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	99*10^189876-7	189878	Robert Price	07/2020
3252	41147^41147+30^30	189867	Henri Lifchitz	09/2024
3253	2^630359+1788953	189757	Enzo Doria	05/2016
3254	2^630228+1871971	189718	Enzo Doria	05/2016
3255	2^630108+781	189682	Lelio R Paula	08/2013
3256	2^629870-1867811	189610	Enzo Doria	04/2016
3257	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
3258	2^629326+2792929	189447	Enzo Doria	02/2016
3259	4*10^189401+13	189402	Robert Price	02/2021
3260	(10^189385-61)/3	189385	Serge Batalov	12/2014
3261	2^629036+1874011	189359	Enzo Doria	06/2016
3262	2^628930+80779	189327	Enzo Doria	07/2016
3263	(134*10^189309-11)/3	189311	Robert Price	01/2022
3264	9*10^189306-11	189307	Mischa Rodermond	04/2023
3265	3^396740-396740^3	189294	Henri Lifchitz	07/2024
3266	2^628582+1179439	189223	Enzo Doria	06/2016
3267	(44*10^188999-503)/9	189000	Robert Price	12/2018
3268	(16*10^188823+167)/3	188824	Robert Price	06/2019
3269	(10^188796+7)/4967/71933	188788	Alfred Reich	08/2021
3270	2^627037-2785843	188757	Enzo Doria	10/2015
3271	(10^188566+7)/311640753181661	188552	Alfred Reich	04/2022
3272	(16*10^188457+161)/3	188458	Robert Price	02/2019
3273	L(901657)	188436	Renaud Lifchitz	11/2008
3274	(19*10^188375+137)/3	188376	Robert Price	03/2022
3275	2^625651+74213	188340	Enzo Doria	04/2016
3276	2^625584-460919	188320	Enzo Doria	06/2015
3277	(8*10^188308-71)/9	188308	Serge Batalov	11/2022
3278	5^269399-3^269399-1	188302	Jon Grantham	08/2023
3279	(14*10^188218+139)/9	188219	Robert Price	11/2021
3280	40760^40821-40821^40760	188195	Norbert Schneider	07/2024
3281	(10^188164+359)/9	188164	Serge Batalov	12/2014
3282	2^624481-113611	187988	Enzo Doria	08/2014
3283	(2^624389+125582)/2	187960	Stefano Morozzi	09/2019
3284	(2^624389+166982)/2	187960	Stefano Morozzi	09/2019
3285	(2^624389+179886)/2	187960	Stefano Morozzi	09/2019
3286	(2^624387+64466)/2	187959	Stefano Morozzi	09/2019
3287	(2^624378+112990)/2	187957	Stefano Morozzi	09/2019
3288	(2^624380+161986)/2	187957	Stefano Morozzi	09/2019
3290	(2^624376+55762)/2	187956	Stefano Morozzi	09/2019
3289	(2^624377+169506)/2	187956	Stefano Morozzi	09/2019
3291	(2^624355+80178)/2	187950	Stefano Morozzi	09/2019
3292	(2^624351+61350)/2	187949	Stefano Morozzi	09/2019
3293	(2^624341+63462)/2	187946	Stefano Morozzi	09/2019
3294	(2^624344+135990)/2	187946	Stefano Morozzi	09/2019
3295	(2^624344+183898)/2	187946	Stefano Morozzi	09/2019
3297	(2^624340+126982)/2	187945	Stefano Morozzi	09/2019
3296	(2^624338+196110)/2	187945	Stefano Morozzi	09/2019
3298	(2^624337+105162)/2	187944	Stefano Morozzi	09/2019
3299	(2^624333+44594)/2	187943	Stefano Morozzi	09/2019
3300	(2^624321+88742)/2	187940	Stefano Morozzi	09/2019
3301	(2^624324+135178)/2	187940	Stefano Morozzi	09/2019
3302	(2^624317+14186)/2	187938	Stefano Morozzi	09/2019
3303	(2^624313+24450)/2	187937	Stefano Morozzi	09/2019
3304	(2^624309+184590)/2	187936	Stefano Morozzi	09/2019
3306	(2^624307+152658)/2	187935	Stefano Morozzi	09/2019
3305	(2^624307+185978)/2	187935	Stefano Morozzi	09/2019
3307	(2^624303+40814)/2	187934	Stefano Morozzi	09/2019
3308	(2^624304+99238)/2	187934	Stefano Morozzi	09/2019
3309	2^624077-112723	187866	Enzo Doria	07/2014
3310	2^624008+1874941	187846	Enzo Doria	06/2016
3311	2^623870+78679	187804	Enzo Doria	05/2016
3312	2^623714-114035	187757	Enzo Doria	11/2014
3313	2^623651-1834251	187738	Enzo Doria	07/2015
3314	(7*10^187645+53)/3	187646	Robert Price	05/2018
3315	21650^43269+43269^21650	187591	Norbert Schneider	02/2023
3316	2^623146+1879609	187586	Enzo Doria	09/2016
3317	(401*10^187512+13)/9	187514	Robert Price	09/2021
3318	(5*10^187471+91)/3	187472	Robert Price	04/2018
3319	2^622500+81931	187392	Enzo Doria	08/2016
3320	(13*10^187382-157)/9	187383	Robert Price	05/2021
3321	2^622300-1861739	187331	Enzo Doria	12/2015
3322	(22*10^187317-91)/3	187318	Robert Price	02/2022
3323	(38*10^187281+349)/9	187282	Robert Price	10/2018
3324	2^622052+76771	187257	Enzo Doria	05/2016
3325	2^622005-24091	187243	Enzo Doria	08/2013
3326	7*10^187205-57	187206	Robert Price	06/2020
3327	2^621879-351787	187205	Enzo Doria	07/2015
3328	(5*10^187168-53)/3	187169	Robert Price	09/2020
3329	(23*10^187164-143)/3	187165	Robert Price	12/2019
3330	2^621700+79411	187151	Enzo Doria	06/2016
3331	2^621597+39	187120	Jon Grantham	08/2023
3332	Phi(271207,-5)	187112	Henri Lifchitz	12/2025
3333	(7*10^187101+131)/3	187102	Robert Price	06/2020
3334	(2*10^187062-71)/3	187062	Robert Price	12/2017
3335	V(1118570)	187013	Serge Batalov	07/2024
3336	2^620929-113203	186919	Enzo Doria	07/2014
3337	10^186842+168223	186843	Patrick De Geest	07/2018
3338	10^186842-8001	186842	Robert Price	03/2018
3339	V(1117640)/13411681/26823361/575709775681/989889277441	186814	Serge Batalov	07/2024
3340	2^620347-1777	186744	Lelio R Paula	07/2013
3341	(11*10^186659+133)/9	186660	Robert Price	04/2022
3342	11^179143-4170	186559	Enzo Doria	12/2012
3343	(13^186535)%(10^186535)	186535	Henri Lifchitz	05/2025
3345	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
3344	Phi(266863,-5)	186529	Henri Lifchitz	12/2025
3346	2*10^186517+33	186518	Robert Price	11/2021
3347	2^619297-2792353	186427	Enzo Doria	02/2016
3348	(49*10^186409+383)/9	186410	Robert Price	04/2019
3349	2^618940-460139	186320	Enzo Doria	06/2015
3350	Phi(343570,2^5)	186109	Henri Lifchitz	12/2025
3351	2^618046+74179	186051	Enzo Doria	04/2016
3352	3*10^186019+11	186020	Robert Price	07/2018
3353	(16*10^185978-19)/3	185979	Robert Price	02/2019
3354	(22*10^185950-7)/3	185951	Robert Price	12/2022
3355	2*10^185930-3	185931	Robert Price	07/2015
3356	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
3357	4*10^185905+91	185906	Robert Price	08/2018
3358	(34*10^185902-601)/9	185903	Robert Price	07/2022
3359	(19*10^185873+131)/3	185874	Robert Price	06/2020
3360	(37*10^185811+377)/9	185812	Robert Price	11/2018
3361	2^617250+9385	185811	Lelio R Paula	07/2013
3362	2^617130+9	185775	Stefano Morozzi	05/2021
3363	39^116749+2	185756	Robert Price	04/2015
3364	2^616924-39719	185713	Enzo Doria	09/2015
3365	2^616712+1867621	185649	Enzo Doria	04/2016
3366	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
3367	8*10^185529-67	185530	Robert Price	08/2019
3368	(5*10^185520-11)/3	185521	Tyler Busby	02/2023
3369	5*2^616124+3	185473	Jon Grantham	07/2023
3370	2^615916+26791	185410	Enzo Doria	12/2023
3371	4*10^185355+9	185356	Robert Price	05/2015
3372	(16*10^185347+89)/3	185348	Robert Price	03/2021
3373	40247^40247-56^56	185327	Henri Lifchitz	08/2024
3374	2^615622+76639	185321	Enzo Doria	05/2016
3375	2^615591+1879223	185312	Enzo Doria	08/2016
3376	2^615587+217013	185311	Enzo Doria	12/2023
3377	2^615503+1876643	185285	Enzo Doria	07/2016
3378	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
3380	(4*10^185221-91)/3	185222	Robert Price	03/2018
3379	(7*10^185221+131)/3	185222	Robert Price	06/2020
3381	(62*10^185216-413)/9	185217	Robert Price	09/2021
3382	(232*10^185180+17)/3	185182	Robert Price	04/2021
3383	56*10^185139-3	185141	Robert Price	03/2020
3384	(28*10^185105+47)/3	185106	Robert Price	02/2021
3385	2^614783-2790097	185069	Enzo Doria	12/2015
3386	2^614745-29323	185057	Enzo Doria	07/2015
3387	(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840	185052	Serge Batalov	07/2013
3388	(49*10^184993-67)/9	184994	Robert Price	03/2019
3389	(5*10^184954-191)/3	184955	Robert Price	05/2021
3390	(14*10^184950+211)/9	184951	Robert Price	04/2018
3391	2^614360+215221	184941	Enzo Doria	11/2023
3392	2^614315+81353	184928	Enzo Doria	08/2016
3393	2^614294-1849961	184921	Enzo Doria	08/2015
3394	2^614266+1877809	184913	Enzo Doria	08/2016
3395	(185*10^184878-11)/3	184880	Robert Price	10/2020
3396	91*10^184867-9	184869	Robert Price	06/2021
3397	(37^117841-1)/581320056003516	184784	Paul Vanderveen	06/2025
3398	39803^40170-40170^39803	184779	Norbert Schneider	05/2024
3399	(14789^44521-1)/(14789^211-1)	184770	Ryan Propper	11/2023
3400	(85*10^184768+77)/9	184769	Robert Price	07/2022
3401	2^613715-1860727	184747	Enzo Doria	11/2015
3402	(4*10^184730+89)/3	184731	Robert Price	08/2021
3403	2*10^184723+41	184724	Robert Price	05/2018
3404	(49*10^184703+293)/9	184704	Robert Price	03/2021
3405	2^613487-349987	184678	Enzo Doria	07/2015
3406	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
3407	14^161089-161089^14	184629	Serge Batalov	05/2016
3408	40008^40109-40109^40008	184588	Norbert Schneider	05/2024
3409	2^613033-114621	184542	Enzo Doria	05/2015
3410	3*2^612759+5	184460	Jon Grantham	07/2023
3411	2^612587+213413	184408	Enzo Doria	09/2023
3413	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
3412	Phi(193247,-9)	184404	Henri Lifchitz	12/2025
3414	2^612424+212341	184358	Enzo Doria	08/2023
3415	2^612341-1604809	184334	Enzo Doria	05/2015
3416	(11*10^184308-161)/3	184309	Robert Price	11/2021
3417	625^65919+624	184302	Alfred Reich	04/2026
3418	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
3419	(14*10^184150+37)/3	184151	Robert Price	12/2018
3420	2^611731-4837	184150	Yves Minet	08/2018
3421	3*10^184124-7	184125	Robert Price	08/2015
3422	2^611644+29371	184124	Enzo Doria	02/2024
3423	9*10^184122-11	184123	Mischa Rodermond	04/2023
3424	2^611628-24537	184119	Enzo Doria	08/2013
3425	3*10^184110+13	184111	Robert Price	07/2018
3426	(14280^44521-1)/(14280^211-1)	184097	Ryan Propper	11/2023
3427	(194*10^184093+1)/3	184095	Robert Price	01/2022
3428	2^611460+71881	184068	Enzo Doria	04/2016
3429	4*10^184004-63	184005	Robert Price	10/2018
3430	2^611111+84083	183963	Boyan Hu	05/2024
3431	2^610982-1867301	183924	Enzo Doria	03/2016
3432	(10^183917+1)/11/9952852373	183906	Alfred Reich	02/2024
3433	3*10^183872-49	183873	Robert Price	07/2018
3434	2^610597+1178897	183809	Enzo Doria	05/2016
3435	(8*10^183773-269)/9	183773	Robert Price	09/2021
3436	(65*10^183768-29)/9	183769	Robert Price	01/2021
3437	(17*10^183764+31)/3	183765	Robert Price	01/2019
3438	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
3439	2^610401+1277	183750	Lelio R Paula	07/2013
3440	2^610356-1849019	183736	Enzo Doria	08/2015
3441	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
3442	23*10^183710-7	183712	Robert Price	02/2020
3443	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
3444	(4*10^183659+149)/9	183659	Robert Price	04/2018
3445	(4*10^183657+41)/9	183657	Serge Batalov	11/2022
3446	(11^176327-1)/31738870	183619	Paul Vanderveen	05/2025
3447	7*10^183596+39	183597	Robert Price	01/2023
3448	2^609846-1834251	183582	Enzo Doria	07/2015
3449	10^183546+1547323	183547	Patrick De Geest	02/2021
3451	10^183546-800000001	183546	Robert Price	09/2020
3450	10^183546-584297	183546	Patrick De Geest	02/2021
3452	7*10^183511+39	183512	Robert Price	01/2023
3453	(23*10^183477-71)/3	183478	Robert Price	07/2020
3454	11^176176-240	183469	Enzo Doria	11/2012
3455	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
3456	6*10^183429+53	183430	Robert Price	05/2020
3457	(28*10^183403+191)/3	183404	Robert Price	02/2020
3458	U(1096855)	183383	Serge Batalov	07/2024
3459	(5^262337-1)/363486427756606700767551233751524443601036	183325	Paul Vanderveen	05/2025
3460	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
3461	2^608965-113989	183317	Enzo Doria	10/2014
3462	A005165(43592)	183312	Serge Batalov	07/2017
3463	(61*10^183294+119)/9	183295	Robert Price	05/2019
3464	2^608814-461261	183272	Enzo Doria	06/2015
3465	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
3466	2^608541-608541^2	183190	Henri Lifchitz	02/2018
3467	2^608293+143807	183115	Enzo Doria	10/2016
3468	Phi(612539,-2)	183111	Henri Lifchitz	02/2026
3469	2^608164-462419	183076	Enzo Doria	08/2015
3470	2^607950-1862303	183012	Enzo Doria	12/2015
3471	5*3^383376+2^383376	182918	Jon Grantham	08/2023
3472	(46*10^182896+683)/9	182897	Robert Price	03/2019
3473	(2*10^182787+73)/3	182787	Robert Price	09/2020
3474	2^607101+1871987	182756	Enzo Doria	05/2016
3475	2^606869-69175	182686	Enzo Doria	11/2015
3476	8*10^182671+71	182672	Robert Price	05/2022
3477	(23*10^182666-71)/3	182667	Robert Price	07/2020
3478	3*10^182614-11	182615	Robert Price	07/2018
3479	2^606560-357	182593	Enzo Doria	05/2014
3480	66*10^182420+7	182422	Robert Price	07/2020
3481	2^605687+1866983	182330	Enzo Doria	03/2016
3482	2^605655-114445	182321	Enzo Doria	02/2015
3483	94*10^182291-3	182293	Robert Price	05/2020
3484	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
3485	(14*10^182177-221)/9	182178	Robert Price	04/2018
3486	2^605174-112751	182176	Enzo Doria	06/2014
3487	(905^61609-1)/904	182154	Anonymous	05/2024
3488	2^604761+1874507	182052	Enzo Doria	06/2016
3489	2^604705+1871957	182035	Enzo Doria	05/2016
3490	(14*10^182000+229)/9	182001	Robert Price	03/2018
3491	(10^181996+41)/3	181996	Robert Price	12/2017
3492	(17*10^181979+91)/9	181980	Robert Price	02/2022
3493	(10^181960+3)/7	181960	Jinyuan Wang	11/2024
3494	(5*10^181950-101)/3	181951	Robert Price	04/2018
3495	2^603915+75233	181797	Enzo Doria	04/2016
3496	39470^39537+39537^39470	181723	Norbert Schneider	12/2022
3497	(10^181710+7)/563747/2019847	181698	Alfred Reich	08/2021
3498	7*10^181594-57	181595	Robert Price	06/2020
3499	8*10^181580+29	181581	Robert Price	11/2021
3500	(83*10^181544+61)/9	181545	Serge Batalov	01/2023

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