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	32303^13914+13914^32303	133846	Hans Havermann	04/2021
3002	30739^22458+22458^30739	133757	Hans Havermann	04/2021
3003	34942^6721+6721^34942	133739	Hans Havermann	04/2021
3004	34792^6935+6935^34792	133638	Hans Havermann	04/2021
3005	(266*10^133603+1)/3	133605	Robert Price	04/2020
3006	32261^13842+13842^32261	133600	Hans Havermann	04/2021
3007	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
3008	(134*10^133573-11)/3	133575	Robert Price	01/2022
3009	62^74521-61^74521	133571	Robert Price	05/2013
3010	(182*10^133543+1)/3	133545	Robert Price	02/2020
3011	(103*10^133535+11)/3	133537	Robert Price	01/2021
3012	32589^12520+12520^32589	133537	Hans Havermann	03/2021
3013	34516^7373+7373^34516	133496	Hans Havermann	04/2021
3014	30135^26882+26882^30135	133482	Hans Havermann	04/2021
3015	2^443198-1867301	133416	Enzo Doria	03/2016
3016	(19*10^133390+101)/3	133391	Robert Price	09/2019
3017	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
3018	36117^4910+4910^36117	133311	Hans Havermann	04/2021
3019	2^442799+1874633	133296	Enzo Doria	06/2016
3020	L(637751)	133283	Henri Lifchitz	09/2008
3021	109^65410-2	133269	Lelio R Paula	10/2017
3022	2^442688-113489	133263	Enzo Doria	08/2014
3023	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
3024	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
3025	2^442437-1849993	133187	Enzo Doria	08/2015
3026	2^442430-2791721	133185	Enzo Doria	03/2016
3027	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
3028	29959^27870+27870^29959	133172	Hans Havermann	03/2021
3029	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
3030	34240^7737+7737^34240	133145	Hans Havermann	03/2021
3031	452^50145+50145^452	133142	Norbert Schneider	09/2020
3032	30659^21796+21796^30659	133011	Hans Havermann	04/2021
3033	33276^9935+9935^33276	133010	Hans Havermann	04/2021
3034	30111^26122+26122^30111	133001	Hans Havermann	04/2021
3035	30790^20869+20869^30790	132998	Hans Havermann	04/2021
3037	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
3036	8*10^132994-27	132995	Robert Price	10/2021
3038	2^441781-2787883	132990	Enzo Doria	03/2016
3039	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
3040	2^441618+37	132941	Lelio R Paula	08/2017
3041	34857^6514+6514^34857	132940	Hans Havermann	04/2021
3042	34065^7988+7988^34065	132937	Hans Havermann	04/2021
3043	35571^5452+5452^35571	132914	Hans Havermann	04/2021
3044	2^441521-113575	132912	Enzo Doria	08/2014
3045	7*10^132884-99	132885	Robert Price	06/2019
3046	(103*10^132879+17)/3	132881	Robert Price	08/2020
3047	2^441396-65	132874	Lelio R Paula	08/2017
3048	33350^9633+9633^33350	132859	Hans Havermann	04/2021
3049	2^441330+1871959	132854	Enzo Doria	05/2016
3050	2^441063+383	132774	Lelio R Paula	06/2012
3051	(10^132753+7)/17/19	132751	Alfred Reich	06/2021
3052	(22*10^132746+53)/3	132747	Robert Price	07/2019
3053	(22*10^132732+119)/3	132733	Robert Price	04/2021
3054	2^440846+1870909	132708	Enzo Doria	05/2016
3055	2^440656-113489	132651	Enzo Doria	08/2014
3056	numbpart(14180123587)	132646	Serge Batalov	04/2017
3057	32950^10591+10591^32950	132622	Hans Havermann	04/2021
3058	33302^9597+9597^33302	132614	Hans Havermann	04/2021
3059	(19*10^132550+191)/3	132551	Robert Price	05/2019
3060	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
3061	(38^83891+1)/39	132529	Robert Price	09/2013
3062	2*10^132493-43	132494	Robert Price	04/2018
3063	31352^16809+16809^31352	132480	Hans Havermann	04/2021
3064	(418*10^132441+23)/9	132443	Robert Price	02/2020
3065	2^439931-21	132433	Lelio R Paula	08/2017
3066	47^79201-46^79201	132432	Robert Price	10/2012
3067	2^439897-113653	132423	Enzo Doria	08/2014
3068	35505^5362+5362^35505	132410	Hans Havermann	03/2021
3069	30079^25222+25222^30079	132402	Hans Havermann	04/2021
3070	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
3071	(695*10^132356+7)/9	132358	Robert Price	12/2021
3072	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
3073	2^439576-113247	132326	Enzo Doria	07/2014
3074	30059^25230+25230^30059	132318	Hans Havermann	04/2021
3075	2^439497-29143	132302	Enzo Doria	07/2015
3076	2^439409-114193	132276	Enzo Doria	12/2014
3077	(44*10^132233-233)/9	132234	Robert Price	01/2019
3078	9*10^132148-7	132149	Robert Price	09/2015
3079	(47*10^132125-119)/9	132126	Robert Price	05/2019
3080	2^438845+1870217	132106	Enzo Doria	05/2016
3081	2^438789+87855	132089	Lelio R Paula	01/2016
3082	2^438774-2786411	132085	Enzo Doria	03/2016
3083	2^438755-1848205	132079	Enzo Doria	07/2015
3084	30502^21381+21381^30502	132075	Hans Havermann	04/2021
3085	2^438739-112087	132074	Enzo Doria	06/2014
3086	35872^4777+4777^35872	131979	Hans Havermann	04/2021
3087	31198^16945+16945^31198	131938	Hans Havermann	03/2021
3088	13907#+(318259#)/(13907#)	131923	Makoto Morimoto	10/2017
3089	L(631181)	131910	Henri Lifchitz	09/2008
3090	(47*10^131886-119)/9	131887	Robert Price	05/2019
3091	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
3092	2^438079-1863877	131875	Enzo Doria	03/2016
3093	(16*10^131872-37)/3	131873	Robert Price	05/2021
3094	(2^438067+5)/329	131869	Lelio R Paula	06/2015
3095	2^437908-113855	131824	Enzo Doria	09/2014
3096	2^437884-286349	131817	Enzo Doria	07/2015
3097	5^188558+4	131797	Tyler NeSmith	05/2021
3098	(11*10^131784-17)/3	131785	Robert Price	06/2018
3100	4*10^131719-93	131720	Robert Price	07/2020
3099	31629^14606+14606^31629	131720	Hans Havermann	04/2021
3101	3^276062-112292	131716	Enzo Doria	07/2014
3102	(7*10^131682+89)/3	131683	Robert Price	08/2020
3103	29512^28969+28969^29512	131681	Hans Havermann	03/2021
3104	2^437343+75953	131654	Enzo Doria	04/2016
3105	35^85243-34^85243	131621	Robert Price	05/2012
3106	(28*10^131586+59)/3	131587	Robert Price	05/2021
3107	(59*10^131575+391)/9	131576	Robert Price	03/2021
3108	39984^1945+1945^39984	131505	Hans Havermann	03/2021
3109	(203*10^131457+1)/3	131459	Robert Price	03/2020
3110	7*10^131421-41	131422	Robert Price	08/2021
3111	87309^32+32^87309	131414	Hans Havermann	03/2021
3112	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
3113	2^436451+1884713	131385	Enzo Doria	03/2017
3114	2^436365+35	131359	Robert Price	11/2015
3115	2^436300+1866871	131340	Enzo Doria	03/2016
3116	(7*10^131339+179)/3	131340	Robert Price	09/2018
3117	14^114592-3	131338	Paul Bourdelais	12/2020
3118	36197^4236+4236^36197	131285	Hans Havermann	04/2021
3119	(37*10^131270+341)/9	131271	Robert Price	08/2018
3120	29863^24790+24790^29863	131227	Hans Havermann	03/2021
3121	(5*10^131223-29)/3	131224	Robert Price	03/2018
3122	29524^27825+27825^29524	131218	Hans Havermann	03/2021
3123	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
3124	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
3125	30639^19136+19136^30639	131192	Hans Havermann	04/2021
3126	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
3127	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
3128	2^435773+1875557	131181	Enzo Doria	06/2016
3130	(16*10^131180+167)/3	131181	Robert Price	06/2019
3129	(26*10^131180-77)/3	131181	Robert Price	11/2019
3131	(25*10^131144-7)/9	131145	Robert Price	05/2018
3132	2^435612-2789939	131133	Enzo Doria	12/2015
3133	33976^7231+7231^33976	131121	Hans Havermann	03/2021
3134	33715^7746+7746^33715	131121	Hans Havermann	03/2021
3135	66^72047-65^72047	131093	Robert Price	09/2013
3136	(5*10^131090+37)/3	131091	Robert Price	03/2018
3137	2^435468+75631	131089	Enzo Doria	04/2016
3138	37^83588-2	131083	Lelio R Paula	08/2015
3139	(4^217720+11)/3	131081	Robert Price	02/2017
3140	30407^20448+20448^30407	131074	Hans Havermann	04/2021
3141	29487^27836+27836^29487	131059	Hans Havermann	04/2021
3142	29962^23615+23615^29962	131030	Hans Havermann	03/2021
3143	2^435202-113193	131009	Enzo Doria	07/2014
3144	41705^1384+1384^41705	131002	Hans Havermann	04/2021
3145	9*10^130998-19	130999	Robert Price	07/2019
3146	36243^4108+4108^36243	130969	Hans Havermann	04/2021
3147	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
3148	2^434835-111937	130899	Enzo Doria	05/2014
3149	(62*10^130895-629)/9	130896	Robert Price	07/2021
3150	2^434685+72257	130854	Enzo Doria	04/2016
3151	(7*10^130825+113)/3	130826	Robert Price	02/2018
3152	2^434539-29317	130810	Enzo Doria	07/2015
3153	(74*10^130791+637)/9	130792	Robert Price	01/2022
3154	2^434469-114259	130789	Enzo Doria	01/2015
3155	2^434246+33	130722	Robert Price	11/2015
3156	30156^21599+21599^30156	130710	Hans Havermann	04/2021
3157	(17*10^130695-161)/9	130695	Robert Price	02/2021
3158	30513^19148+19148^30513	130661	Hans Havermann	03/2021
3159	29736^24761+24761^29736	130654	Hans Havermann	04/2021
3160	9*10^130638+41	130639	Robert Price	08/2020
3161	2^433911-91	130621	Lelio R Paula	06/2017
3162	30786^17449+17449^30786	130588	Hans Havermann	03/2021
3163	2^433744-114419	130570	Enzo Doria	02/2015
3165	2^433708+1869451	130560	Enzo Doria	05/2016
3164	2^433710+93	130560	Lelio R Paula	06/2017
3166	(9629^32768+1)/120501441265666	130520	Kellen Shenton	05/2021
3167	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
3168	3^273521+10	130503	Tyler NeSmith	01/2021
3169	41659^1356+1356^41659	130487	Hans Havermann	03/2021
3170	4*10^130480+9	130481	Robert Price	05/2015
3171	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
3172	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
3173	(31*10^130414-49)/9	130415	Robert Price	11/2021
3174	33481^7848+7848^33481	130401	Hans Havermann	03/2021
3175	(22*10^130392+203)/9	130393	Robert Price	10/2021
3176	29773^23950+23950^29773	130386	Hans Havermann	04/2021
3177	2^433023-113497	130353	Enzo Doria	08/2014
3178	31175^15178+15178^31175	130350	Hans Havermann	04/2021
3179	2^433002+1179379	130347	Enzo Doria	06/2016
3180	2^432974+19	130339	Robert Price	08/2015
3181	31903^12168+12168^31903	130331	Hans Havermann	04/2021
3182	29387^27112+27112^29387	130278	Hans Havermann	04/2021
3183	29577^25370+25370^29577	130267	Hans Havermann	04/2021
3184	31738^12685+12685^31738	130231	Hans Havermann	03/2021
3185	44235^878+878^44235	130206	Hans Havermann	04/2021
3186	32160^11171+11171^32160	130187	Hans Havermann	04/2021
3187	29489^25956+25956^29489	130172	Hans Havermann	04/2021
3188	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
3189	33005^8766+8766^33005	130133	Hans Havermann	04/2021
3190	2^432217+41	130111	Lelio R Paula	06/2017
3191	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
3192	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
3193	97^65480-2	130094	Lelio R Paula	05/2017
3194	36007^4102+4102^36007	130094	Hans Havermann	04/2021
3195	4*10^130088-89	130089	Robert Price	11/2018
3196	2^432117-113215	130081	Enzo Doria	07/2014
3197	2^431804+72511	129986	Enzo Doria	04/2016
3198	(13*10^129896+137)/3	129897	Robert Price	06/2021
3199	(13*10^129890+71)/3	129891	Robert Price	06/2021
3200	37832^2709+2709^37832	129871	Hans Havermann	04/2021
3201	31055^15184+15184^31055	129853	Hans Havermann	04/2021
3202	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
3203	31385^13702+13702^31385	129833	Hans Havermann	04/2021
3204	(47*10^129789-119)/9	129790	Robert Price	05/2019
3205	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
3206	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
3207	2^430807+1869563	129686	Enzo Doria	05/2016
3208	2^430721-21429	129660	Enzo Doria	07/2013
3209	(4*10^129618+89)/3	129619	Robert Price	08/2021
3210	2^430415-276271	129568	Enzo Doria	07/2015
3211	32282^10311+10311^32282	129558	Hans Havermann	04/2021
3212	29486^24741+24741^29486	129545	Hans Havermann	04/2021
3213	(29*10^129543+313)/9	129544	Robert Price	04/2021
3214	37095^3104+3104^37095	129533	Hans Havermann	04/2021
3215	31132^14459+14459^31132	129514	Hans Havermann	04/2021
3216	32582^9435+9435^32582	129506	Hans Havermann	03/2021
3217	30442^17953+17953^30442	129505	Hans Havermann	03/2021
3218	(199*10^129487-7)/3	129489	Robert Price	05/2020
3219	2^430142-2791721	129486	Enzo Doria	03/2016
3220	(7*10^129472-13)/3	129473	Robert Price	07/2018
3221	(8*10^129469+79)/3	129470	Robert Price	10/2020
3222	31678^12213+12213^31678	129463	Hans Havermann	04/2021
3223	31100^14439+14439^31100	129362	Hans Havermann	04/2021
3224	33009^8288+8288^33009	129345	Hans Havermann	04/2021
3225	29675^22804+22804^29675	129324	Hans Havermann	04/2021
3226	29068^28099+28099^29068	129315	Hans Havermann	04/2021
3227	2^429568-21017	129313	Enzo Doria	07/2013
3228	(10^129295+83)/3	129295	Robert Price	08/2021
3229	(853*10^129274-7)/9	129276	Robert Price	07/2021
3230	30958^14961+14961^30958	129249	Hans Havermann	04/2021
3231	(11*10^129239-179)/3	129240	Robert Price	09/2018
3232	28659^28988+28988^28659	129208	Norbert Schneider	02/2021
3233	29423^24616+24616^29423	129203	Hans Havermann	03/2021
3234	2^429194-112685	129201	Enzo Doria	06/2014
3235	2^429145-2780449	129186	Enzo Doria	04/2016
3236	32500^9427+9427^32500	129168	Hans Havermann	04/2021
3237	33577^7014+7014^33577	129136	Hans Havermann	03/2021
3238	2^428892-113453	129110	Enzo Doria	07/2014
3239	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
3240	2^428727-113959	129060	Enzo Doria	10/2014
3241	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
3242	(10^129051-31)/3	129051	Serge Batalov	12/2014
3243	(134*10^129038+7)/3	129040	Robert Price	02/2020
3244	2^428564+71161	129011	Enzo Doria	04/2016
3245	28781^28930+28930^28781	129002	Norbert Schneider	02/2021
3246	29065^27424+27424^29065	128995	Hans Havermann	04/2021
3247	2^428502-113285	128992	Enzo Doria	07/2014
3248	2^428421-21373	128968	Enzo Doria	06/2013
3249	L(616787)	128901	Henri Lifchitz	09/2008
3250	20^99055-3	128874	Paul Bourdelais	12/2020

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Probable Primes Top 10000

(288949 PRPs in the top)