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 ?
7251	2^257636-110235	77557	Enzo Doria	05/2014
7253	(23*10^77556+97)/3	77557	Robert Price	02/2017
7252	(2^257639+2630)/2	77557	Stefano Morozzi	01/2020
7254	(2^257625+3354)/2	77553	Stefano Morozzi	01/2020
7255	2^257621-110071	77552	Enzo Doria	04/2014
7256	19580^9129+9129^19580	77546	Hans Havermann	03/2020
7257	2^257567-64875	77536	Lelio R Paula	06/2013
7258	(2^257429+2394)/2	77494	Stefano Morozzi	01/2020
7259	(2^257373+1206)/2	77477	Stefano Morozzi	01/2020
7260	2*7^91674+9	77474	Lelio R Paula	10/2014
7261	(2^257248+2442)/2	77440	Stefano Morozzi	01/2020
7262	(17*10^77427-47)/3	77428	Robert Price	05/2017
7263	10^77418+841683	77419	Patrick De Geest	06/2013
7264	10^77418-33	77418	Robert Price	05/2011
7265	19^60539-36	77415	Lelio R Paula	03/2015
7266	37401!!-1024	77397	Robert Price	11/2015
7267	(2^257095+1410)/2	77394	Stefano Morozzi	01/2020
7268	11^74313-18750	77390	Enzo Doria	12/2012
7270	2^257044-112883	77378	Enzo Doria	06/2014
7269	8*10^77377+51	77378	Robert Price	05/2017
7271	2*7^91553+9	77372	Lelio R Paula	10/2014
7272	713^27118+27118^713	77371	Norbert Schneider	12/2016
7273	18652^14043+14043^18652	77359	Hans Havermann	03/2020
7274	2^256920-111155	77341	Enzo Doria	05/2014
7275	2^256896-6555	77334	Lelio R Paula	06/2013
7276	(52*10^77322-7)/9	77323	Robert Price	12/2014
7277	2^256849-112939	77320	Enzo Doria	06/2014
7278	17275^18246+18246^17275	77316	Norbert Schneider	01/2020
7279	(4*10^77309-31)/9	77309	Erik Branger	05/2011
7280	(3^161988+7)/41864	77284	Lelio R Paula	10/2012
7281	(14^67421-1)/13	77272	Paul Bourdelais	09/2008
7282	(2^256679+3554)/2	77268	Stefano Morozzi	01/2020
7284	5*3^161923-4	77258	Lelio R Paula	06/2014
7283	20465^5958+5958^20465	77258	Hans Havermann	02/2020
7285	(2^256591+954)/2	77242	Stefano Morozzi	01/2020
7286	2^256552-1499	77230	Yves Minet	05/2013
7287	(2^256493+3126)/2	77212	Stefano Morozzi	01/2020
7288	2^256460-112757	77203	Enzo Doria	06/2014
7289	(2^256444+2578)/2	77198	Stefano Morozzi	01/2020
7290	2^256398+23299	77184	Yves Minet	02/2011
7291	2^256391-1155*256391	77182	Henri Lifchitz	03/2005
7292	(2^256391-9)/56593	77177	Lelio R Paula	10/2012
7293	(2^256338+3834)/2	77166	Stefano Morozzi	01/2020
7294	(2^256339+546)/2	77166	Stefano Morozzi	01/2020
7295	(2^256308+9)/10585	77153	Lelio R Paula	10/2012
7296	21^58348-2	77149	Lelio R Paula	08/2013
7297	(17*2^256291-1)/4785	77149	Lelio R Paula	02/2014
7298	(5*2^256274-1)/2141	77144	Lelio R Paula	02/2014
7299	(2^256244+2326)/2	77137	Stefano Morozzi	01/2020
7300	19^60321+82	77136	Lelio R Paula	03/2015
7301	5*2^256233-3	77135	Lelio R Paula	06/2014
7302	(2^256155+1566)/2	77111	Stefano Morozzi	01/2020
7303	3*2^256149+7	77110	Lelio R Paula	06/2014
7304	(2^256128+1890)/2	77102	Stefano Morozzi	01/2020
7305	3^161594-106	77100	Lelio R Paula	02/2015
7306	2^256114-185	77098	Lelio R Paula	03/2012
7307	8^85349-85349^8	77078	Norbert Schneider	05/2017
7308	2^256043-2786377	77077	Enzo Doria	03/2016
7309	2^255973+1869947	77056	Enzo Doria	05/2016
7310	12^71393-43	77046	Lelio R Paula	02/2015
7311	(2^255882+3630)/2	77028	Stefano Morozzi	01/2020
7312	15^65490+44	77023	Lelio R Paula	02/2015
7313	(3^161411-7)/940	77010	Lelio R Paula	10/2012
7314	lucasU(1107,1,25297)-lucasU(1107,1,25296)	77005	Mike Oakes	05/2009
7315	(570^27943-1)/569	77005	Serge Batalov	12/2016
7316	2^255750-75	76989	Lelio R Paula	03/2012
7317	3*6^98926-5	76980	Lelio R Paula	10/2014
7318	(2^255708+478)/2	76976	Stefano Morozzi	01/2020
7319	18^61320-1433	76974	Enzo Doria	03/2013
7320	6^98916-17093	76972	Enzo Doria	02/2013
7321	(2^255691+806)/2	76971	Stefano Morozzi	01/2020
7322	2^255659-110131	76962	Enzo Doria	04/2014
7323	69805!4-128	76956	Robert Price	11/2019
7324	12^71303+91	76949	Lelio R Paula	02/2015
7325	18^61298+59	76946	Lelio R Paula	02/2015
7326	(223^32768+1)/131074	76945	Lelio R Paula	02/2009
7327	(2^255613-5)/281517	76942	Lelio R Paula	10/2012
7328	18^61290-11	76936	Lelio R Paula	02/2015
7329	(2^255567+1286)/2	76934	Stefano Morozzi	01/2020
7331	63^42752-2	76926	Lelio R Paula	08/2013
7330	(11*2^255545-1)/117	76926	Lelio R Paula	02/2014
7332	2^255517+56387	76919	Yves Minet	02/2011
7333	18376^15329+15329^18376	76914	Hans Havermann	03/2020
7334	2^255499-112567	76913	Enzo Doria	06/2014
7335	2^255492+345	76911	Lelio R Paula	06/2013
7336	(2^255488+1678)/2	76910	Stefano Morozzi	01/2020
7337	10^76875+217591	76876	Patrick De Geest	05/2013
7339	10^76875-53	76875	Robert Price	05/2011
7338	11^73819-5880	76875	Enzo Doria	01/2013
7340	2^255313+18915	76857	Lelio R Paula	06/2013
7341	(2^255320-1017)/1446667	76853	Lelio R Paula	10/2012
7342	2^255296+5775	76852	Lelio R Paula	06/2013
7343	14^67052-29	76851	Lelio R Paula	02/2015
7344	(8*10^76840+43)/3	76841	Robert Price	10/2017
7345	(2^255246+1642)/2	76837	Stefano Morozzi	01/2020
7346	(2^255243+2250)/2	76836	Stefano Morozzi	01/2020
7347	(2^255240+1218)/2	76835	Stefano Morozzi	01/2020
7348	(7*10^76818-313)/9	76818	Robert Price	11/2016
7349	10^76801+69	76802	Robert Price	03/2011
7350	10^76801-80943	76801	Patrick De Geest	06/2013
7351	2^255105+57	76795	Lelio R Paula	03/2012
7352	(lucasV(1,2,510187)+2)/(3511)	76789	Mike Oakes	04/2017
7353	(2^255097-7)/20020055	76785	Lelio R Paula	10/2012
7354	(2^255063+3098)/2	76782	Stefano Morozzi	01/2020
7355	2^255055+1869353	76780	Enzo Doria	05/2016
7356	17^62396-90	76776	Lelio R Paula	03/2015
7357	18797^12130+12130^18797	76765	Hans Havermann	03/2020
7358	7^90833-60	76763	Lelio R Paula	02/2015
7359	13^68901-56	76752	Lelio R Paula	03/2015
7360	2^254961+1869917	76751	Enzo Doria	05/2016
7361	(2^254950+594)/2	76748	Stefano Morozzi	01/2020
7362	20734^5027+5027^20734	76743	Hans Havermann	03/2020
7363	9*5^109791-8	76742	Lelio R Paula	10/2014
7364	(2^254908+982)/2	76735	Stefano Morozzi	01/2020
7365	(2^254903+2766)/2	76734	Stefano Morozzi	01/2020
7366	82^40089+40089^82	76723	Serge Batalov	02/2012
7367	2^254861-2790013	76721	Enzo Doria	03/2016
7368	(10^278+1)*(10^115926+1)/(10^834+1)/(10^38642+1)/20459779741	76718	Makoto Kamada	03/2019
7369	10^76705+13	76706	Robert Price	01/2011
7370	10^76705-94077	76705	Patrick De Geest	06/2013
7371	(5*2^254785-1)/999	76696	Lelio R Paula	02/2014
7372	2^254758-110405	76690	Enzo Doria	05/2014
7373	(2^254721+470)/2	76679	Stefano Morozzi	01/2020
7374	2^254716-3779	76678	Yves Minet	04/2017
7375	2^254708-110507	76675	Enzo Doria	05/2014
7376	(47*10^76672+133)/9	76673	Robert Price	04/2017
7377	2^254670-112901	76664	Enzo Doria	06/2014
7378	(3^160665+7)/981350	76651	Lelio R Paula	10/2012
7379	2^254598-113183	76642	Enzo Doria	07/2014
7380	19^59932+22	76639	Lelio R Paula	01/2015
7381	2^254569-112213	76633	Enzo Doria	06/2014
7382	2*5^109626+9	76626	Lelio R Paula	10/2014
7383	2^254521+1872527	76619	Enzo Doria	05/2016
7384	(2^254515+2570)/2	76617	Stefano Morozzi	01/2020
7385	(76*10^76615+167)/9	76616	Robert Price	08/2016
7386	(2^254495+918)/2	76611	Stefano Morozzi	01/2020
7387	25^54799-24^54799	76606	Robert Price	07/2012
7388	(24737*2^254464+1)/9	76605	Lelio R Paula	06/2014
7389	25863^916+916^25863	76604	Hans Havermann	01/2020
7390	(2^254458+2398)/2	76600	Stefano Morozzi	01/2020
7391	(2^254434+1354)/2	76592	Stefano Morozzi	01/2020
7392	(2^254410+2842)/2	76585	Stefano Morozzi	01/2020
7393	19878^7121+7121^19878	76581	Hans Havermann	01/2020
7394	12^70961-85	76580	Lelio R Paula	02/2015
7395	18867^11452+11452^18867	76579	Hans Havermann	01/2020
7396	(2^254333+1806)/2	76562	Stefano Morozzi	01/2020
7397	7^90590-38	76558	Lelio R Paula	02/2015
7398	2^254304+5227	76554	Lelio R Paula	06/2013
7399	(76*10^76547-211)/9	76548	Robert Price	10/2017
7401	18^60979-5363	76546	Enzo Doria	03/2013
7400	(2^254278+3250)/2	76546	Stefano Morozzi	01/2020
7402	(21181*2^254264+1)/55314379	76538	Lelio R Paula	06/2014
7404	(34*10^76547-7)/9/61/94529/214807	76536	Makoto Morimoto	05/2016
7403	(7*10^76536-313)/9	76536	Robert Price	11/2016
7406	2^254239-27	76534	Lelio R Paula	03/2012
7405	2^254238-1841	76534	Yves Minet	03/2013
7407	(2^254235+3978)/2	76533	Stefano Morozzi	01/2020
7409	(10^76537-1)/9/66127969	76529	Jens K. Andersen	04/2009
7408	(2^254223+3938)/2	76529	Stefano Morozzi	01/2020
7410	2^254189-112225	76519	Enzo Doria	06/2014
7411	18^60938-1397	76494	Enzo Doria	03/2013
7413	2^254075-2788417	76485	Enzo Doria	03/2016
7412	18239^15612+15612^18239	76485	Hans Havermann	01/2020
7414	7*10^76483-23	76484	Robert Price	04/2016
7415	18471^13822+13822^18471	76481	Hans Havermann	01/2020
7416	18850^11407+11407^18850	76478	Hans Havermann	01/2020
7417	2^254042-112913	76475	Enzo Doria	06/2014
7418	14^66723-37	76474	Lelio R Paula	02/2015
7419	(2^254040+2970)/2	76474	Stefano Morozzi	01/2020
7420	2^254037-110305	76473	Enzo Doria	05/2014
7421	(2^254008+2290)/2	76464	Stefano Morozzi	01/2020
7422	15927^18196+18196^15927	76463	Norbert Schneider	12/2019
7423	(2^253979+1110)/2	76455	Stefano Morozzi	01/2020
7424	2^253931-111109	76441	Enzo Doria	05/2014
7425	2^253926-1167	76440	Lelio R Paula	05/2013
7426	(49*10^76438-13)/9	76439	Robert Price	07/2015
7427	(2^253876+1302)/2	76424	Stefano Morozzi	01/2020
7428	(21*2^253845-1)/143	76415	Lelio R Paula	02/2014
7429	10^76374+31	76375	Robert Price	03/2011
7430	10^76374-222159	76374	Patrick De Geest	05/2013
7431	(2^253660+490)/2	76359	Stefano Morozzi	01/2020
7432	19227^9352+9352^19227	76349	Hans Havermann	01/2020
7433	(2^253617+2874)/2	76347	Stefano Morozzi	01/2020
7434	2^253561-110533	76330	Enzo Doria	05/2014
7435	(2^253546+954)/2	76325	Stefano Morozzi	01/2020
7436	gcd(V(917285),5F(183457)(F(183457)+1)+1)	76321	Serge Batalov	04/2015
7437	9*5^109182+2	76316	Lelio R Paula	10/2014
7438	11^73279-3690	76313	Enzo Doria	12/2012
7439	(598*10^76309-31)/9	76311	Robert Price	02/2017
7440	11^73274-24000	76308	Enzo Doria	12/2012
7441	7^90291-6	76305	Theodore Burton	11/2005
7442	(2^253479+3650)/2	76305	Stefano Morozzi	01/2020
7443	(2^253460+2902)/2	76299	Stefano Morozzi	01/2020
7444	(21181*2^253432+1)/21437	76291	Lelio R Paula	06/2014
7445	(2^253399+3254)/2	76281	Stefano Morozzi	01/2020
7446	69247!4+4	76280	Robert Price	09/2019
7447	6^98025+145	76279	Lelio R Paula	01/2015
7448	(2^253382+1978)/2	76276	Stefano Morozzi	01/2020
7449	2^253355+1155	76268	Lelio R Paula	05/2013
7450	(73*10^76262+413)/9	76263	Robert Price	10/2017
7451	2^253292-71219	76249	Enzo Doria	04/2016
7452	7^90221-36	76246	Lelio R Paula	02/2015
7453	(2^253273+3486)/2	76243	Stefano Morozzi	01/2020
7454	(2^253238+894)/2	76232	Stefano Morozzi	01/2020
7455	18^60727-3473	76229	Enzo Doria	03/2013
7456	(2^253210+1170)/2	76224	Stefano Morozzi	01/2020
7457	(78557*2^253184+1)/3	76221	Lelio R Paula	06/2014
7458	(8*10^76220-83)/3	76221	Robert Price	10/2017
7459	18568^12717+12717^18568	76211	Hans Havermann	01/2020
7460	(44791^20480+1)/(44791^4096+1)	76206	Serge Batalov	01/2017
7461	19443^8294+8294^19443	76193	Hans Havermann	12/2019
7462	11^73163-2010	76192	Enzo Doria	12/2012
7463	19006^10201+10201^19006	76189	Hans Havermann	12/2019
7464	2^253060+54615	76179	Lelio R Paula	05/2013
7465	(2^253049+3966)/2	76176	Stefano Morozzi	01/2020
7466	2^253029+1869761	76170	Enzo Doria	05/2016
7467	(2^253028+1906)/2	76169	Stefano Morozzi	01/2020
7468	2^252955-111007	76148	Enzo Doria	05/2014
7469	2*5^108931+7	76140	Lelio R Paula	10/2014
7470	(86*10^76128+121)/9	76129	Robert Price	03/2017
7471	22154*29^52050+9	76123	Curtis Bright	05/2015
7472	18915^10574+10574^18915	76119	Hans Havermann	01/2020
7473	3^159530-112358	76116	Enzo Doria	06/2014
7474	11^73089-48	76115	Lelio R Paula	02/2015
7475	86^39337-85	76098	Norbert Schneider	10/2015
7476	(3^159505-7)/313297316	76095	Lelio R Paula	06/2012
7477	6^97783+77	76090	Lelio R Paula	01/2015
7478	(2^252716+1842)/2	76075	Stefano Morozzi	01/2020
7479	2^252712-105	76074	Lelio R Paula	03/2012
7480	(10^76069-19)/9	76069	Robert Price	10/2017
7482	131^35927+2	76068	Lelio R Paula	05/2013
7481	(41*10^76067+373)/9	76068	Robert Price	04/2017
7483	2^252683-139	76066	Lelio R Paula	03/2012
7484	137^35597-136	76061	Norbert Schneider	05/2015
7485	3^159413+106	76060	Lelio R Paula	01/2015
7486	(2^252593+1682)/2	76038	Stefano Morozzi	01/2020
7487	9^79677+38^79677-24^79677-3*2^79677	76032	Mike Oakes	12/2010
7488	22235^2626+2626^22235	76029	Hans Havermann	12/2019
7489	(2^252557-9)/71	76026	Lelio R Paula	07/2012
7491	(85*10^76021-103)/9	76022	Robert Price	10/2017
7490	(2^252539+2690)/2	76022	Stefano Morozzi	01/2020
7492	11^72989+80	76011	Lelio R Paula	02/2015
7493	99877!6-36	75996	Robert Price	11/2018
7494	2^252449-459523	75995	Enzo Doria	05/2015
7495	20^58408+73	75991	Lelio R Paula	01/2015
7496	2^252418-1421	75986	Yves Minet	01/2013
7497	(11*2^252396-1)/5	75980	Lelio R Paula	02/2014
7498	20871^4366+4366^20871	75973	Hans Havermann	01/2020
7499	2^252365-110689	75970	Enzo Doria	05/2014
7500	11^72949-1020	75969	Enzo Doria	11/2012

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