301	(3*2^218822-1)/11	65872	Lelio R Paula	01/2014
9302	2^218796-113297	65865	Enzo Doria	07/2014
9303	2^218797+73727	65865	Enzo Doria	04/2016
9304	3^138040-110	65862	Lelio R Paula	06/2013
9305	11^63240-1950	65858	Enzo Doria	12/2012
9306	2^218764-111873	65855	Enzo Doria	05/2014
9307	(34*10^65839-7)/9/37	65839	Makoto Morimoto	04/2016
9308	3^137988+26	65838	Lelio R Paula	06/2013
9309	(2^218693+3150)/2	65833	Stefano Morozzi	12/2019
9310	2^218680-719	65830	Yves Minet	05/2012
9311	(2^218642+3094)/2	65818	Stefano Morozzi	12/2019
9312	(2^218614+1522)/2	65810	Stefano Morozzi	12/2019
9313	18^52424+17	65807	Lelio R Paula	08/2013
9314	19062^2827+2827^19062	65790	Hans Havermann	08/2019
9315	(2*15683^15683+1)/732384425	65789	David Broadhurst	09/2010
9316	(23*2^218517+1)/19003	65778	Lelio R Paula	07/2012
9317	(5*10^65773+1)/3	65774	Erik Branger	12/2013
9318	160^29839-159	65769	Norbert Schneider	12/2018
9319	2^218457-17329	65763	Enzo Doria	05/2013
9320	151703#+223381	65759	Nicolas PALAU	10/2016
9321	2^218436+40755	65756	Lelio R Paula	10/2011
9322	2^218399-4627	65745	Yves Minet	05/2019
9323	(F(44)^7433-F(43)^7433)/F(42)	65744	Wayne Halsdorf	03/2012
9324	15952^13219+13219^15952	65742	Hans Havermann	08/2019
9325	(2^218377+2894)/2	65738	Stefano Morozzi	12/2019
9326	157^29934+29934^157	65733	Serge Batalov	05/2014
9327	211^28273-2	65715	Lelio R Paula	09/2013
9328	(59*10^65712+31)/9	65713	Robert Price	09/2015
9331	611^23586+23586^611	65712	Norbert Schneider	08/2016
9330	p(13991)#/2+32	65712	Robert Price	12/2016
9329	15865^13864+13864^15865	65712	Hans Havermann	07/2019
9332	2^218282-18485	65710	Enzo Doria	05/2013
9333	2^218274-111251	65708	Enzo Doria	05/2014
9334	2*F(314335)-1	65693	Henri Lifchitz	12/2009
9335	(2^218224+3222)/2	65692	Stefano Morozzi	12/2019
9336	2^218200+427	65685	Henri Lifchitz	01/2005
9337	(2^218179+2838)/2	65679	Stefano Morozzi	12/2019
9338	(10199^16384+10197^16384)/2	65676	Jeppe Stig Nielsen	04/2018
9339	(10199^(2^14)+(10197)^(2^14))/2	65676	Robert Price	05/2018
9340	46532!3+3	65667	Robert Price	10/2014
9341	2^218120-147	65661	Lelio R Paula	08/2011
9342	452^24729+24729^452	65659	Norbert Schneider	09/2016
9343	5817^17440+17440^5817	65657	Norbert Schneider	06/2019
9344	2^218102-114893	65656	Enzo Doria	05/2015
9345	(2^218101+1442)/2	65655	Stefano Morozzi	12/2019
9346	(15*2^218083-1)/17	65650	Lelio R Paula	01/2014
9348	(15*2^218081+1)/18941	65646	Lelio R Paula	08/2012
9347	(2^218070+3610)/2	65646	Stefano Morozzi	12/2019
9349	15818^14115+14115^15818	65640	Hans Havermann	08/2019
9350	(306^26407-1)/305	65638	Eric Chen	09/2017
9352	19^51326+36	65634	Lelio R Paula	08/2013
9351	(21*2^218045-1)/451583	65634	Lelio R Paula	01/2014
9353	(2^218010+2194)/2	65628	Stefano Morozzi	12/2019
9354	2^217989-33	65622	Lelio R Paula	08/2011
9355	(13*2^217961+1)/3	65614	Lelio R Paula	06/2012
9356	4*6^84315-5	65611	Lelio R Paula	09/2014
9357	(315047^11933+1)/315048	65607	Faysal YAtim	06/2008
9358	6^84303+55	65601	Lelio R Paula	07/2013
9359	16585^9024+9024^16585	65601	Hans Havermann	08/2019
9360	18462^3575+3575^18462	65601	Hans Havermann	08/2019
9361	15963^12862+12862^15963	65597	Hans Havermann	08/2019
9362	(-lucasV(1,2,435857)+2)/(1738598017)	65595	Mike Oakes	04/2017
9363	(9787*2^217873-1)/37	65589	Lelio R Paula	04/2015
9364	5*2^217858+3	65583	Lelio R Paula	04/2014
9365	(19*10^65572+119)/3	65573	Robert Price	02/2017
9367	20^50399+51	65571	Lelio R Paula	08/2013
9366	7162^17009+17009^7162	65571	Norbert Schneider	07/2018
9368	11^62946-5670	65552	Enzo Doria	01/2013
9369	2^217742-3911	65547	Yves Minet	08/2009
9370	(19*10^65545+77)/3	65546	Robert Price	08/2016
9371	2^217731+131	65544	Lelio R Paula	08/2011
9372	2^217720-111287	65541	Enzo Doria	05/2014
9373	(365^25579+1)/366	65539	Eric Chen	10/2017
9374	10^65537+27	65538	Robert Price	01/2011
9375	10^65537-76859	65537	Patrick De Geest	05/2013
9376	(28*10^65532+359)/9	65533	Robert Price	11/2017
9377	(10223*2^217676+1)/3	65531	Lelio R Paula	06/2014
9378	PadovanNumber[536485]	65518	Eric W. Weisstein	05/2009
9379	5*10^65509+23	65510	Robert Price	11/2017
9380	(8*10^65507-83)/3	65508	Robert Price	10/2017
9381	7*10^65492-47	65493	Robert Price	02/2017
9382	2^217547-1868407	65489	Enzo Doria	04/2016
9383	2^217531-111769	65484	Enzo Doria	05/2014
9384	7^77484-18	65482	Lelio R Paula	06/2013
9385	5754^17413+17413^5754	65473	Norbert Schneider	05/2019
9386	2^217488-113285	65471	Enzo Doria	07/2014
9387	(2^217488+2622)/2	65471	Stefano Morozzi	12/2019
9388	151153#/30-30	65468	Henri Lifchitz	12/2011
9389	2^217466+4257	65464	Lelio R Paula	10/2011
9390	(2^217455+1190)/2	65461	Stefano Morozzi	12/2019
9391	46396!3-81	65455	Robert Price	09/2014
9392	2^217421-113185	65451	Enzo Doria	07/2014
9393	(6883*2^217440-1)/1061193295893	65448	Lelio R Paula	04/2015
9394	2^217408-2145	65447	Lelio R Paula	10/2011
9395	2^217398-16947	65444	Enzo Doria	05/2013
9396	16097^11628+11628^16097	65443	Hans Havermann	07/2019
9397	(2^217387+2838)/2	65440	Stefano Morozzi	12/2019
9398	8*5^93613+3	65434	Lelio R Paula	09/2014
9399	15929^12810+12810^15929	65430	Hans Havermann	07/2019
9400	11^62828-5310	65429	Enzo Doria	01/2013
9401	10^65426+13	65427	Robert Price	01/2011
9402	2^217341-6555	65427	Lelio R Paula	10/2011
9403	10^65426-54849	65426	Patrick De Geest	05/2013
9404	(21*2^217363-1)/56003626667	65424	Lelio R Paula	01/2014
9405	30011^14608-108	65405	Enzo Doria	07/2012
9406	(2^217250+2602)/2	65399	Stefano Morozzi	12/2019
9407	119^31504-2	65389	Lelio R Paula	10/2017
9408	(43^40031-1)/42	65388	Robert Price	04/2014
9409	2^217190+94395	65381	Henri Lifchitz	02/2005
9410	15^55587+46	65376	Lelio R Paula	08/2013
9411	18443^3502+3502^18443	65368	Hans Havermann	07/2019
9412	(2^217112+2386)/2	65357	Stefano Morozzi	12/2019
9413	2^217088-111833	65350	Enzo Doria	05/2014
9414	(2^217075+2478)/2	65346	Stefano Morozzi	12/2019
9415	(2^217075+618)/2	65346	Stefano Morozzi	12/2019
9416	(13*2^217069-1)/1682945	65340	Lelio R Paula	01/2014
9417	(10^65340+47)/3	65340	Robert Price	11/2017
9418	(62*10^65331+1)/9	65332	Serge Batalov	11/2010
9419	(2^217001+2162)/2	65324	Stefano Morozzi	12/2019
9420	2^216947-111351	65308	Enzo Doria	05/2014
9421	-E(18022)/775201845682685322943949235068359	65307	Thomas Ritschel	02/2017
9422	(13*10^65297+83)/3	65298	Robert Price	09/2016
9423	16413^9502+9502^16413	65288	Hans Havermann	07/2019
9424	(2^216878+2938)/2	65287	Stefano Morozzi	12/2019
9425	(2^216877+1074)/2	65287	Stefano Morozzi	12/2019
9426	5^93400-8	65284	Lelio R Paula	06/2013
9427	2^216802-165	65264	Lelio R Paula	08/2011
9428	2^216799-28635	65264	Lelio R Paula	10/2011
9429	5*10^65255+51	65256	Robert Price	01/2017
9430	2^216762-167	65252	Lelio R Paula	08/2011
9431	11^62657-5790	65251	Enzo Doria	01/2013
9432	3^136756-112880	65250	Enzo Doria	06/2014
9433	2^216752+21	65249	Lelio R Paula	08/2011
9434	3*10^65247+11	65248	Robert Price	11/2017
9435	11^62651-2700	65245	Enzo Doria	12/2012
9436	15130^15609-15609^15130	65244	Norbert Schneider	07/2018
9438	Pell-LucasQ(170413)/2	65230	Eric W. Weisstein	12/2006
9437	gcd(V(790525),5F(158105)(F(158105)+1)+1)	65230	Serge Batalov	04/2015
9439	(2^216684+1330)/2	65229	Stefano Morozzi	12/2019
9440	(2^216676-1017)/637	65224	Lelio R Paula	04/2012
9441	2^216652-2327	65219	Yves Minet	10/2013
9442	(9179*2^216648-1)/4667	65218	Lelio R Paula	04/2015
9443	(5*10^65203-119)/3	65204	Robert Price	04/2016
9444	15977^12034+12034^15977	65193	Hans Havermann	07/2019
9445	2^216555-113269	65190	Enzo Doria	07/2014
9446	(2^216550+3510)/2	65188	Stefano Morozzi	12/2019
9447	(2^216539+1986)/2	65185	Stefano Morozzi	12/2019
9448	(2^216537+3426)/2	65184	Stefano Morozzi	12/2019
9450	(9513^16384+1)/2	65181	Henri Lifchitz	02/2007
9449	15753^13730+13730^15753	65181	Hans Havermann	07/2019
9451	(2^216507+1274)/2	65175	Stefano Morozzi	12/2019
9452	2^216474+12915	65166	Lelio R Paula	02/2013
9453	19^50958-32	65163	Lelio R Paula	08/2013
9454	2^216442-112133	65156	Enzo Doria	06/2014
9455	2^216437-112213	65155	Enzo Doria	06/2014
9456	2^216435-112767	65154	Enzo Doria	06/2014
9457	2^216420+12705	65149	Lelio R Paula	02/2013
9458	(2^216383+3114)/2	65138	Stefano Morozzi	12/2019
9459	8*3^136507-7	65132	Lelio R Paula	04/2014
9460	(-lucasV(1,2,432719)-2)/(5*461)	65128	Mike Oakes	03/2017
9461	16803^7496+7496^16803	65109	Hans Havermann	07/2019
9462	15132^15575-15575^15132	65102	Norbert Schneider	07/2018
9463	(2^216244+1530)/2	65096	Stefano Morozzi	12/2019
9464	5*10^65086-51	65087	Robert Price	10/2017
9465	2^216197-111769	65082	Enzo Doria	05/2014
9467	6^83631-79	65078	Lelio R Paula	07/2013
9466	572^23601+23601^572	65078	Norbert Schneider	08/2016
9468	(3^136399-7)/544220	65074	Lelio R Paula	04/2012
9469	15592^14911+14911^15592	65074	Hans Havermann	07/2019
9470	2^216154-1421	65069	Yves Minet	01/2013
9471	2^216145-112663	65067	Enzo Doria	06/2014
9472	(7*10^65064+53)/3	65065	Robert Price	10/2017
9473	132013*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
9474	132019*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
9475	148918*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
9476	194014*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
9477	223864*10^65050+2^216091-1	65056	Gilbert Mozzo	04/2014
9479	82090*10^65050+2^216091-1	65055	Gilbert Mozzo	07/2012
9480	95133*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
9478	98142*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
9481	((2^216091-1)*34009-48)/25	65054	Serge Batalov	01/2012
9482	5977*10^65050+2^216091-1	65054	Gilbert Mozzo	03/2012
9483	(2^216102+2074)/2	65053	Stefano Morozzi	12/2019
9484	7*2^216091+2^298-13	65051	Peter Lesala	03/2007
9485	2^216091+2*29208-1	65050	Makoto Morimoto	10/2013
9486	15845^12736+12736^15845	65045	Hans Havermann	07/2019
9487	(10^(232521+1)-610^32521-1)/3	65043	Robert Price	02/2016
9488	p(13861)#/2+256	65039	Robert Price	05/2017
9489	(2^216091-2096)/(2^432918437*5220283)	65036	Makoto Morimoto	10/2017
9490	11^62439-4380	65024	Enzo Doria	01/2013
9491	16489^8776+8776^16489	65022	Hans Havermann	07/2019
9492	(2^215959+1994)/2	65010	Stefano Morozzi	12/2019
9493	3^136244+2	65005	Mike Oakes	11/2009
9494	13^58343-50	64991	Lelio R Paula	07/2013
9495	331^25791-10002	64989	Enzo Doria	07/2012
9496	(2^215887+2090)/2	64989	Stefano Morozzi	12/2019
9497	2^215877+131	64986	Lelio R Paula	08/2011
9498	4*5^92959+9	64977	Lelio R Paula	09/2014
9499	(2^215839+2478)/2	64974	Stefano Morozzi	12/2019
9500	(2^215822+702)/2	64969	Stefano Morozzi	12/2019

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