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 ?
6501	2^260678-111065	78472	Enzo Doria	05/2014
6502	18^62501-97	78456	Lelio R Paula	02/2015
6503	53^45498-2	78452	Lelio R Paula	08/2013
6504	2^260513-111121	78423	Enzo Doria	05/2014
6505	37845!2-64	78412	Robert Price	06/2015
6506	2^260469-110695	78409	Enzo Doria	05/2014
6507	(11*10^78408-113)/3	78409	Robert Price	01/2017
6508	2^260447+8415	78403	Lelio R Paula	07/2013
6509	37837!2-64	78394	Robert Price	06/2015
6510	(19*2^260379-1)/53	78382	Lelio R Paula	02/2014
6511	2^260377-113233	78382	Enzo Doria	07/2014
6513	9^82138+6^82138-2^82138	78380	Mike Oakes	08/2010
6512	69^42624+2	78380	Lelio R Paula	05/2013
6514	2^260369-1859713	78379	Enzo Doria	03/2016
6515	14*10^78362+1089	78364	Jens K. Andersen	11/2007
6516	5^112070-54	78334	Lelio R Paula	02/2015
6517	(10^(239165+1)+5410^39165-1)/9	78331	Robert Price	04/2017
6518	2^260182-113453	78323	Enzo Doria	07/2014
6519	f(16405)	78319	Robert Price	09/2017
6520	(78557*2^260084+1)/519	78296	Lelio R Paula	06/2014
6522	10^78288+9^(78288+1)	78289	Robert Price	08/2016
6521	10^78288+39109	78289	Patrick De Geest	12/2016
6523	10^78288-216299	78288	Patrick De Geest	12/2016
6524	5^111997+36	78283	Lelio R Paula	02/2015
6525	(21^59183+1)/22	78252	Paul Bourdelais	03/2010
6526	(88*10^78242-7)/9	78243	Robert Price	11/2014
6527	2*6^100547+7	78242	Lelio R Paula	10/2014
6528	2^259860-111089	78226	Enzo Doria	05/2014
6529	37^49875-2	78215	Lelio R Paula	09/2013
6530	(13*10^78213+401)/9	78214	Robert Price	10/2017
6531	7*5^111893-4	78211	Lelio R Paula	10/2014
6532	(11*2^259809-1)/1437	78209	Lelio R Paula	02/2014
6533	7^92511-6	78181	Theodore Burton	11/2005
6534	(3^163859-4)/253	78179	Lelio R Paula	10/2012
6535	(27*2^259666-1)/625691	78163	Lelio R Paula	02/2014
6536	3*10^78146+17	78147	Robert Price	03/2017
6537	(576^28307+1)/577	78137	Richard Fischer	01/2018
6538	2^259503+74333	78119	Enzo Doria	04/2016
6539	(31*2^259504-1)/13365	78116	Lelio R Paula	02/2014
6541	(58547^16384+1)/2	78111	Lelio R Paula	11/2011
6540	6^100379+13	78111	Lelio R Paula	03/2015
6542	2^259469-109909	78108	Enzo Doria	04/2014
6543	15^66413-26	78108	Lelio R Paula	02/2015
6544	7^92410-9266	78096	Mike Oakes	02/2010
6545	2^259398+75799	78087	Enzo Doria	04/2016
6546	2^259394+1876189	78086	Enzo Doria	07/2016
6547	PIPrime(78073)	78073	Eric W. Weisstein	07/2006
6548	5*2^259344-7	78072	Lelio R Paula	06/2014
6549	14^68097-87	78048	Lelio R Paula	02/2015
6550	2^259233-475573	78037	Paul Bourdelais	03/2013
6551	181^34554-2	78012	Lelio R Paula	10/2017
6552	3^163500-28	78010	Robert Price	12/2013
6553	(65*10^77992+691)/9	77993	Robert Price	08/2016
6554	2^259013-112591	77971	Enzo Doria	06/2014
6555	7*10^77969-11	77970	Robert Price	10/2017
6556	6^100193-100193^6	77966	Norbert Schneider	04/2017
6557	2^258863-110235	77926	Enzo Doria	05/2014
6558	2^258852+1605	77923	Lelio R Paula	06/2013
6559	(11*10^77909+49)/3	77910	Robert Price	05/2016
6560	2*7^92187-9	77908	Lelio R Paula	10/2014
6561	2^258763-110155	77896	Enzo Doria	04/2014
6562	2^258694-110387	77875	Enzo Doria	05/2014
6563	11^74773-94	77869	Lelio R Paula	02/2015
6564	6^100067+125	77868	Lelio R Paula	03/2015
6565	15^66205+8	77864	Lelio R Paula	07/2014
6566	5^111373-18136	77847	Enzo Doria	05/2014
6567	2^258524-109877	77824	Enzo Doria	04/2014
6568	6^100002-16643	77817	Enzo Doria	02/2013
6569	(13*10^77811+347)/9	77812	Robert Price	10/2017
6570	65^42916+28	77803	Lelio R Paula	01/2016
6571	(89*10^77781-17)/9	77782	Robert Price	11/2015
6572	2^258382-110405	77781	Enzo Doria	05/2014
6573	5^111278-14996	77780	Enzo Doria	02/2013
6574	14^67862+61	77779	Lelio R Paula	02/2015
6575	10^77777+48483	77778	Patrick De Geest	11/2010
6576	10^77777-183243	77777	Patrick De Geest	11/2010
6577	(27*2^258352+1)/43	77772	Lelio R Paula	08/2012
6578	337^30756-10002	77740	Enzo Doria	07/2012
6579	10^77726+99	77727	Robert Price	03/2011
6580	10^77726-85947	77726	Patrick De Geest	06/2013
6581	89^39870-2	77723	Lelio R Paula	08/2013
6582	7^91966-32	77721	Lelio R Paula	02/2015
6583	35^50327+2	77709	Lelio R Paula	05/2013
6584	24^56298+23	77704	Norbert Schneider	12/2016
6585	(2^258105+78557)/19	77697	Lelio R Paula	10/2012
6586	2^258079+179	77690	Lelio R Paula	03/2012
6587	2^258062-113111	77685	Enzo Doria	07/2014
6588	10^77669+123456789	77670	Robert Price	10/2019
6589	80^40807-79	77660	Norbert Schneider	03/2015
6590	70385!4-4	77658	Robert Price	11/2019
6591	(10^77637+359)/9	77637	Serge Batalov	12/2014
6592	2^257862-165	77625	Lelio R Paula	03/2012
6593	(25*2^257853+1)/3	77623	Lelio R Paula	07/2012
6594	(2^257869+1)/(3*18645362967379)	77613	Henri Lifchitz	04/2005
6595	6^99728+71	77604	Lelio R Paula	01/2015
6596	2^257778-112767	77599	Enzo Doria	06/2014
6597	(31*2^257771+1)/537	77596	Lelio R Paula	07/2012
6598	2^257729-73	77585	Lelio R Paula	03/2012
6599	2^257689-63	77573	Lelio R Paula	03/2012
6600	(47*10^77572+493)/9	77573	Robert Price	11/2017
6601	(78557*2^257665+1)/6108725	77564	Lelio R Paula	06/2014
6602	(3^162563+8)/2885	77559	Lelio R Paula	10/2012
6603	2^257636-110235	77557	Enzo Doria	05/2014
6604	(23*10^77556+97)/3	77557	Robert Price	02/2017
6605	2^257621-110071	77552	Enzo Doria	04/2014
6606	2^257567-64875	77536	Lelio R Paula	06/2013
6607	2*7^91674+9	77474	Lelio R Paula	10/2014
6608	(17*10^77427-47)/3	77428	Robert Price	05/2017
6609	10^77418+841683	77419	Patrick De Geest	06/2013
6610	10^77418-33	77418	Robert Price	05/2011
6611	19^60539-36	77415	Lelio R Paula	03/2015
6612	37401!!-1024	77397	Robert Price	11/2015
6613	11^74313-18750	77390	Enzo Doria	12/2012
6614	2^257044-112883	77378	Enzo Doria	06/2014
6615	8*10^77377+51	77378	Robert Price	05/2017
6616	2*7^91553+9	77372	Lelio R Paula	10/2014
6617	713^27118+27118^713	77371	Norbert Schneider	12/2016
6618	2^256920-111155	77341	Enzo Doria	05/2014
6619	2^256896-6555	77334	Lelio R Paula	06/2013
6620	(52*10^77322-7)/9	77323	Robert Price	12/2014
6621	2^256849-112939	77320	Enzo Doria	06/2014
6622	(4*10^77309-31)/9	77309	Erik Branger	05/2011
6623	(3^161988+7)/41864	77284	Lelio R Paula	10/2012
6624	(14^67421-1)/13	77272	Paul Bourdelais	09/2008
6625	5*3^161923-4	77258	Lelio R Paula	06/2014
6626	2^256552-1499	77230	Yves Minet	05/2013
6627	2^256460-112757	77203	Enzo Doria	06/2014
6628	2^256398+23299	77184	Yves Minet	02/2011
6629	2^256391-1155*256391	77182	Henri Lifchitz	03/2005
6630	(2^256391-9)/56593	77177	Lelio R Paula	10/2012
6631	(2^256308+9)/10585	77153	Lelio R Paula	10/2012
6632	21^58348-2	77149	Lelio R Paula	08/2013
6633	(17*2^256291-1)/4785	77149	Lelio R Paula	02/2014
6634	(5*2^256274-1)/2141	77144	Lelio R Paula	02/2014
6635	19^60321+82	77136	Lelio R Paula	03/2015
6636	5*2^256233-3	77135	Lelio R Paula	06/2014
6637	3*2^256149+7	77110	Lelio R Paula	06/2014
6638	3^161594-106	77100	Lelio R Paula	02/2015
6639	2^256114-185	77098	Lelio R Paula	03/2012
6640	8^85349-85349^8	77078	Norbert Schneider	05/2017
6641	2^256043-2786377	77077	Enzo Doria	03/2016
6642	2^255973+1869947	77056	Enzo Doria	05/2016
6643	12^71393-43	77046	Lelio R Paula	02/2015
6644	15^65490+44	77023	Lelio R Paula	02/2015
6645	(3^161411-7)/940	77010	Lelio R Paula	10/2012
6646	lucasU(1107,1,25297)-lucasU(1107,1,25296)	77005	Mike Oakes	05/2009
6647	(570^27943-1)/569	77005	Serge Batalov	12/2016
6648	2^255750-75	76989	Lelio R Paula	03/2012
6649	3*6^98926-5	76980	Lelio R Paula	10/2014
6650	18^61320-1433	76974	Enzo Doria	03/2013
6651	6^98916-17093	76972	Enzo Doria	02/2013
6652	2^255659-110131	76962	Enzo Doria	04/2014
6653	69805!4-128	76956	Robert Price	11/2019
6654	12^71303+91	76949	Lelio R Paula	02/2015
6655	18^61298+59	76946	Lelio R Paula	02/2015
6656	(223^32768+1)/131074	76945	Lelio R Paula	02/2009
6657	(2^255613-5)/281517	76942	Lelio R Paula	10/2012
6658	18^61290-11	76936	Lelio R Paula	02/2015
6660	63^42752-2	76926	Lelio R Paula	08/2013
6659	(11*2^255545-1)/117	76926	Lelio R Paula	02/2014
6661	2^255517+56387	76919	Yves Minet	02/2011
6662	2^255499-112567	76913	Enzo Doria	06/2014
6663	2^255492+345	76911	Lelio R Paula	06/2013
6664	10^76875+217591	76876	Patrick De Geest	05/2013
6666	10^76875-53	76875	Robert Price	05/2011
6665	11^73819-5880	76875	Enzo Doria	01/2013
6667	2^255313+18915	76857	Lelio R Paula	06/2013
6668	(2^255320-1017)/1446667	76853	Lelio R Paula	10/2012
6669	2^255296+5775	76852	Lelio R Paula	06/2013
6670	14^67052-29	76851	Lelio R Paula	02/2015
6671	(8*10^76840+43)/3	76841	Robert Price	10/2017
6672	(7*10^76818-313)/9	76818	Robert Price	11/2016
6673	10^76801+69	76802	Robert Price	03/2011
6674	10^76801-80943	76801	Patrick De Geest	06/2013
6675	2^255105+57	76795	Lelio R Paula	03/2012
6676	(lucasV(1,2,510187)+2)/(3511)	76789	Mike Oakes	04/2017
6677	(2^255097-7)/20020055	76785	Lelio R Paula	10/2012
6678	2^255055+1869353	76780	Enzo Doria	05/2016
6679	17^62396-90	76776	Lelio R Paula	03/2015
6680	7^90833-60	76763	Lelio R Paula	02/2015
6681	13^68901-56	76752	Lelio R Paula	03/2015
6682	2^254961+1869917	76751	Enzo Doria	05/2016
6683	9*5^109791-8	76742	Lelio R Paula	10/2014
6684	82^40089+40089^82	76723	Serge Batalov	02/2012
6685	2^254861-2790013	76721	Enzo Doria	03/2016
6686	(10^278+1)*(10^115926+1)/(10^834+1)/(10^38642+1)/20459779741	76718	Makoto Kamada	03/2019
6687	10^76705+13	76706	Robert Price	01/2011
6688	10^76705-94077	76705	Patrick De Geest	06/2013
6689	(5*2^254785-1)/999	76696	Lelio R Paula	02/2014
6690	2^254758-110405	76690	Enzo Doria	05/2014
6691	2^254716-3779	76678	Yves Minet	04/2017
6692	2^254708-110507	76675	Enzo Doria	05/2014
6693	(47*10^76672+133)/9	76673	Robert Price	04/2017
6694	2^254670-112901	76664	Enzo Doria	06/2014
6695	(3^160665+7)/981350	76651	Lelio R Paula	10/2012
6696	2^254598-113183	76642	Enzo Doria	07/2014
6697	19^59932+22	76639	Lelio R Paula	01/2015
6698	2^254569-112213	76633	Enzo Doria	06/2014
6699	2*5^109626+9	76626	Lelio R Paula	10/2014
6700	2^254521+1872527	76619	Enzo Doria	05/2016
6701	(76*10^76615+167)/9	76616	Robert Price	08/2016
6702	25^54799-24^54799	76606	Robert Price	07/2012
6703	(24737*2^254464+1)/9	76605	Lelio R Paula	06/2014
6704	12^70961-85	76580	Lelio R Paula	02/2015
6705	7^90590-38	76558	Lelio R Paula	02/2015
6706	2^254304+5227	76554	Lelio R Paula	06/2013
6707	(76*10^76547-211)/9	76548	Robert Price	10/2017
6708	18^60979-5363	76546	Enzo Doria	03/2013
6709	(21181*2^254264+1)/55314379	76538	Lelio R Paula	06/2014
6711	(34*10^76547-7)/9/61/94529/214807	76536	Makoto Morimoto	05/2016
6710	(7*10^76536-313)/9	76536	Robert Price	11/2016
6713	2^254239-27	76534	Lelio R Paula	03/2012
6712	2^254238-1841	76534	Yves Minet	03/2013
6714	(10^76537-1)/9/66127969	76529	Jens K. Andersen	04/2009
6715	2^254189-112225	76519	Enzo Doria	06/2014
6716	18^60938-1397	76494	Enzo Doria	03/2013
6717	2^254075-2788417	76485	Enzo Doria	03/2016
6718	7*10^76483-23	76484	Robert Price	04/2016
6719	2^254042-112913	76475	Enzo Doria	06/2014
6720	14^66723-37	76474	Lelio R Paula	02/2015
6721	2^254037-110305	76473	Enzo Doria	05/2014
6722	2^253931-111109	76441	Enzo Doria	05/2014
6723	2^253926-1167	76440	Lelio R Paula	05/2013
6724	(49*10^76438-13)/9	76439	Robert Price	07/2015
6725	(21*2^253845-1)/143	76415	Lelio R Paula	02/2014
6726	10^76374+31	76375	Robert Price	03/2011
6727	10^76374-222159	76374	Patrick De Geest	05/2013
6728	2^253561-110533	76330	Enzo Doria	05/2014
6729	gcd(V(917285),5F(183457)(F(183457)+1)+1)	76321	Serge Batalov	04/2015
6730	9*5^109182+2	76316	Lelio R Paula	10/2014
6731	11^73279-3690	76313	Enzo Doria	12/2012
6732	(598*10^76309-31)/9	76311	Robert Price	02/2017
6733	11^73274-24000	76308	Enzo Doria	12/2012
6734	7^90291-6	76305	Theodore Burton	11/2005
6735	(21181*2^253432+1)/21437	76291	Lelio R Paula	06/2014
6736	69247!4+4	76280	Robert Price	09/2019
6737	6^98025+145	76279	Lelio R Paula	01/2015
6738	2^253355+1155	76268	Lelio R Paula	05/2013
6739	(73*10^76262+413)/9	76263	Robert Price	10/2017
6740	2^253292-71219	76249	Enzo Doria	04/2016
6741	7^90221-36	76246	Lelio R Paula	02/2015
6742	18^60727-3473	76229	Enzo Doria	03/2013
6743	(78557*2^253184+1)/3	76221	Lelio R Paula	06/2014
6744	(8*10^76220-83)/3	76221	Robert Price	10/2017
6745	(44791^20480+1)/(44791^4096+1)	76206	Serge Batalov	01/2017
6746	11^73163-2010	76192	Enzo Doria	12/2012
6747	2^253060+54615	76179	Lelio R Paula	05/2013
6748	2^253029+1869761	76170	Enzo Doria	05/2016
6749	2^252955-111007	76148	Enzo Doria	05/2014
6750	2*5^108931+7	76140	Lelio R Paula	10/2014

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Probable Primes Top 10000

(255244 PRPs in the top)