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	34015^11134+11134^34015	137647	Hans Havermann	06/2021
3002	2^457240-59939	137643	Enzo Doria	10/2015
3003	(856*10^137633-1)/9	137635	Robert Price	03/2020
3004	36232^6289+6289^36232	137631	Hans Havermann	05/2021
3005	2^457120-21575	137607	Enzo Doria	07/2013
3007	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
3006	30963^27722+27722^30963	137564	Hans Havermann	04/2021
3008	33722^12003+12003^33722	137562	Hans Havermann	06/2021
3009	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
3010	41901^1918+1918^41901	137555	Hans Havermann	06/2021
3011	(7*10^137551-1)/3	137552	Robert Price	08/2022
3012	32930^15021+15021^32930	137539	Hans Havermann	05/2021
3013	31178^25785+25785^31178	137538	Hans Havermann	05/2021
3014	419^52446+52446^419	137525	Norbert Schneider	11/2020
3015	2^456796-113513	137510	Enzo Doria	08/2014
3016	31788^21137+21137^31788	137485	Hans Havermann	04/2021
3017	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
3018	2^456503-114361	137422	Enzo Doria	01/2015
3019	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
3020	36248^6147+6147^36248	137332	Hans Havermann	05/2021
3021	31986^19651+19651^31986	137329	Hans Havermann	05/2021
3022	31817^20656+20656^31817	137292	Hans Havermann	05/2021
3023	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
3024	2^455922+76249	137247	Enzo Doria	05/2016
3025	31310^24171+24171^31310	137241	Hans Havermann	05/2021
3026	14^119741-119741^14	137239	Serge Batalov	04/2016
3027	35014^8297+8297^35014	137218	Hans Havermann	05/2021
3028	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
3030	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
3029	124^65536+57^65536	137195	Serge Batalov	03/2018
3031	2^455689+72677	137177	Enzo Doria	04/2016
3032	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
3033	31287^24128+24128^31287	137116	Hans Havermann	05/2021
3034	(37^87421-1)/36	137093	Robert Price	03/2012
3035	36233^6070+6070^36233	137077	Hans Havermann	05/2021
3036	38418^3697+3697^38418	137070	Hans Havermann	04/2021
3037	2^455323-57	137066	Lelio R Paula	09/2017
3038	(56*10^137019+583)/9	137020	Robert Price	08/2021
3039	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
3040	2^455025-112723	136977	Enzo Doria	06/2014
3041	33876^11039+11039^33876	136959	Hans Havermann	05/2021
3042	35142^7873+7873^35142	136919	Hans Havermann	05/2021
3043	66*10^136894+7	136896	Robert Price	07/2020
3044	2^454675-1777	136871	Yves Minet	10/2011
3045	31676^20931+20931^31676	136866	Hans Havermann	05/2021
3046	3*10^136829+29	136830	Robert Price	05/2018
3047	4*10^136813-57	136814	Robert Price	10/2018
3048	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
3049	37359^4588+4588^37359	136795	Hans Havermann	05/2021
3050	2^454348-53	136773	Lelio R Paula	09/2017
3051	31^91680-2	136729	Lelio R Paula	05/2017
3052	2^454199-113697	136728	Enzo Doria	09/2014
3053	30785^27622+27622^30785	136725	Hans Havermann	05/2021
3054	32973^14014+14014^32973	136725	Hans Havermann	05/2021
3056	7*10^136716+69	136717	Robert Price	07/2019
3055	36002^6273+6273^36002	136717	Hans Havermann	05/2021
3057	6*10^136692+53	136693	Robert Price	05/2020
3058	(13*10^136687+47)/3	136688	Robert Price	10/2018
3059	2^453935-2791357	136649	Enzo Doria	01/2016
3060	2^453906-69131	136640	Enzo Doria	11/2015
3061	33232^12915+12915^33232	136620	Hans Havermann	05/2021
3062	2^453791+1873913	136605	Enzo Doria	06/2016
3063	34166^9951+9951^34166	136592	Hans Havermann	05/2021
3064	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
3065	31102^24635+24635^31102	136587	Hans Havermann	05/2021
3066	580^49413+49413^580	136550	Norbert Schneider	02/2019
3067	2^453503-2788297	136519	Enzo Doria	11/2015
3068	34989^7958+7958^34989	136486	Hans Havermann	12/2020
3069	(2*10^136484+187)/9	136484	Robert Price	06/2022
3070	31007^25158+25158^31007	136452	Hans Havermann	11/2020
3071	2^453267-113827	136447	Enzo Doria	09/2014
3072	32234^17085+17085^32234	136435	Hans Havermann	12/2020
3073	2^453102+1877629	136398	Enzo Doria	08/2016
3074	31016^24981+24981^31016	136397	Hans Havermann	12/2020
3075	(62*10^136384-791)/9	136385	Robert Price	06/2019
3076	34171^9798+9798^34171	136382	Hans Havermann	12/2020
3077	(17*10^136354-113)/3	136355	Robert Price	06/2021
3078	32756^14541+14541^32756	136350	Hans Havermann	11/2020
3079	32205^17086+17086^32205	136313	Hans Havermann	12/2020
3080	(25*10^136303+161)/3	136304	Robert Price	09/2019
3081	35337^7196+7196^35337	136299	Hans Havermann	12/2020
3082	(182*10^136291+1)/3	136293	Robert Price	02/2020
3083	(88*10^136234+83)/9	136235	Robert Price	03/2022
3084	23*10^136225-7	136227	Robert Price	02/2020
3085	L(651821)	136223	Henri Lifchitz	09/2008
3086	2^452460+77701	136205	Enzo Doria	05/2016
3087	2^452440-114755	136199	Enzo Doria	04/2015
3088	32286^16489+16489^32286	136157	Hans Havermann	11/2020
3089	(47*10^136141+493)/9	136142	Robert Price	03/2019
3090	40392^2339+2339^40392	136082	Hans Havermann	12/2020
3091	2*10^136057-43	136058	Robert Price	04/2018
3092	(2^451956-5)/181	136051	Lelio R Paula	07/2015
3093	2^451947-22165	136050	Enzo Doria	07/2013
3094	2^451787-21805	136002	Enzo Doria	07/2013
3095	2^451734-112817	135986	Enzo Doria	06/2014
3096	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
3097	2^451705-21879	135977	Enzo Doria	07/2013
3098	2^451560-112349	135934	Enzo Doria	06/2014
3099	2^451530+45	135925	Lelio R Paula	08/2017
3100	31622^19875+19875^31622	135922	Hans Havermann	11/2020
3101	(25*10^135906-73)/3	135907	Robert Price	09/2019
3102	2^451450-21743	135900	Enzo Doria	07/2013
3103	35218^7199+7199^35218	135846	Hans Havermann	11/2020
3104	35661^6446+6446^35661	135844	Hans Havermann	11/2020
3105	31869^18248+18248^31869	135801	Hans Havermann	12/2020
3106	(77*10^135789+157)/9	135790	Robert Price	05/2022
3107	2^450805+65	135706	Lelio R Paula	08/2017
3108	30761^25728+25728^30761	135669	Hans Havermann	12/2020
3109	2*10^135663+69	135664	Robert Price	06/2020
3110	33962^9867+9867^33962	135651	Hans Havermann	11/2020
3111	34474^8605+8605^34474	135647	Hans Havermann	11/2020
3112	34501^8508+8508^34501	135583	Hans Havermann	12/2020
3113	35487^6614+6614^35487	135577	Hans Havermann	12/2020
3114	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
3115	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
3116	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
3117	(76*10^135553-49)/9	135554	Robert Price	07/2022
3118	(844*10^135527-7)/9	135529	Robert Price	05/2021
3119	40387^2260+2260^40387	135463	Hans Havermann	12/2020
3120	2^449944-113247	135447	Enzo Doria	07/2014
3121	2^449770-113247	135395	Enzo Doria	07/2014
3122	2^449637-21471	135355	Enzo Doria	07/2013
3123	2^449571-75	135335	Lelio R Paula	08/2017
3124	(14*10^135301-53)/3	135302	Robert Price	12/2018
3125	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
3126	(13*10^135279+437)/9	135280	Robert Price	04/2018
3127	2^449330-35	135262	Lelio R Paula	08/2017
3128	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
3129	(13*10^135184-43)/3	135185	Robert Price	11/2018
3130	2^449049-115309	135178	Enzo Doria	07/2015
3131	(10^135174+191)/3	135174	Robert Price	02/2018
3132	2^449030-15	135172	Lelio R Paula	08/2017
3133	(157*10^135151-1)/3	135153	Robert Price	01/2022
3134	(2^448966+100280245065)	135153	Paul Bourdelais	05/2022
3135	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
3136	(37*10^135099+251)/9	135100	Robert Price	09/2021
3137	32221^15586+15586^32221	135095	Hans Havermann	12/2020
3138	2^448762-351401	135091	Enzo Doria	07/2015
3139	2*10^135083-43	135084	Robert Price	04/2018
3140	31357^20278+20278^31357	135056	Hans Havermann	12/2020
3141	32242^15445+15445^32242	135055	Hans Havermann	12/2020
3142	k(198476)	135054	Robert Price	07/2020
3143	32461^14470+14470^32461	135053	Hans Havermann	12/2020
3144	31353^20288+20288^31353	135045	Hans Havermann	12/2020
3145	5*10^135019+77	135020	Robert Price	12/2018
3146	(10^135011+719)/9	135011	Serge Batalov	12/2014
3147	(197*10^134978+7)/3	134980	Robert Price	12/2020
3148	2^448386-2786261	134978	Enzo Doria	03/2016
3149	(73*10^134939+143)/9	134940	Robert Price	07/2019
3150	33957^9392+9392^33957	134903	Hans Havermann	12/2020
3151	2^448113-113949	134896	Enzo Doria	11/2014
3152	30958^22755+22755^30958	134887	Hans Havermann	12/2020
3153	2^447888-2786639	134828	Enzo Doria	03/2016
3154	2^447870-396765	134823	Enzo Doria	07/2013
3155	2^447766-21791	134791	Enzo Doria	07/2013
3156	(19*10^134786-49)/3	134787	Robert Price	05/2019
3157	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
3158	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
3159	2^447552-1019	134727	Yves Minet	02/2014
3160	(2*10^134720-41)/3	134720	Robert Price	02/2018
3161	(25*10^134695-97)/9	134696	Robert Price	01/2022
3162	2^447437-113569	134692	Enzo Doria	08/2014
3163	2^447426-65	134689	Lelio R Paula	08/2017
3164	2^447357-2797573	134668	Enzo Doria	04/2016
3165	2^447278+93	134645	Lelio R Paula	08/2017
3166	33193^11370+11370^33193	134623	Hans Havermann	12/2020
3167	30736^23979+23979^30736	134619	Hans Havermann	11/2020
3168	2^447094-113193	134589	Enzo Doria	07/2014
3169	3^282041-9934	134568	Enzo Doria	05/2014
3170	2^447019-109039	134567	Enzo Doria	04/2014
3171	31376^19437+19437^31376	134561	Hans Havermann	12/2020
3172	2^446990-22041	134558	Enzo Doria	07/2013
3173	123^64370+122	134528	Karsten Bonath	04/2018
3174	30100^29461+29461^30100	134525	Hans Havermann	11/2020
3175	31251^20158+20158^31251	134519	Hans Havermann	11/2020
3176	2^446782-39701	134495	Enzo Doria	09/2015
3177	31817^16858+16858^31817	134485	Hans Havermann	12/2020
3178	32448^13937+13937^32448	134471	Hans Havermann	12/2020
3179	2^446494-16485	134409	Enzo Doria	04/2013
3180	30042^29785+29785^30042	134408	Hans Havermann	12/2020
3181	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
3182	2^446441+65	134393	Lelio R Paula	08/2017
3183	(10^134385+719)/9	134385	Serge Batalov	12/2014
3184	30043^29688+29688^30043	134370	Hans Havermann	12/2020
3185	(2*10^134364+529)/9	134364	Robert Price	01/2018
3186	34657^7512+7512^34657	134323	Hans Havermann	11/2020
3187	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
3188	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
3189	42035^1564+1564^42035	134270	Hans Havermann	12/2020
3191	(2^446022-7)/339	134264	Lelio R Paula	07/2015
3190	30621^24248+24248^30621	134264	Hans Havermann	12/2020
3192	30341^26562+26562^30341	134237	Hans Havermann	11/2020
3193	10^134209+99867	134210	Patrick De Geest	05/2021
3194	10^134209-80000001	134209	Robert Price	04/2021
3195	10^134209-323283	134209	Patrick De Geest	05/2021
3196	29976^29953+29953^29976	134186	Hans Havermann	12/2020
3197	35038^6755+6755^35038	134183	Hans Havermann	12/2020
3198	63^74568+2	134174	Lelio R Paula	06/2017
3199	2^445671-22071	134161	Enzo Doria	07/2013
3200	532^49205+49205^532	134129	Norbert Schneider	02/2019
3201	36453^4780+4780^36453	134127	Hans Havermann	04/2021
3202	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
3203	2^445515-113859	134114	Enzo Doria	10/2014
3205	(22*10^134111-37)/3	134112	Robert Price	04/2019
3204	31083^20636+20636^31083	134112	Hans Havermann	04/2021
3206	31622^17379+17379^31622	134079	Hans Havermann	04/2021
3207	(277*10^134059-7)/9	134061	Robert Price	02/2022
3208	2^445328-216917	134058	Enzo Doria	05/2014
3209	2^445202+1874899	134020	Enzo Doria	06/2016
3210	(35*10^134003-89)/9	134004	Robert Price	02/2022
3211	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
3212	(35*10^133979-593)/9	133980	Robert Price	07/2018
3213	2*10^133955+51	133956	Robert Price	05/2018
3214	(49*10^133952+437)/9	133953	Robert Price	09/2021
3215	2^444964-113639	133948	Enzo Doria	08/2014
3216	31811^16240+16240^31811	133943	Hans Havermann	04/2021
3217	10^133902+167841	133903	Patrick De Geest	05/2021
3219	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
3218	10^133902-100001	133902	Robert Price	07/2020
3220	2^444784-113859	133894	Enzo Doria	10/2014
3221	32303^13914+13914^32303	133846	Hans Havermann	04/2021
3222	30739^22458+22458^30739	133757	Hans Havermann	04/2021
3223	34942^6721+6721^34942	133739	Hans Havermann	04/2021
3224	(2^444046+100280245065)	133672	Paul Bourdelais	05/2022
3225	34792^6935+6935^34792	133638	Hans Havermann	04/2021
3226	(266*10^133603+1)/3	133605	Robert Price	04/2020
3227	32261^13842+13842^32261	133600	Hans Havermann	04/2021
3228	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
3229	(134*10^133573-11)/3	133575	Robert Price	01/2022
3230	62^74521-61^74521	133571	Robert Price	05/2013
3231	(182*10^133543+1)/3	133545	Robert Price	02/2020
3232	(103*10^133535+11)/3	133537	Robert Price	01/2021
3233	32589^12520+12520^32589	133537	Hans Havermann	03/2021
3234	34516^7373+7373^34516	133496	Hans Havermann	04/2021
3235	8*10^133487-37	133488	Robert Price	03/2022
3236	30135^26882+26882^30135	133482	Hans Havermann	04/2021
3237	2^443198-1867301	133416	Enzo Doria	03/2016
3238	(19*10^133390+101)/3	133391	Robert Price	09/2019
3239	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
3240	36117^4910+4910^36117	133311	Hans Havermann	04/2021
3241	2^442799+1874633	133296	Enzo Doria	06/2016
3242	L(637751)	133283	Henri Lifchitz	09/2008
3243	109^65410-2	133269	Lelio R Paula	10/2017
3244	2^442688-113489	133263	Enzo Doria	08/2014
3245	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
3246	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
3247	2^442437-1849993	133187	Enzo Doria	08/2015
3248	2^442430-2791721	133185	Enzo Doria	03/2016
3249	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
3250	29959^27870+27870^29959	133172	Hans Havermann	03/2021

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Probable Primes Top 10000

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