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 ?
3001	2^467605-1855603	140764	Enzo Doria	09/2015
3002	5*10^140744-7	140745	Robert Price	09/2015
3003	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
3004	2^467401-1850023	140702	Enzo Doria	08/2015
3005	(14*10^140693+13)/9	140694	Tyler Busby	02/2023
3006	(266*10^140681-17)/3	140683	Robert Price	07/2020
3007	(2^467270+78557)/23247	140658	Lelio R Paula	07/2015
3008	32138^23781+23781^32138	140644	Hans Havermann	05/2021
3009	31654^27735+27735^31654	140640	Hans Havermann	05/2021
3010	(29*2^467205+1)/2780517107	140635	Lelio R Paula	08/2015
3011	2^467166-1854941	140631	Enzo Doria	09/2015
3012	(203*10^140615-11)/3	140617	Robert Price	12/2020
3013	(85*10^140609+473)/9	140610	Robert Price	01/2020
3014	39231^3836+3836^39231	140600	Hans Havermann	06/2021
3015	2^466866-1840571	140541	Enzo Doria	06/2015
3016	2^466829-459523	140530	Enzo Doria	05/2015
3017	2^466692-113213	140489	Enzo Doria	07/2014
3018	23*10^140464-3	140466	Robert Price	10/2021
3019	(2*10^140461-17)/3	140461	Serge Batalov	11/2022
3020	31335^30364+30364^31335	140455	Hans Havermann	05/2021
3021	32795^19126+19126^32795	140416	Hans Havermann	05/2021
3022	(44*10^140410-503)/9	140411	Robert Price	12/2018
3023	153^64265-2	140400	Lelio R Paula	11/2017
3024	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
3025	(29*10^140337-17)/3	140338	Robert Price	09/2019
3026	2^466181-112735	140335	Enzo Doria	07/2014
3027	(16*10^140290-37)/3	140291	Robert Price	05/2021
3028	(5*10^140281-119)/3	140282	Robert Price	03/2018
3029	34568^11415+11415^34568	140259	Hans Havermann	05/2021
3030	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
3031	33632^14781+14781^33632	140236	Hans Havermann	05/2021
3032	31803^25670+25670^31803	140233	Hans Havermann	05/2021
3033	2^465803-114817	140221	Enzo Doria	05/2015
3034	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
3035	2^465503-112735	140131	Enzo Doria	07/2014
3036	(16*10^140091+167)/3	140092	Robert Price	06/2019
3037	(8*10^140087-137)/3	140088	Robert Price	03/2022
3038	6^179964+179964^6-1	140040	Robert Price	04/2014
3039	(89*10^140008-179)/9	140009	Robert Price	12/2019
3040	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
3041	2^465072-344789	140001	Enzo Doria	07/2015
3042	34742^10683+10683^34742	139965	Hans Havermann	05/2021
3043	5*10^139945+81	139946	Robert Price	03/2019
3044	32648^19335+19335^32648	139941	Hans Havermann	05/2021
3045	2^464864-17	139939	Lelio R Paula	09/2017
3046	8*10^139920+51	139921	Robert Price	08/2019
3047	(85*10^139913-1)/3	139915	Robert Price	02/2020
3048	31203^30436+30436^31203	139896	Hans Havermann	04/2021
3049	(16^116139+619)/5	139845	Anonymous	08/2022
3050	4*10^139839-27	139840	Robert Price	08/2021
3051	33582^14573+14573^33582	139821	Hans Havermann	05/2021
3052	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
3054	2*10^139800-21	139801	Robert Price	09/2020
3053	32628^19261+19261^32628	139801	Hans Havermann	04/2021
3055	(13*10^139782+191)/3	139783	Robert Price	11/2018
3056	(64*10^139776+791)/9	139777	Robert Price	01/2022
3057	(695*10^139772+7)/9	139774	Robert Price	12/2021
3058	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
3059	(74*10^139723+133)/9	139724	Robert Price	06/2019
3060	3*10^139722+13	139723	Robert Price	07/2018
3061	31577^26592+26592^31577	139721	Hans Havermann	05/2021
3062	77*10^139692+3	139694	Robert Price	06/2020
3063	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
3064	(18203^(2^15)+(18201)^(2^15))/2	139597	Robert Price	05/2018
3065	39640^3321+3321^39640	139584	Hans Havermann	05/2021
3066	36663^6410+6410^36663	139571	Hans Havermann	05/2021
3067	2^463633-2788423	139568	Enzo Doria	11/2015
3068	33659^13978+13978^33659	139532	Hans Havermann	05/2021
3069	31811^24318+24318^31811	139521	Hans Havermann	04/2021
3070	34149^12172+12172^34149	139512	Hans Havermann	04/2021
3071	(29*10^139476+313)/9	139477	Robert Price	04/2021
3072	31721^24940+24940^31721	139474	Hans Havermann	05/2021
3073	32833^17698+17698^32833	139473	Hans Havermann	05/2021
3074	2^463271-109501	139459	Enzo Doria	04/2014
3075	(5*10^139457+79)/3	139458	Robert Price	03/2018
3076	2^463237-99	139449	Lelio R Paula	09/2017
3077	(49*10^139442+383)/9	139443	Robert Price	04/2019
3078	31155^29902+29902^31155	139441	Hans Havermann	05/2021
3079	(7*10^139417-547)/9	139417	Robert Price	01/2018
3080	(10^139398+191)/3	139398	Robert Price	02/2018
3081	23*10^139386-3	139388	Robert Price	10/2021
3082	2^463019+79463	139383	Enzo Doria	06/2016
3083	3^292129-112756	139381	Enzo Doria	07/2014
3084	(15*2^462951+1)/527	139361	Lelio R Paula	08/2015
3085	31922^23205+23205^31922	139359	Hans Havermann	05/2021
3087	2^462855-1865707	139334	Enzo Doria	02/2016
3086	31237^28876+28876^31237	139334	Hans Havermann	05/2021
3088	(86*10^139315+121)/9	139316	Robert Price	08/2019
3089	2^462786-292043	139313	Enzo Doria	08/2015
3090	38915^3798+3798^38915	139299	Hans Havermann	05/2021
3091	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
3092	34065^12248+12248^34065	139260	Hans Havermann	05/2021
3093	36425^6654+6654^36425	139256	Hans Havermann	05/2021
3094	39252^3527+3527^39252	139243	Hans Havermann	05/2021
3095	(17*10^139239+67)/3	139240	Robert Price	01/2019
3096	31887^23248+23248^31887	139231	Hans Havermann	05/2021
3097	(25*10^139210-97)/9	139211	Robert Price	01/2022
3098	2^462238-935	139148	Yves Minet	02/2014
3099	(29*10^139134-119)/9	139135	Robert Price	12/2021
3100	(109*10^139100-7)/3	139102	Robert Price	03/2021
3101	38744^3885+3885^38744	139068	Hans Havermann	05/2021
3102	31112^29499+29499^31112	139065	Hans Havermann	05/2021
3103	2*10^139043-63	139044	Robert Price	01/2022
3104	36390^6613+6613^36390	139025	Hans Havermann	04/2021
3105	2*10^138975+33	138976	Robert Price	11/2021
3106	42437^1882+1882^42437	138966	Hans Havermann	05/2021
3107	32151^20990+20990^32151	138958	Hans Havermann	05/2021
3108	32154^20933+20933^32154	138933	Hans Havermann	04/2021
3109	31082^29499+29499^31082	138931	Hans Havermann	04/2021
3110	2^461228+1870441	138844	Enzo Doria	05/2016
3111	2^461204-113675	138837	Enzo Doria	08/2014
3112	(2^461139-7)/47	138815	Lelio R Paula	08/2015
3113	(17*10^138812-521)/9	138813	Robert Price	04/2018
3114	3*10^138811-11	138812	Robert Price	07/2018
3115	(28*10^138768+173)/3	138769	Robert Price	12/2019
3116	(17*2^460963+1)/124051613	138757	Lelio R Paula	08/2015
3117	(379*10^138737-1)/9	138739	Robert Price	02/2020
3118	(43*10^138648+101)/9	138649	Robert Price	11/2018
3119	2^460567-113541	138645	Enzo Doria	08/2014
3120	(10^138622+161)/9	138622	Robert Price	09/2021
3121	7*10^138604+3	138605	Robert Price	08/2015
3122	(133*10^138600+17)/3	138602	Robert Price	11/2021
3123	33912^12203+12203^33912	138581	Hans Havermann	05/2021
3124	2^460330+69	138574	Lelio R Paula	09/2017
3125	(17*10^138569-77)/3	138570	Robert Price	08/2019
3126	31186^27725+27725^31186	138556	Hans Havermann	05/2021
3127	(16*10^138545+89)/3	138546	Robert Price	03/2021
3128	39753^3056+3056^39753	138546	Hans Havermann	05/2021
3129	31282^26847+26847^31282	138545	Hans Havermann	05/2021
3130	6*10^138520-37	138521	Robert Price	02/2021
3132	2^460078-69581	138498	Enzo Doria	12/2015
3131	31830^22447+22447^31830	138498	Hans Havermann	05/2021
3133	37384^5065+5065^37384	138492	Hans Havermann	05/2021
3134	34774^9585+9585^34774	138456	Hans Havermann	05/2021
3135	10^138444-5001	138444	Robert Price	12/2021
3136	2^459768+1531	138404	Lelio R Paula	06/2012
3137	(266*10^138328-17)/3	138330	Robert Price	07/2020
3138	32963^15696+15696^32963	138306	Hans Havermann	05/2021
3139	2^459343-113611	138277	Enzo Doria	08/2014
3140	(28*10^138240+113)/3	138241	Robert Price	03/2020
3141	2^459199+1874393	138233	Enzo Doria	06/2016
3142	33339^14002+14002^33339	138230	Hans Havermann	05/2021
3143	2^459063-345307	138192	Enzo Doria	06/2015
3144	2*10^138162-43	138163	Robert Price	04/2018
3145	2^458927-112747	138151	Enzo Doria	06/2014
3146	2^458927-69217	138151	Enzo Doria	11/2015
3147	30907^29458+29458^30907	138130	Hans Havermann	05/2021
3148	32882^15837+15837^32882	138094	Hans Havermann	05/2021
3149	39252^3295+3295^39252	138083	Hans Havermann	05/2021
3150	33789^12190+12190^33789	138062	Hans Havermann	06/2021
3151	555555*2^458524+1513	138036	Darren Bedwell	08/2009
3152	30931^29002+29002^30931	138028	Hans Havermann	05/2021
3153	2^458465+2^32+1	138012	T. D. Noe	06/2007
3154	32206^19275+19275^32206	138003	Hans Havermann	05/2021
3155	2^458321-113053	137969	Enzo Doria	07/2014
3156	6^177298+323	137965	Riley Fisher	03/2023
3157	2^458298+79459	137962	Enzo Doria	06/2016
3158	2^458248-21815	137947	Enzo Doria	07/2013
3159	2^458194+1876549	137931	Enzo Doria	07/2016
3160	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
3161	(318259#+2625)/(3^257^5*22965193)	137899	Makoto Morimoto	06/2019
3162	(793*10^137887+53)/9	137889	Robert Price	01/2022
3163	2^457937+57	137853	Lelio R Paula	09/2017
3164	(8*10^137845+13)/3	137846	Robert Price	06/2018
3165	2^457822+105	137819	Donovan Johnson	06/2006
3166	2^457754-113711	137798	Enzo Doria	09/2014
3167	11^132315-360	137792	Enzo Doria	09/2012
3168	32072^19689+19689^32072	137725	Hans Havermann	06/2021
3169	44592^1225+1225^44592	137707	Hans Havermann	05/2021
3170	2^457347-37	137676	Lelio R Paula	09/2017
3171	2^457322-2786393	137668	Enzo Doria	10/2015
3172	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
3173	34015^11134+11134^34015	137647	Hans Havermann	06/2021
3174	2^457240-59939	137643	Enzo Doria	10/2015
3175	(856*10^137633-1)/9	137635	Robert Price	03/2020
3176	36232^6289+6289^36232	137631	Hans Havermann	05/2021
3177	2^457120-21575	137607	Enzo Doria	07/2013
3179	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
3178	30963^27722+27722^30963	137564	Hans Havermann	04/2021
3180	33722^12003+12003^33722	137562	Hans Havermann	06/2021
3181	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
3182	41901^1918+1918^41901	137555	Hans Havermann	06/2021
3183	(7*10^137551-1)/3	137552	Robert Price	08/2022
3184	32930^15021+15021^32930	137539	Hans Havermann	05/2021
3185	31178^25785+25785^31178	137538	Hans Havermann	05/2021
3186	419^52446+52446^419	137525	Norbert Schneider	11/2020
3187	2^456796-113513	137510	Enzo Doria	08/2014
3188	31788^21137+21137^31788	137485	Hans Havermann	04/2021
3189	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
3190	2^456503-114361	137422	Enzo Doria	01/2015
3191	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
3192	36248^6147+6147^36248	137332	Hans Havermann	05/2021
3193	31986^19651+19651^31986	137329	Hans Havermann	05/2021
3194	31817^20656+20656^31817	137292	Hans Havermann	05/2021
3195	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
3196	2^455922+76249	137247	Enzo Doria	05/2016
3197	31310^24171+24171^31310	137241	Hans Havermann	05/2021
3198	14^119741-119741^14	137239	Serge Batalov	04/2016
3199	35014^8297+8297^35014	137218	Hans Havermann	05/2021
3200	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
3202	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
3201	124^65536+57^65536	137195	Serge Batalov	03/2018
3203	2^455689+72677	137177	Enzo Doria	04/2016
3204	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
3205	31287^24128+24128^31287	137116	Hans Havermann	05/2021
3206	(37^87421-1)/36	137093	Robert Price	03/2012
3207	36233^6070+6070^36233	137077	Hans Havermann	05/2021
3208	(8*10^137073-17)/9	137073	Serge Batalov	11/2022
3209	38418^3697+3697^38418	137070	Hans Havermann	04/2021
3210	2^455323-57	137066	Lelio R Paula	09/2017
3211	(56*10^137019+583)/9	137020	Robert Price	08/2021
3212	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
3213	2^455025-112723	136977	Enzo Doria	06/2014
3214	33876^11039+11039^33876	136959	Hans Havermann	05/2021
3215	35142^7873+7873^35142	136919	Hans Havermann	05/2021
3216	66*10^136894+7	136896	Robert Price	07/2020
3217	2^454675-1777	136871	Yves Minet	10/2011
3218	31676^20931+20931^31676	136866	Hans Havermann	05/2021
3219	3*10^136829+29	136830	Robert Price	05/2018
3220	4*10^136813-57	136814	Robert Price	10/2018
3221	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
3222	37359^4588+4588^37359	136795	Hans Havermann	05/2021
3223	2^454348-53	136773	Lelio R Paula	09/2017
3224	31^91680-2	136729	Lelio R Paula	05/2017
3225	2^454199-113697	136728	Enzo Doria	09/2014
3226	30785^27622+27622^30785	136725	Hans Havermann	05/2021
3227	32973^14014+14014^32973	136725	Hans Havermann	05/2021
3229	7*10^136716+69	136717	Robert Price	07/2019
3228	36002^6273+6273^36002	136717	Hans Havermann	05/2021
3230	6*10^136692+53	136693	Robert Price	05/2020
3231	(13*10^136687+47)/3	136688	Robert Price	10/2018
3232	2^453935-2791357	136649	Enzo Doria	01/2016
3233	2^453906-69131	136640	Enzo Doria	11/2015
3234	33232^12915+12915^33232	136620	Hans Havermann	05/2021
3235	2^453791+1873913	136605	Enzo Doria	06/2016
3236	34166^9951+9951^34166	136592	Hans Havermann	05/2021
3237	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
3238	31102^24635+24635^31102	136587	Hans Havermann	05/2021
3239	580^49413+49413^580	136550	Norbert Schneider	02/2019
3240	2^453503-2788297	136519	Enzo Doria	11/2015
3241	34989^7958+7958^34989	136486	Hans Havermann	12/2020
3242	(2*10^136484+187)/9	136484	Robert Price	06/2022
3243	31007^25158+25158^31007	136452	Hans Havermann	11/2020
3244	2^453267-113827	136447	Enzo Doria	09/2014
3245	32234^17085+17085^32234	136435	Hans Havermann	12/2020
3246	2^453102+1877629	136398	Enzo Doria	08/2016
3247	31016^24981+24981^31016	136397	Hans Havermann	12/2020
3248	(62*10^136384-791)/9	136385	Robert Price	06/2019
3249	34171^9798+9798^34171	136382	Hans Havermann	12/2020
3250	(17*10^136354-113)/3	136355	Robert Price	06/2021

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Probable Primes Top 10000

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