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 ?
3251	14^119741-119741^14	137239	Serge Batalov	04/2016
3252	35014^8297+8297^35014	137218	Hans Havermann	05/2021
3253	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
3255	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
3254	124^65536+57^65536	137195	Serge Batalov	03/2018
3256	2^455689+72677	137177	Enzo Doria	04/2016
3257	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
3258	31287^24128+24128^31287	137116	Hans Havermann	05/2021
3259	(37^87421-1)/36	137093	Robert Price	03/2012
3260	36233^6070+6070^36233	137077	Hans Havermann	05/2021
3261	(8*10^137073-17)/9	137073	Serge Batalov	11/2022
3262	38418^3697+3697^38418	137070	Hans Havermann	04/2021
3263	2^455323-57	137066	Lelio R Paula	09/2017
3264	(56*10^137019+583)/9	137020	Robert Price	08/2021
3265	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
3266	2^455025-112723	136977	Enzo Doria	06/2014
3267	33876^11039+11039^33876	136959	Hans Havermann	05/2021
3268	35142^7873+7873^35142	136919	Hans Havermann	05/2021
3269	66*10^136894+7	136896	Robert Price	07/2020
3270	2^454675-1777	136871	Yves Minet	10/2011
3271	31676^20931+20931^31676	136866	Hans Havermann	05/2021
3272	3*10^136829+29	136830	Robert Price	05/2018
3273	4*10^136813-57	136814	Robert Price	10/2018
3274	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
3275	37359^4588+4588^37359	136795	Hans Havermann	05/2021
3276	2^454348-53	136773	Lelio R Paula	09/2017
3277	31^91680-2	136729	Lelio R Paula	05/2017
3278	2^454199-113697	136728	Enzo Doria	09/2014
3279	30785^27622+27622^30785	136725	Hans Havermann	05/2021
3280	32973^14014+14014^32973	136725	Hans Havermann	05/2021
3282	7*10^136716+69	136717	Robert Price	07/2019
3281	36002^6273+6273^36002	136717	Hans Havermann	05/2021
3283	6*10^136692+53	136693	Robert Price	05/2020
3284	(13*10^136687+47)/3	136688	Robert Price	10/2018
3285	2^453935-2791357	136649	Enzo Doria	01/2016
3286	2^453906-69131	136640	Enzo Doria	11/2015
3287	33232^12915+12915^33232	136620	Hans Havermann	05/2021
3288	2^453791+1873913	136605	Enzo Doria	06/2016
3289	34166^9951+9951^34166	136592	Hans Havermann	05/2021
3290	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
3291	31102^24635+24635^31102	136587	Hans Havermann	05/2021
3292	580^49413+49413^580	136550	Norbert Schneider	02/2019
3293	2^453503-2788297	136519	Enzo Doria	11/2015
3294	34989^7958+7958^34989	136486	Hans Havermann	12/2020
3295	(2*10^136484+187)/9	136484	Robert Price	06/2022
3296	31007^25158+25158^31007	136452	Hans Havermann	11/2020
3297	2^453267-113827	136447	Enzo Doria	09/2014
3298	32234^17085+17085^32234	136435	Hans Havermann	12/2020
3299	2^453102+1877629	136398	Enzo Doria	08/2016
3300	31016^24981+24981^31016	136397	Hans Havermann	12/2020
3301	(62*10^136384-791)/9	136385	Robert Price	06/2019
3302	34171^9798+9798^34171	136382	Hans Havermann	12/2020
3303	(17*10^136354-113)/3	136355	Robert Price	06/2021
3304	32756^14541+14541^32756	136350	Hans Havermann	11/2020
3305	32205^17086+17086^32205	136313	Hans Havermann	12/2020
3306	(25*10^136303+161)/3	136304	Robert Price	09/2019
3307	35337^7196+7196^35337	136299	Hans Havermann	12/2020
3308	(182*10^136291+1)/3	136293	Robert Price	02/2020
3309	(88*10^136234+83)/9	136235	Robert Price	03/2022
3310	23*10^136225-7	136227	Robert Price	02/2020
3311	L(651821)	136223	Henri Lifchitz	09/2008
3312	2^452460+77701	136205	Enzo Doria	05/2016
3313	2^452440-114755	136199	Enzo Doria	04/2015
3314	32286^16489+16489^32286	136157	Hans Havermann	11/2020
3315	(47*10^136141+493)/9	136142	Robert Price	03/2019
3316	40392^2339+2339^40392	136082	Hans Havermann	12/2020
3317	2*10^136057-43	136058	Robert Price	04/2018
3318	(2^451956-5)/181	136051	Lelio R Paula	07/2015
3319	2^451947-22165	136050	Enzo Doria	07/2013
3320	2^451787-21805	136002	Enzo Doria	07/2013
3321	2^451734-112817	135986	Enzo Doria	06/2014
3322	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
3323	2^451705-21879	135977	Enzo Doria	07/2013
3324	2^451560-112349	135934	Enzo Doria	06/2014
3325	2^451530+45	135925	Lelio R Paula	08/2017
3326	31622^19875+19875^31622	135922	Hans Havermann	11/2020
3327	(25*10^135906-73)/3	135907	Robert Price	09/2019
3328	2^451450-21743	135900	Enzo Doria	07/2013
3329	(7*10^135879+11)/9	135879	Tyler Busby	01/2023
3330	35218^7199+7199^35218	135846	Hans Havermann	11/2020
3331	35661^6446+6446^35661	135844	Hans Havermann	11/2020
3332	31869^18248+18248^31869	135801	Hans Havermann	12/2020
3333	(77*10^135789+157)/9	135790	Robert Price	05/2022
3334	2^450805+65	135706	Lelio R Paula	08/2017
3335	30761^25728+25728^30761	135669	Hans Havermann	12/2020
3336	2*10^135663+69	135664	Robert Price	06/2020
3337	33962^9867+9867^33962	135651	Hans Havermann	11/2020
3338	34474^8605+8605^34474	135647	Hans Havermann	11/2020
3339	34501^8508+8508^34501	135583	Hans Havermann	12/2020
3340	35487^6614+6614^35487	135577	Hans Havermann	12/2020
3341	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
3342	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
3343	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
3344	(76*10^135553-49)/9	135554	Robert Price	07/2022
3345	(844*10^135527-7)/9	135529	Robert Price	05/2021
3346	40387^2260+2260^40387	135463	Hans Havermann	12/2020
3347	2^449944-113247	135447	Enzo Doria	07/2014
3348	2^449770-113247	135395	Enzo Doria	07/2014
3349	2^449637-21471	135355	Enzo Doria	07/2013
3350	2^449571-75	135335	Lelio R Paula	08/2017
3351	(14*10^135301-53)/3	135302	Robert Price	12/2018
3352	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
3353	(13*10^135279+437)/9	135280	Robert Price	04/2018
3354	2^449330-35	135262	Lelio R Paula	08/2017
3355	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
3356	(13*10^135184-43)/3	135185	Robert Price	11/2018
3357	2^449049-115309	135178	Enzo Doria	07/2015
3358	(10^135174+191)/3	135174	Robert Price	02/2018
3359	2^449030-15	135172	Lelio R Paula	08/2017
3360	(157*10^135151-1)/3	135153	Robert Price	01/2022
3361	(2^448966+100280245065)	135153	Paul Bourdelais	05/2022
3362	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
3363	(37*10^135099+251)/9	135100	Robert Price	09/2021
3364	32221^15586+15586^32221	135095	Hans Havermann	12/2020
3365	2^448762-351401	135091	Enzo Doria	07/2015
3366	2*10^135083-43	135084	Robert Price	04/2018
3367	31357^20278+20278^31357	135056	Hans Havermann	12/2020
3368	32242^15445+15445^32242	135055	Hans Havermann	12/2020
3369	k(198476)	135054	Robert Price	07/2020
3370	32461^14470+14470^32461	135053	Hans Havermann	12/2020
3371	31353^20288+20288^31353	135045	Hans Havermann	12/2020
3372	5*10^135019+77	135020	Robert Price	12/2018
3373	(10^135011+719)/9	135011	Serge Batalov	12/2014
3374	(197*10^134978+7)/3	134980	Robert Price	12/2020
3375	2^448386-2786261	134978	Enzo Doria	03/2016
3376	(73*10^134939+143)/9	134940	Robert Price	07/2019
3377	33957^9392+9392^33957	134903	Hans Havermann	12/2020
3378	2^448113-113949	134896	Enzo Doria	11/2014
3379	30958^22755+22755^30958	134887	Hans Havermann	12/2020
3380	2^447888-2786639	134828	Enzo Doria	03/2016
3381	2^447870-396765	134823	Enzo Doria	07/2013
3382	2^447766-21791	134791	Enzo Doria	07/2013
3383	(19*10^134786-49)/3	134787	Robert Price	05/2019
3384	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
3385	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
3386	2^447552-1019	134727	Yves Minet	02/2014
3387	(2*10^134720-41)/3	134720	Robert Price	02/2018
3388	(25*10^134695-97)/9	134696	Robert Price	01/2022
3389	2^447437-113569	134692	Enzo Doria	08/2014
3390	2^447426-65	134689	Lelio R Paula	08/2017
3391	2^447357-2797573	134668	Enzo Doria	04/2016
3392	2^447278+93	134645	Lelio R Paula	08/2017
3393	33193^11370+11370^33193	134623	Hans Havermann	12/2020
3394	30736^23979+23979^30736	134619	Hans Havermann	11/2020
3395	2^447094-113193	134589	Enzo Doria	07/2014
3396	3^282041-9934	134568	Enzo Doria	05/2014
3397	2^447019-109039	134567	Enzo Doria	04/2014
3398	31376^19437+19437^31376	134561	Hans Havermann	12/2020
3399	2^446990-22041	134558	Enzo Doria	07/2013
3400	123^64370+122	134528	Karsten Bonath	04/2018
3401	30100^29461+29461^30100	134525	Hans Havermann	11/2020
3402	31251^20158+20158^31251	134519	Hans Havermann	11/2020
3403	2^446782-39701	134495	Enzo Doria	09/2015
3404	31817^16858+16858^31817	134485	Hans Havermann	12/2020
3405	32448^13937+13937^32448	134471	Hans Havermann	12/2020
3406	2^446494-16485	134409	Enzo Doria	04/2013
3407	30042^29785+29785^30042	134408	Hans Havermann	12/2020
3408	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
3409	2^446441+65	134393	Lelio R Paula	08/2017
3410	(10^134385+719)/9	134385	Serge Batalov	12/2014
3411	30043^29688+29688^30043	134370	Hans Havermann	12/2020
3412	(2*10^134364+529)/9	134364	Robert Price	01/2018
3413	34657^7512+7512^34657	134323	Hans Havermann	11/2020
3414	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
3415	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
3416	42035^1564+1564^42035	134270	Hans Havermann	12/2020
3418	(2^446022-7)/339	134264	Lelio R Paula	07/2015
3417	30621^24248+24248^30621	134264	Hans Havermann	12/2020
3419	30341^26562+26562^30341	134237	Hans Havermann	11/2020
3420	10^134209+99867	134210	Patrick De Geest	05/2021
3421	10^134209-80000001	134209	Robert Price	04/2021
3422	10^134209-323283	134209	Patrick De Geest	05/2021
3423	29976^29953+29953^29976	134186	Hans Havermann	12/2020
3424	35038^6755+6755^35038	134183	Hans Havermann	12/2020
3425	63^74568+2	134174	Lelio R Paula	06/2017
3426	2^445671-22071	134161	Enzo Doria	07/2013
3427	532^49205+49205^532	134129	Norbert Schneider	02/2019
3428	36453^4780+4780^36453	134127	Hans Havermann	04/2021
3429	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
3430	2^445515-113859	134114	Enzo Doria	10/2014
3432	(22*10^134111-37)/3	134112	Robert Price	04/2019
3431	31083^20636+20636^31083	134112	Hans Havermann	04/2021
3433	31622^17379+17379^31622	134079	Hans Havermann	04/2021
3434	(277*10^134059-7)/9	134061	Robert Price	02/2022
3435	2^445328-216917	134058	Enzo Doria	05/2014
3436	2^445202+1874899	134020	Enzo Doria	06/2016
3437	(35*10^134003-89)/9	134004	Robert Price	02/2022
3438	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
3439	(35*10^133979-593)/9	133980	Robert Price	07/2018
3440	2*10^133955+51	133956	Robert Price	05/2018
3441	(49*10^133952+437)/9	133953	Robert Price	09/2021
3442	2^444964-113639	133948	Enzo Doria	08/2014
3443	31811^16240+16240^31811	133943	Hans Havermann	04/2021
3444	10^133902+167841	133903	Patrick De Geest	05/2021
3446	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
3445	10^133902-100001	133902	Robert Price	07/2020
3447	2^444784-113859	133894	Enzo Doria	10/2014
3448	32303^13914+13914^32303	133846	Hans Havermann	04/2021
3449	(2276213*2^444444+1)/3	133797	Alex_soldier	11/2022
3450	(1403559*2^444444+1)/5	133797	Alex_soldier	11/2022
3451	(1209887*2^444444+1)/9	133797	Alex_soldier	11/2022
3452	(608239*2^444444+1)/25	133796	Alex_soldier	11/2022
3453	(1824587*2^444444+1)/27	133796	Alex_soldier	11/2022
3454	(40795*2^444444+1)/7	133795	Alex_soldier	11/2022
3455	30739^22458+22458^30739	133757	Hans Havermann	04/2021
3456	34942^6721+6721^34942	133739	Hans Havermann	04/2021
3457	(2^444046+100280245065)	133672	Paul Bourdelais	05/2022
3458	34792^6935+6935^34792	133638	Hans Havermann	04/2021
3459	(266*10^133603+1)/3	133605	Robert Price	04/2020
3460	32261^13842+13842^32261	133600	Hans Havermann	04/2021
3461	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
3462	(134*10^133573-11)/3	133575	Robert Price	01/2022
3463	62^74521-61^74521	133571	Robert Price	05/2013
3464	(182*10^133543+1)/3	133545	Robert Price	02/2020
3465	(103*10^133535+11)/3	133537	Robert Price	01/2021
3466	32589^12520+12520^32589	133537	Hans Havermann	03/2021
3467	34516^7373+7373^34516	133496	Hans Havermann	04/2021
3468	8*10^133487-37	133488	Robert Price	03/2022
3469	30135^26882+26882^30135	133482	Hans Havermann	04/2021
3470	2^443198-1867301	133416	Enzo Doria	03/2016
3471	(19*10^133390+101)/3	133391	Robert Price	09/2019
3472	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
3473	36117^4910+4910^36117	133311	Hans Havermann	04/2021
3474	2^442799+1874633	133296	Enzo Doria	06/2016
3475	L(637751)	133283	Henri Lifchitz	09/2008
3476	109^65410-2	133269	Lelio R Paula	10/2017
3477	2^442688-113489	133263	Enzo Doria	08/2014
3478	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
3479	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
3480	2^442437-1849993	133187	Enzo Doria	08/2015
3481	2^442430-2791721	133185	Enzo Doria	03/2016
3482	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
3483	29959^27870+27870^29959	133172	Hans Havermann	03/2021
3484	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
3485	34240^7737+7737^34240	133145	Hans Havermann	03/2021
3486	452^50145+50145^452	133142	Norbert Schneider	09/2020
3487	30659^21796+21796^30659	133011	Hans Havermann	04/2021
3488	33276^9935+9935^33276	133010	Hans Havermann	04/2021
3489	30111^26122+26122^30111	133001	Hans Havermann	04/2021
3490	30790^20869+20869^30790	132998	Hans Havermann	04/2021
3492	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
3491	8*10^132994-27	132995	Robert Price	10/2021
3493	(109*10^132992+11)/3	132994	Robert Price	06/2022
3494	2^441781-2787883	132990	Enzo Doria	03/2016
3495	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
3496	2^441618+37	132941	Lelio R Paula	08/2017
3497	34857^6514+6514^34857	132940	Hans Havermann	04/2021
3498	34065^7988+7988^34065	132937	Hans Havermann	04/2021
3499	35571^5452+5452^35571	132914	Hans Havermann	04/2021
3500	2^441521-113575	132912	Enzo Doria	08/2014

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