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	2^348003-20377	104760	Enzo Doria	06/2013
3252	2^347994-741	104757	Lelio R Paula	12/2016
3253	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
3254	2^347910-109937	104732	Enzo Doria	04/2014
3255	5^149794+28	104702	Lelio R Paula	11/2016
3256	105^51800-2	104698	Lelio R Paula	10/2017
3257	(16^86939+3^86939)/19	104684	Robert Price	06/2013
3258	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
3259	2^347731-18609	104678	Enzo Doria	05/2013
3260	4*6^134519+7	104677	Lelio R Paula	11/2014
3261	2^347612-18545	104642	Enzo Doria	05/2013
3262	6^134465+95	104635	Lelio R Paula	11/2016
3263	2^347517-17301	104614	Enzo Doria	05/2013
3264	3^219222-310	104596	Lelio R Paula	11/2016
3265	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
3266	2^347372-17853	104570	Enzo Doria	05/2013
3267	2^347314+99	104552	Lelio R Paula	09/2011
3268	2^347300-22233	104548	Enzo Doria	06/2013
3269	2^347287-19845	104544	Enzo Doria	06/2013
3270	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
3271	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
3272	7*2^347239-3	104531	Lelio R Paula	09/2014
3273	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
3274	5*3^219047+8	104513	Lelio R Paula	09/2014
3275	2^347148-109073	104502	Enzo Doria	04/2014
3276	2^347129-20145	104497	Enzo Doria	06/2013
3277	4*10^104461-57	104462	Robert Price	10/2018
3278	2^346923-19585	104435	Enzo Doria	05/2013
3279	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
3280	2^346854+346854^2+1	104414	Robert Price	06/2014
3281	2^346834+11715	104408	Lelio R Paula	04/2015
3282	79^55009+78	104387	Norbert Schneider	02/2015
3283	3^218744+58	104368	Lelio R Paula	11/2016
3284	2^346649+65	104352	Lelio R Paula	09/2011
3285	2^346638-17265	104349	Enzo Doria	05/2013
3286	5*10^104326+77	104327	Robert Price	12/2018
3288	2^346527-111817	104316	Enzo Doria	05/2014
3287	6^134055+101	104316	Lelio R Paula	11/2016
3289	6^134013+163	104283	Lelio R Paula	11/2016
3290	18^83049-89	104250	Lelio R Paula	01/2017
3291	2^346213+484049	104221	Enzo Doria	04/2017
3292	18^83021-91	104214	Lelio R Paula	01/2017
3293	10^104212+128779	104213	Patrick De Geest	05/2016
3294	10^104212+237447	104213	Patrick De Geest	05/2016
3295	10^104212+242139	104213	Patrick De Geest	05/2016
3296	10^104212+269199	104213	Patrick De Geest	05/2016
3297	(10^104212-71)/1	104212	Serge Batalov	12/2014
3298	2^346078+7695	104180	Lelio R Paula	12/2016
3299	2^346055-19537	104173	Enzo Doria	05/2013
3300	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
3301	2^346037-20125	104168	Enzo Doria	06/2013
3302	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
3303	6^133854-17993	104159	Enzo Doria	03/2013
3304	2^345990+1874239	104154	Enzo Doria	06/2016
3305	2^345988-20373	104153	Enzo Doria	06/2013
3306	(26*10^104132-503)/9	104133	Robert Price	07/2018
3307	3*5^148968+8	104125	Lelio R Paula	11/2014
3308	(7*10^104113+53)/3	104114	Robert Price	05/2018
3309	p(21253)#/2+8	104113	Robert Price	01/2017
3310	322^41507+41507^322	104094	Norbert Schneider	12/2014
3311	6^133768-17423	104092	Enzo Doria	03/2013
3312	2^345786-19557	104092	Enzo Doria	05/2013
3313	171^46606-2	104072	Lelio R Paula	10/2017
3314	2^345704-149	104068	Lelio R Paula	09/2011
3315	6^133704-17273	104042	Enzo Doria	02/2013
3316	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
3317	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
3318	2^345547+11	104021	Lelio R Paula	09/2011
3319	(19*10^104014-49)/3	104015	Robert Price	05/2019
3320	2^345504+723	104008	Lelio R Paula	09/2011
3321	2^345498-20037	104006	Enzo Doria	06/2013
3322	18^82854-37	104005	Lelio R Paula	01/2017
3323	2^345486-109065	104002	Enzo Doria	04/2014
3324	2^345487-1851507	104002	Enzo Doria	08/2015
3325	2^345476+777	103999	Lelio R Paula	09/2011
3326	4*10^103981-83	103982	Robert Price	10/2018
3327	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
3328	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
3329	(19*10^103907+77)/3	103908	Robert Price	05/2019
3330	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
3331	2^345106-112181	103888	Enzo Doria	06/2014
3332	2^345079+99	103880	Lelio R Paula	09/2011
3333	11^99736-1500	103865	Enzo Doria	12/2012
3334	2^344842-20157	103808	Enzo Doria	06/2013
3335	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
3336	2^344802-20765	103796	Enzo Doria	06/2013
3337	2^344794-3821	103794	Yves Minet	05/2011
3338	2^344782-109103	103790	Enzo Doria	04/2014
3339	3^217521-112292	103784	Enzo Doria	06/2014
3340	2^344759-3505	103783	Lelio R Paula	11/2016
3341	2^344735-147	103776	Lelio R Paula	09/2011
3342	L(496533)-p(496533)	103770	Robert Price	02/2018
3343	2*10^103749-69	103750	Robert Price	03/2018
3344	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
3345	2^344607-108891	103738	Enzo Doria	03/2014
3346	2^344541-19561	103718	Enzo Doria	05/2013
3347	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
3348	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
3349	2^344444-455	103688	Yves Minet	03/2012
3350	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
3351	2^344317-109933	103650	Enzo Doria	04/2014
3352	2^344309-1852033	103648	Enzo Doria	08/2015
3353	2^344213-21253	103619	Enzo Doria	06/2013
3354	2^344196-465	103614	Lelio R Paula	11/2016
3355	2^344187-20001	103611	Enzo Doria	06/2013
3356	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
3357	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
3358	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
3359	2^344085-20365	103580	Enzo Doria	06/2013
3360	5^148169+54	103566	Lelio R Paula	11/2016
3361	2^344017-108795	103560	Enzo Doria	03/2014
3362	2^343971-5077	103546	Lelio R Paula	09/2011
3363	(7*10^103531+71)/3	103532	Robert Price	05/2018
3364	2^343899+141	103524	Lelio R Paula	08/2011
3365	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
3366	6^133029-67	103517	Lelio R Paula	11/2016
3367	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
3368	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
3369	5^148014-24	103458	Lelio R Paula	11/2016
3370	(22*10^103450+53)/3	103451	Robert Price	07/2019
3371	2^343604+9931	103436	Yves Minet	01/2011
3372	2^343601-21189	103435	Enzo Doria	06/2013
3373	2^343508-115229	103407	Enzo Doria	06/2015
3374	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
3375	3^216685-113056	103386	Enzo Doria	07/2014
3376	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
3377	11^99262-20	103371	Lelio R Paula	12/2016
3378	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
3379	2^343356-2791889	103361	Enzo Doria	03/2016
3380	(25*10^103360-241)/9	103361	Robert Price	05/2018
3381	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
3382	2^343182-171	103309	Lelio R Paula	08/2011
3383	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
3384	2^343079-1835611	103278	Enzo Doria	05/2015
3385	2^343063-1147	103273	Yves Minet	06/2013
3386	9*6^132689+7	103254	Lelio R Paula	11/2014
3387	2^342979-18085	103247	Enzo Doria	05/2013
3388	(16*10^103244-31)/3	103245	Robert Price	03/2019
3389	2^342966-16995	103244	Lelio R Paula	11/2016
3390	(16*10^103214-31)/3	103215	Robert Price	03/2019
3391	(37*10^103211+611)/9	103212	Robert Price	11/2018
3392	5^147650+16	103203	Lelio R Paula	11/2016
3393	gcd(Phi(852060,10),(10^42603+1)^3(10^42603+1-10^21302)+(10^85206+10^42603)(10^21302+1)+10^127809)	103201	Serge Batalov	04/2015
3394	2^342817+2707067	103199	Enzo Doria	03/2016
3395	43^63177-42	103198	Theodore Burton	02/2007
3396	2^342805-21025	103195	Enzo Doria	06/2013
3397	2^342714+12285	103168	Lelio R Paula	11/2016
3398	18^82178-4481	103156	Enzo Doria	03/2013
3399	2^342665-17349	103153	Enzo Doria	05/2013
3400	2^342612+175	103137	Lelio R Paula	08/2011
3401	5*2^342585-3	103130	Lelio R Paula	09/2014
3402	(16*10^103127+77)/3	103128	Robert Price	03/2019
3403	2^342503-19209	103104	Enzo Doria	05/2013
3404	2^342476+51	103096	Lelio R Paula	08/2011
3405	2^342460-18885	103091	Enzo Doria	05/2013
3406	7^121968+82	103075	Lelio R Paula	10/2016
3407	2^342392-108863	103071	Enzo Doria	03/2014
3408	3^216014+28	103065	Lelio R Paula	11/2016
3409	2^342353-108879	103059	Enzo Doria	03/2014
3410	10^103055+276081	103056	Patrick De Geest	12/2016
3411	10^103055-53	103055	Lelio R Paula	11/2016
3412	(58*10^103046+419)/9	103047	Robert Price	05/2019
3413	7^121933+4	103046	Lelio R Paula	11/2014
3414	19^80560-68	103017	Lelio R Paula	10/2016
3415	2^342209+76607	103016	Enzo Doria	05/2016
3417	328^40945+40945^328	103013	Norbert Schneider	12/2014
3416	12^95454-91	103013	Lelio R Paula	10/2016
3418	25833^9716+9716^25833	103009	Hans Havermann	01/2019
3419	65^56809-64^56809	102990	Robert Price	08/2013
3420	5^147338-6	102985	Lelio R Paula	11/2014
3421	2^342084-112739	102978	Enzo Doria	06/2014
3422	9*6^132330+7	102974	Lelio R Paula	11/2014
3423	2^342034-16737	102963	Enzo Doria	05/2013
3424	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
3425	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
3426	2^341991-17421	102950	Enzo Doria	05/2013
3427	2^341969-112225	102943	Enzo Doria	06/2014
3428	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
3429	2^341859+1869413	102910	Enzo Doria	05/2016
3430	10^102909+61	102910	Lelio R Paula	11/2016
3431	10^102909-67049	102909	Patrick De Geest	12/2016
3432	23814^20935+20935^23814	102898	Hans Havermann	02/2019
3433	28345^4264+4264^28345	102888	Hans Havermann	02/2019
3434	25665^10204+10204^25665	102886	Hans Havermann	02/2019
3435	26288^8181+8181^26288	102860	Hans Havermann	02/2019
3436	2^341659+1836773	102850	Enzo Doria	03/2016
3437	2^341608-110639	102835	Enzo Doria	05/2014
3438	10^102824+49	102825	Lelio R Paula	11/2016
3439	10^102824-168011	102824	Patrick De Geest	12/2016
3440	11^98708-8	102794	Lelio R Paula	10/2016
3441	2^341466+4429	102792	Lelio R Paula	09/2011
3442	2^341460-107	102790	Lelio R Paula	08/2011
3443	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
3444	2^341355+21	102759	Lelio R Paula	08/2011
3445	2^341246+40755	102726	Lelio R Paula	11/2016
3446	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
3447	7^121547+78	102720	Lelio R Paula	10/2016
3448	2^341223-461197	102719	Enzo Doria	06/2015
3449	27838^4893+4893^27838	102711	Hans Havermann	03/2019
3451	2^341190-20577	102709	Enzo Doria	06/2013
3450	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
3452	6^131976-65	102698	Lelio R Paula	10/2016
3453	2^341134+2533	102692	Henri Lifchitz	09/2005
3454	13^92184-54	102688	Lelio R Paula	10/2016
3455	2^341116-20873	102687	Enzo Doria	06/2013
3456	2^341094-19953	102680	Enzo Doria	06/2013
3457	23761^20950+20950^23761	102676	Hans Havermann	03/2019
3458	2^341053+129	102668	Lelio R Paula	08/2011
3459	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
3460	7^121471+94	102655	Lelio R Paula	10/2016
3462	2^341004-173	102653	Lelio R Paula	08/2011
3461	20^78901+3	102653	Lelio R Paula	10/2016
3463	5^146853-52	102646	Lelio R Paula	10/2016
3464	2^340969-216931	102642	Enzo Doria	05/2014
3465	122^49196+121	102641	Norbert Schneider	10/2018
3466	2^340952+1870021	102637	Enzo Doria	05/2016
3467	5*2^340940-3	102634	Lelio R Paula	08/2014
3468	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
3469	25876^9239+9239^25876	102615	Hans Havermann	02/2019
3470	(4*10^102612+83)/3	102613	Robert Price	02/2018
3472	75^54717+74	102598	Norbert Schneider	01/2015
3471	(17*10^102597+13)/3	102598	Robert Price	01/2019
3473	2^340806-20393	102593	Enzo Doria	06/2013
3474	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
3475	6^131821+77	102577	Lelio R Paula	10/2016
3476	2^340688-29	102558	Henri Lifchitz	05/2005
3477	2^340685-109101	102557	Enzo Doria	04/2014
3478	65^56567-64	102552	Norbert Schneider	11/2014
3479	26230^8121+8121^26230	102550	Hans Havermann	03/2019
3480	2^340547-108897	102515	Enzo Doria	03/2014
3481	25592^10119+10119^25592	102500	Hans Havermann	02/2019
3482	7^121268+82	102484	Lelio R Paula	10/2016
3483	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
3484	2^340434-5955	102481	Lelio R Paula	11/2016
3485	(2^340381+47)/7	102465	Lelio R Paula	12/2013
3486	111^50095+110	102461	Norbert Schneider	04/2017
3487	2^340291-20301	102438	Enzo Doria	06/2013
3488	12^94915+89	102431	Lelio R Paula	10/2016
3489	24466^15349+15349^24466	102417	Hans Havermann	03/2019
3490	2^340208-20373	102413	Enzo Doria	06/2013
3491	6^131598-17273	102404	Enzo Doria	02/2013
3492	2^340115-21181	102385	Enzo Doria	06/2013
3493	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
3494	89^52511-88^52511	102365	Robert Price	06/2015
3495	3^214539-112756	102362	Enzo Doria	07/2014
3496	2^340000-19877	102351	Enzo Doria	06/2013
3497	2^339990-114845	102348	Enzo Doria	05/2015
3498	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
3499	20^78661-99	102341	Lelio R Paula	09/2016
3500	2^339951-19585	102336	Enzo Doria	05/2013

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Probable Primes Top 10000

(253466 PRPs in the top)