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	34742^10683+10683^34742	139965	Hans Havermann	05/2021
3002	5*10^139945+81	139946	Robert Price	03/2019
3003	32648^19335+19335^32648	139941	Hans Havermann	05/2021
3004	2^464864-17	139939	Lelio R Paula	09/2017
3005	8*10^139920+51	139921	Robert Price	08/2019
3006	(85*10^139913-1)/3	139915	Robert Price	02/2020
3007	31203^30436+30436^31203	139896	Hans Havermann	04/2021
3008	(16^116139+619)/5	139845	Anonymous	08/2022
3009	4*10^139839-27	139840	Robert Price	08/2021
3010	33582^14573+14573^33582	139821	Hans Havermann	05/2021
3011	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
3013	2*10^139800-21	139801	Robert Price	09/2020
3012	32628^19261+19261^32628	139801	Hans Havermann	04/2021
3014	(13*10^139782+191)/3	139783	Robert Price	11/2018
3015	(64*10^139776+791)/9	139777	Robert Price	01/2022
3016	(695*10^139772+7)/9	139774	Robert Price	12/2021
3017	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
3018	(74*10^139723+133)/9	139724	Robert Price	06/2019
3019	3*10^139722+13	139723	Robert Price	07/2018
3020	31577^26592+26592^31577	139721	Hans Havermann	05/2021
3021	77*10^139692+3	139694	Robert Price	06/2020
3022	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
3023	(18203^(2^15)+(18201)^(2^15))/2	139597	Robert Price	05/2018
3024	39640^3321+3321^39640	139584	Hans Havermann	05/2021
3025	36663^6410+6410^36663	139571	Hans Havermann	05/2021
3026	2^463633-2788423	139568	Enzo Doria	11/2015
3027	33659^13978+13978^33659	139532	Hans Havermann	05/2021
3028	31811^24318+24318^31811	139521	Hans Havermann	04/2021
3029	34149^12172+12172^34149	139512	Hans Havermann	04/2021
3030	(29*10^139476+313)/9	139477	Robert Price	04/2021
3031	31721^24940+24940^31721	139474	Hans Havermann	05/2021
3032	32833^17698+17698^32833	139473	Hans Havermann	05/2021
3033	2^463271-109501	139459	Enzo Doria	04/2014
3034	(5*10^139457+79)/3	139458	Robert Price	03/2018
3035	2^463237-99	139449	Lelio R Paula	09/2017
3036	(49*10^139442+383)/9	139443	Robert Price	04/2019
3037	31155^29902+29902^31155	139441	Hans Havermann	05/2021
3038	(7*10^139417-547)/9	139417	Robert Price	01/2018
3039	(10^139398+191)/3	139398	Robert Price	02/2018
3040	23*10^139386-3	139388	Robert Price	10/2021
3041	2^463019+79463	139383	Enzo Doria	06/2016
3042	3^292129-112756	139381	Enzo Doria	07/2014
3043	(15*2^462951+1)/527	139361	Lelio R Paula	08/2015
3044	31922^23205+23205^31922	139359	Hans Havermann	05/2021
3046	2^462855-1865707	139334	Enzo Doria	02/2016
3045	31237^28876+28876^31237	139334	Hans Havermann	05/2021
3047	(86*10^139315+121)/9	139316	Robert Price	08/2019
3048	2^462786-292043	139313	Enzo Doria	08/2015
3049	38915^3798+3798^38915	139299	Hans Havermann	05/2021
3050	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
3051	34065^12248+12248^34065	139260	Hans Havermann	05/2021
3052	36425^6654+6654^36425	139256	Hans Havermann	05/2021
3053	39252^3527+3527^39252	139243	Hans Havermann	05/2021
3054	(17*10^139239+67)/3	139240	Robert Price	01/2019
3055	31887^23248+23248^31887	139231	Hans Havermann	05/2021
3056	(25*10^139210-97)/9	139211	Robert Price	01/2022
3057	2^462238-935	139148	Yves Minet	02/2014
3058	(29*10^139134-119)/9	139135	Robert Price	12/2021
3059	(109*10^139100-7)/3	139102	Robert Price	03/2021
3060	38744^3885+3885^38744	139068	Hans Havermann	05/2021
3061	31112^29499+29499^31112	139065	Hans Havermann	05/2021
3062	2*10^139043-63	139044	Robert Price	01/2022
3063	36390^6613+6613^36390	139025	Hans Havermann	04/2021
3064	2*10^138975+33	138976	Robert Price	11/2021
3065	42437^1882+1882^42437	138966	Hans Havermann	05/2021
3066	32151^20990+20990^32151	138958	Hans Havermann	05/2021
3067	32154^20933+20933^32154	138933	Hans Havermann	04/2021
3068	31082^29499+29499^31082	138931	Hans Havermann	04/2021
3069	2^461228+1870441	138844	Enzo Doria	05/2016
3070	2^461204-113675	138837	Enzo Doria	08/2014
3071	(2^461139-7)/47	138815	Lelio R Paula	08/2015
3072	(17*10^138812-521)/9	138813	Robert Price	04/2018
3073	3*10^138811-11	138812	Robert Price	07/2018
3074	(28*10^138768+173)/3	138769	Robert Price	12/2019
3075	(17*2^460963+1)/124051613	138757	Lelio R Paula	08/2015
3076	(379*10^138737-1)/9	138739	Robert Price	02/2020
3077	(43*10^138648+101)/9	138649	Robert Price	11/2018
3078	2^460567-113541	138645	Enzo Doria	08/2014
3079	(10^138622+161)/9	138622	Robert Price	09/2021
3080	7*10^138604+3	138605	Robert Price	08/2015
3081	(133*10^138600+17)/3	138602	Robert Price	11/2021
3082	33912^12203+12203^33912	138581	Hans Havermann	05/2021
3083	2^460330+69	138574	Lelio R Paula	09/2017
3084	(17*10^138569-77)/3	138570	Robert Price	08/2019
3085	31186^27725+27725^31186	138556	Hans Havermann	05/2021
3086	(16*10^138545+89)/3	138546	Robert Price	03/2021
3087	39753^3056+3056^39753	138546	Hans Havermann	05/2021
3088	31282^26847+26847^31282	138545	Hans Havermann	05/2021
3089	6*10^138520-37	138521	Robert Price	02/2021
3091	2^460078-69581	138498	Enzo Doria	12/2015
3090	31830^22447+22447^31830	138498	Hans Havermann	05/2021
3092	37384^5065+5065^37384	138492	Hans Havermann	05/2021
3093	34774^9585+9585^34774	138456	Hans Havermann	05/2021
3094	10^138444-5001	138444	Robert Price	12/2021
3095	2^459768+1531	138404	Lelio R Paula	06/2012
3096	(266*10^138328-17)/3	138330	Robert Price	07/2020
3097	32963^15696+15696^32963	138306	Hans Havermann	05/2021
3098	2^459343-113611	138277	Enzo Doria	08/2014
3099	(28*10^138240+113)/3	138241	Robert Price	03/2020
3100	2^459199+1874393	138233	Enzo Doria	06/2016
3101	33339^14002+14002^33339	138230	Hans Havermann	05/2021
3102	2^459063-345307	138192	Enzo Doria	06/2015
3103	2*10^138162-43	138163	Robert Price	04/2018
3104	2^458927-112747	138151	Enzo Doria	06/2014
3105	2^458927-69217	138151	Enzo Doria	11/2015
3106	30907^29458+29458^30907	138130	Hans Havermann	05/2021
3107	32882^15837+15837^32882	138094	Hans Havermann	05/2021
3108	39252^3295+3295^39252	138083	Hans Havermann	05/2021
3109	33789^12190+12190^33789	138062	Hans Havermann	06/2021
3110	555555*2^458524+1513	138036	Darren Bedwell	08/2009
3111	30931^29002+29002^30931	138028	Hans Havermann	05/2021
3112	2^458465+2^32+1	138012	T. D. Noe	06/2007
3113	32206^19275+19275^32206	138003	Hans Havermann	05/2021
3114	2^458321-113053	137969	Enzo Doria	07/2014
3115	2^458298+79459	137962	Enzo Doria	06/2016
3116	2^458248-21815	137947	Enzo Doria	07/2013
3117	2^458194+1876549	137931	Enzo Doria	07/2016
3118	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
3119	(318259#+2625)/(3^257^5*22965193)	137899	Makoto Morimoto	06/2019
3120	(793*10^137887+53)/9	137889	Robert Price	01/2022
3121	2^457937+57	137853	Lelio R Paula	09/2017
3122	(8*10^137845+13)/3	137846	Robert Price	06/2018
3123	2^457822+105	137819	Donovan Johnson	06/2006
3124	2^457754-113711	137798	Enzo Doria	09/2014
3125	11^132315-360	137792	Enzo Doria	09/2012
3126	32072^19689+19689^32072	137725	Hans Havermann	06/2021
3127	44592^1225+1225^44592	137707	Hans Havermann	05/2021
3128	2^457347-37	137676	Lelio R Paula	09/2017
3129	2^457322-2786393	137668	Enzo Doria	10/2015
3130	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
3131	34015^11134+11134^34015	137647	Hans Havermann	06/2021
3132	2^457240-59939	137643	Enzo Doria	10/2015
3133	(856*10^137633-1)/9	137635	Robert Price	03/2020
3134	36232^6289+6289^36232	137631	Hans Havermann	05/2021
3135	2^457120-21575	137607	Enzo Doria	07/2013
3137	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
3136	30963^27722+27722^30963	137564	Hans Havermann	04/2021
3138	33722^12003+12003^33722	137562	Hans Havermann	06/2021
3139	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
3140	41901^1918+1918^41901	137555	Hans Havermann	06/2021
3141	(7*10^137551-1)/3	137552	Robert Price	08/2022
3142	32930^15021+15021^32930	137539	Hans Havermann	05/2021
3143	31178^25785+25785^31178	137538	Hans Havermann	05/2021
3144	419^52446+52446^419	137525	Norbert Schneider	11/2020
3145	2^456796-113513	137510	Enzo Doria	08/2014
3146	31788^21137+21137^31788	137485	Hans Havermann	04/2021
3147	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
3148	2^456503-114361	137422	Enzo Doria	01/2015
3149	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
3150	36248^6147+6147^36248	137332	Hans Havermann	05/2021
3151	31986^19651+19651^31986	137329	Hans Havermann	05/2021
3152	31817^20656+20656^31817	137292	Hans Havermann	05/2021
3153	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
3154	2^455922+76249	137247	Enzo Doria	05/2016
3155	31310^24171+24171^31310	137241	Hans Havermann	05/2021
3156	14^119741-119741^14	137239	Serge Batalov	04/2016
3157	35014^8297+8297^35014	137218	Hans Havermann	05/2021
3158	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
3160	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
3159	124^65536+57^65536	137195	Serge Batalov	03/2018
3161	2^455689+72677	137177	Enzo Doria	04/2016
3162	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
3163	31287^24128+24128^31287	137116	Hans Havermann	05/2021
3164	(37^87421-1)/36	137093	Robert Price	03/2012
3165	36233^6070+6070^36233	137077	Hans Havermann	05/2021
3166	(8*10^137073-17)/9	137073	Serge Batalov	11/2022
3167	38418^3697+3697^38418	137070	Hans Havermann	04/2021
3168	2^455323-57	137066	Lelio R Paula	09/2017
3169	(56*10^137019+583)/9	137020	Robert Price	08/2021
3170	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
3171	2^455025-112723	136977	Enzo Doria	06/2014
3172	33876^11039+11039^33876	136959	Hans Havermann	05/2021
3173	35142^7873+7873^35142	136919	Hans Havermann	05/2021
3174	66*10^136894+7	136896	Robert Price	07/2020
3175	2^454675-1777	136871	Yves Minet	10/2011
3176	31676^20931+20931^31676	136866	Hans Havermann	05/2021
3177	3*10^136829+29	136830	Robert Price	05/2018
3178	4*10^136813-57	136814	Robert Price	10/2018
3179	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
3180	37359^4588+4588^37359	136795	Hans Havermann	05/2021
3181	2^454348-53	136773	Lelio R Paula	09/2017
3182	31^91680-2	136729	Lelio R Paula	05/2017
3183	2^454199-113697	136728	Enzo Doria	09/2014
3184	30785^27622+27622^30785	136725	Hans Havermann	05/2021
3185	32973^14014+14014^32973	136725	Hans Havermann	05/2021
3187	7*10^136716+69	136717	Robert Price	07/2019
3186	36002^6273+6273^36002	136717	Hans Havermann	05/2021
3188	6*10^136692+53	136693	Robert Price	05/2020
3189	(13*10^136687+47)/3	136688	Robert Price	10/2018
3190	2^453935-2791357	136649	Enzo Doria	01/2016
3191	2^453906-69131	136640	Enzo Doria	11/2015
3192	33232^12915+12915^33232	136620	Hans Havermann	05/2021
3193	2^453791+1873913	136605	Enzo Doria	06/2016
3194	34166^9951+9951^34166	136592	Hans Havermann	05/2021
3195	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
3196	31102^24635+24635^31102	136587	Hans Havermann	05/2021
3197	580^49413+49413^580	136550	Norbert Schneider	02/2019
3198	2^453503-2788297	136519	Enzo Doria	11/2015
3199	34989^7958+7958^34989	136486	Hans Havermann	12/2020
3200	(2*10^136484+187)/9	136484	Robert Price	06/2022
3201	31007^25158+25158^31007	136452	Hans Havermann	11/2020
3202	2^453267-113827	136447	Enzo Doria	09/2014
3203	32234^17085+17085^32234	136435	Hans Havermann	12/2020
3204	2^453102+1877629	136398	Enzo Doria	08/2016
3205	31016^24981+24981^31016	136397	Hans Havermann	12/2020
3206	(62*10^136384-791)/9	136385	Robert Price	06/2019
3207	34171^9798+9798^34171	136382	Hans Havermann	12/2020
3208	(17*10^136354-113)/3	136355	Robert Price	06/2021
3209	32756^14541+14541^32756	136350	Hans Havermann	11/2020
3210	32205^17086+17086^32205	136313	Hans Havermann	12/2020
3211	(25*10^136303+161)/3	136304	Robert Price	09/2019
3212	35337^7196+7196^35337	136299	Hans Havermann	12/2020
3213	(182*10^136291+1)/3	136293	Robert Price	02/2020
3214	(88*10^136234+83)/9	136235	Robert Price	03/2022
3215	23*10^136225-7	136227	Robert Price	02/2020
3216	L(651821)	136223	Henri Lifchitz	09/2008
3217	2^452460+77701	136205	Enzo Doria	05/2016
3218	2^452440-114755	136199	Enzo Doria	04/2015
3219	32286^16489+16489^32286	136157	Hans Havermann	11/2020
3220	(47*10^136141+493)/9	136142	Robert Price	03/2019
3221	40392^2339+2339^40392	136082	Hans Havermann	12/2020
3222	2*10^136057-43	136058	Robert Price	04/2018
3223	(2^451956-5)/181	136051	Lelio R Paula	07/2015
3224	2^451947-22165	136050	Enzo Doria	07/2013
3225	2^451787-21805	136002	Enzo Doria	07/2013
3226	2^451734-112817	135986	Enzo Doria	06/2014
3227	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
3228	2^451705-21879	135977	Enzo Doria	07/2013
3229	2^451560-112349	135934	Enzo Doria	06/2014
3230	2^451530+45	135925	Lelio R Paula	08/2017
3231	31622^19875+19875^31622	135922	Hans Havermann	11/2020
3232	(25*10^135906-73)/3	135907	Robert Price	09/2019
3233	2^451450-21743	135900	Enzo Doria	07/2013
3234	(7*10^135879+11)/9	135879	Tyler Busby	01/2023
3235	35218^7199+7199^35218	135846	Hans Havermann	11/2020
3236	35661^6446+6446^35661	135844	Hans Havermann	11/2020
3237	31869^18248+18248^31869	135801	Hans Havermann	12/2020
3238	(77*10^135789+157)/9	135790	Robert Price	05/2022
3239	2^450805+65	135706	Lelio R Paula	08/2017
3240	30761^25728+25728^30761	135669	Hans Havermann	12/2020
3241	2*10^135663+69	135664	Robert Price	06/2020
3242	33962^9867+9867^33962	135651	Hans Havermann	11/2020
3243	34474^8605+8605^34474	135647	Hans Havermann	11/2020
3244	34501^8508+8508^34501	135583	Hans Havermann	12/2020
3245	35487^6614+6614^35487	135577	Hans Havermann	12/2020
3246	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
3247	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
3248	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
3249	(76*10^135553-49)/9	135554	Robert Price	07/2022
3250	(844*10^135527-7)/9	135529	Robert Price	05/2021

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PRP Records

Probable Primes Top 10000

(291910 PRPs in the top)