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	2^351460-17289	105801	Enzo Doria	05/2013
3252	19^82735+22	105798	Lelio R Paula	01/2017
3253	2^351435-109077	105793	Enzo Doria	04/2014
3254	2^351393+1089	105780	Lelio R Paula	01/2017
3255	2^351364+72631	105772	Enzo Doria	04/2016
3256	2^351305+1872467	105754	Enzo Doria	05/2016
3257	3^221649+16	105754	Lelio R Paula	11/2016
3258	8*3^221637-5	105749	Lelio R Paula	09/2014
3259	2^351279-2780449	105746	Enzo Doria	03/2016
3260	15^89903-26	105735	Lelio R Paula	02/2017
3261	2^351213-73	105726	Lelio R Paula	10/2011
3262	2^351192-4589	105720	Yves Minet	07/2011
3263	20^81250-33	105709	Lelio R Paula	12/2016
3264	2^351076-113159	105685	Enzo Doria	07/2014
3265	93^53688-2	105684	Lelio R Paula	09/2013
3266	2^351060-4559	105680	Yves Minet	07/2011
3267	((10^52836-1)10000/9+5927)10^52836+(10^52836-1)/9	105676	Hans Havermann	08/2019
3268	11^101473-750	105674	Enzo Doria	11/2012
3269	3*5^151181-8	105672	Lelio R Paula	11/2014
3270	15^89831-34	105650	Lelio R Paula	02/2017
3272	11^101448-360	105648	Enzo Doria	08/2012
3271	3*7^125011+4	105648	Lelio R Paula	11/2014
3273	2^350943-113269	105645	Enzo Doria	07/2014
3274	2^350868-19725	105622	Enzo Doria	06/2013
3275	2^350858-59291	105619	Enzo Doria	10/2015
3276	2^350851+135	105617	Lelio R Paula	10/2011
3277	2^350841-741	105614	Lelio R Paula	01/2017
3278	3*10^105582+77	105583	Robert Price	09/2018
3279	8*10^105571+3	105572	Robert Price	08/2015
3280	2^350674-78557	105564	Jorge Menendez	03/2018
3281	2*5^151026-3	105563	Lelio R Paula	11/2014
3282	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
3283	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
3284	3^221211+236	105545	Lelio R Paula	11/2016
3285	(32*10^105530-77)/9	105531	Robert Price	06/2018
3286	10^105515+33	105516	Lelio R Paula	11/2016
3287	10^105515-41033	105515	Patrick De Geest	12/2016
3288	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
3289	17^85732-72	105489	Lelio R Paula	01/2017
3290	2^350307-110329	105453	Enzo Doria	05/2014
3291	2^350253-20365	105437	Enzo Doria	06/2013
3292	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
3293	2^350139-109009	105403	Enzo Doria	04/2014
3294	3*5^150763+4	105380	Lelio R Paula	11/2014
3295	12^97643+91	105375	Lelio R Paula	02/2017
3296	6*5^150744-7	105367	Lelio R Paula	11/2014
3297	2^349996-112169	105360	Enzo Doria	06/2014
3298	11^101142-1080	105329	Enzo Doria	12/2012
3299	(68*10^105320-41)/9	105321	Robert Price	10/2013
3300	3^220712-9934	105307	Enzo Doria	05/2014
3301	7*10^105296+9	105297	Robert Price	09/2015
3302	2^349739+1873373	105282	Enzo Doria	06/2016
3303	7^124574+24	105278	Lelio R Paula	11/2016
3304	2^349708-20957	105273	Enzo Doria	06/2013
3305	2^349649-20469	105255	Enzo Doria	06/2013
3306	2^349607-20109	105243	Enzo Doria	06/2013
3307	2^349594-19085	105239	Enzo Doria	05/2013
3308	2^349530+1874479	105220	Enzo Doria	06/2016
3309	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
3310	3^220464-112852	105189	Enzo Doria	07/2014
3311	2^349419-17349	105186	Enzo Doria	05/2013
3312	2^349400-2579	105180	Yves Minet	07/2014
3313	8*5^150471+3	105176	Lelio R Paula	11/2014
3314	655^37342+37342^655	105165	Norbert Schneider	08/2018
3315	13^94403+94	105160	Lelio R Paula	12/2016
3316	2^349301-112309	105151	Enzo Doria	06/2014
3317	9*2^349220+5	105127	Lelio R Paula	09/2014
3318	7*3^220317+8	105119	Lelio R Paula	09/2014
3319	7^124386+88	105119	Lelio R Paula	11/2016
3320	2^349171-19657	105111	Enzo Doria	06/2013
3321	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
3322	(2^349111-5)/3	105093	Lelio R Paula	12/2013
3323	675^37142+37142^675	105087	Norbert Schneider	08/2018
3324	2^348981-2797573	105054	Enzo Doria	04/2016
3325	2^348869-6555	105021	Lelio R Paula	01/2017
3326	5^150217+78	104998	Lelio R Paula	11/2016
3327	(28*10^104972+149)/3	104973	Robert Price	12/2019
3328	2^348703-113005	104971	Enzo Doria	06/2014
3330	2^348612-809	104943	Yves Minet	05/2013
3329	(73*10^104942-1)/9	104943	Robert Price	01/2015
3331	2^348583-350407	104934	Enzo Doria	06/2015
3332	2^348531-949	104919	Yves Minet	05/2012
3333	20^80636-59	104910	Lelio R Paula	12/2016
3334	8*10^104893-13	104894	Robert Price	08/2019
3335	2^348437+35	104890	Lelio R Paula	09/2011
3336	2^348348+135	104864	Lelio R Paula	09/2011
3337	(2^348284+9)/25	104843	Lelio R Paula	12/2013
3338	75^55914-74	104843	Norbert Schneider	01/2015
3339	2^348268+255255	104840	Lelio R Paula	01/2017
3340	5^149985-52	104836	Lelio R Paula	11/2016
3341	2^348224-20249	104826	Enzo Doria	06/2013
3342	2^348212-20105	104823	Enzo Doria	06/2013
3343	20^80562+19	104814	Lelio R Paula	12/2016
3344	2*10^104811-87	104812	Robert Price	04/2018
3345	2^348149-20053	104804	Enzo Doria	06/2013
3346	2^348095-171	104788	Lelio R Paula	09/2011
3347	2^348003-20377	104760	Enzo Doria	06/2013
3348	2^347994-741	104757	Lelio R Paula	12/2016
3349	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
3350	2^347910-109937	104732	Enzo Doria	04/2014
3351	5^149794+28	104702	Lelio R Paula	11/2016
3352	105^51800-2	104698	Lelio R Paula	10/2017
3353	(16^86939+3^86939)/19	104684	Robert Price	06/2013
3354	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
3355	2^347731-18609	104678	Enzo Doria	05/2013
3356	4*6^134519+7	104677	Lelio R Paula	11/2014
3357	2^347612-18545	104642	Enzo Doria	05/2013
3358	6^134465+95	104635	Lelio R Paula	11/2016
3359	2^347517-17301	104614	Enzo Doria	05/2013
3360	3^219222-310	104596	Lelio R Paula	11/2016
3361	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
3362	2^347372-17853	104570	Enzo Doria	05/2013
3363	2^347314+99	104552	Lelio R Paula	09/2011
3364	2^347300-22233	104548	Enzo Doria	06/2013
3365	2^347287-19845	104544	Enzo Doria	06/2013
3366	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
3367	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
3368	7*2^347239-3	104531	Lelio R Paula	09/2014
3369	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
3370	5*3^219047+8	104513	Lelio R Paula	09/2014
3371	2^347148-109073	104502	Enzo Doria	04/2014
3372	2^347129-20145	104497	Enzo Doria	06/2013
3373	4*10^104461-57	104462	Robert Price	10/2018
3374	2^346923-19585	104435	Enzo Doria	05/2013
3375	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
3376	2^346854+346854^2+1	104414	Robert Price	06/2014
3377	2^346834+11715	104408	Lelio R Paula	04/2015
3378	79^55009+78	104387	Norbert Schneider	02/2015
3379	3^218744+58	104368	Lelio R Paula	11/2016
3380	9*10^104361+89	104362	Robert Price	11/2019
3381	2^346649+65	104352	Lelio R Paula	09/2011
3382	2^346638-17265	104349	Enzo Doria	05/2013
3383	5*10^104326+77	104327	Robert Price	12/2018
3385	2^346527-111817	104316	Enzo Doria	05/2014
3384	6^134055+101	104316	Lelio R Paula	11/2016
3386	92105!4+8	104312	Robert Price	09/2019
3387	6^134013+163	104283	Lelio R Paula	11/2016
3388	18^83049-89	104250	Lelio R Paula	01/2017
3389	2^346213+484049	104221	Enzo Doria	04/2017
3390	18^83021-91	104214	Lelio R Paula	01/2017
3391	10^104212+128779	104213	Patrick De Geest	05/2016
3392	10^104212+237447	104213	Patrick De Geest	05/2016
3393	10^104212+242139	104213	Patrick De Geest	05/2016
3394	10^104212+269199	104213	Patrick De Geest	05/2016
3395	(10^104212-71)/1	104212	Serge Batalov	12/2014
3396	2^346078+7695	104180	Lelio R Paula	12/2016
3397	2^346055-19537	104173	Enzo Doria	05/2013
3398	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
3399	2^346037-20125	104168	Enzo Doria	06/2013
3400	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
3401	6^133854-17993	104159	Enzo Doria	03/2013
3402	2^345990+1874239	104154	Enzo Doria	06/2016
3403	2^345988-20373	104153	Enzo Doria	06/2013
3404	(26*10^104132-503)/9	104133	Robert Price	07/2018
3405	3*5^148968+8	104125	Lelio R Paula	11/2014
3406	(7*10^104113+53)/3	104114	Robert Price	05/2018
3407	p(21253)#/2+8	104113	Robert Price	01/2017
3408	322^41507+41507^322	104094	Norbert Schneider	12/2014
3409	6^133768-17423	104092	Enzo Doria	03/2013
3410	2^345786-19557	104092	Enzo Doria	05/2013
3411	171^46606-2	104072	Lelio R Paula	10/2017
3412	2^345704-149	104068	Lelio R Paula	09/2011
3413	6^133704-17273	104042	Enzo Doria	02/2013
3414	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
3415	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
3416	2^345547+11	104021	Lelio R Paula	09/2011
3417	(19*10^104014-49)/3	104015	Robert Price	05/2019
3418	2^345504+723	104008	Lelio R Paula	09/2011
3419	2^345498-20037	104006	Enzo Doria	06/2013
3420	18^82854-37	104005	Lelio R Paula	01/2017
3421	2^345486-109065	104002	Enzo Doria	04/2014
3422	2^345487-1851507	104002	Enzo Doria	08/2015
3423	2^345476+777	103999	Lelio R Paula	09/2011
3424	4*10^103981-83	103982	Robert Price	10/2018
3425	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
3426	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
3427	(19*10^103907+77)/3	103908	Robert Price	05/2019
3428	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
3429	2^345106-112181	103888	Enzo Doria	06/2014
3430	2^345079+99	103880	Lelio R Paula	09/2011
3431	11^99736-1500	103865	Enzo Doria	12/2012
3432	2^344842-20157	103808	Enzo Doria	06/2013
3433	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
3434	2^344802-20765	103796	Enzo Doria	06/2013
3435	2^344794-3821	103794	Yves Minet	05/2011
3436	2^344782-109103	103790	Enzo Doria	04/2014
3437	3^217521-112292	103784	Enzo Doria	06/2014
3438	2^344759-3505	103783	Lelio R Paula	11/2016
3439	2^344735-147	103776	Lelio R Paula	09/2011
3440	L(496533)-p(496533)	103770	Robert Price	02/2018
3441	2*10^103749-69	103750	Robert Price	03/2018
3442	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
3443	2^344607-108891	103738	Enzo Doria	03/2014
3444	2^344541-19561	103718	Enzo Doria	05/2013
3445	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
3446	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
3447	2^344444-455	103688	Yves Minet	03/2012
3448	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
3449	2^344317-109933	103650	Enzo Doria	04/2014
3450	2^344309-1852033	103648	Enzo Doria	08/2015
3451	2^344213-21253	103619	Enzo Doria	06/2013
3452	2^344196-465	103614	Lelio R Paula	11/2016
3453	2^344187-20001	103611	Enzo Doria	06/2013
3454	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
3455	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
3456	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
3457	2^344085-20365	103580	Enzo Doria	06/2013
3458	5^148169+54	103566	Lelio R Paula	11/2016
3459	2^344017-108795	103560	Enzo Doria	03/2014
3460	2^343971-5077	103546	Lelio R Paula	09/2011
3461	(7*10^103531+71)/3	103532	Robert Price	05/2018
3462	2^343899+141	103524	Lelio R Paula	08/2011
3463	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
3464	6^133029-67	103517	Lelio R Paula	11/2016
3465	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
3466	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
3467	5^148014-24	103458	Lelio R Paula	11/2016
3468	(22*10^103450+53)/3	103451	Robert Price	07/2019
3469	2^343604+9931	103436	Yves Minet	01/2011
3470	2^343601-21189	103435	Enzo Doria	06/2013
3471	2^343508-115229	103407	Enzo Doria	06/2015
3472	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
3473	3^216685-113056	103386	Enzo Doria	07/2014
3474	91355!4+1024	103381	Robert Price	09/2019
3475	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
3476	11^99262-20	103371	Lelio R Paula	12/2016
3477	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
3478	2^343356-2791889	103361	Enzo Doria	03/2016
3479	(25*10^103360-241)/9	103361	Robert Price	05/2018
3480	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
3481	2^343182-171	103309	Lelio R Paula	08/2011
3482	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
3483	2^343079-1835611	103278	Enzo Doria	05/2015
3484	2^343063-1147	103273	Yves Minet	06/2013
3485	9*6^132689+7	103254	Lelio R Paula	11/2014
3486	2^342979-18085	103247	Enzo Doria	05/2013
3487	(16*10^103244-31)/3	103245	Robert Price	03/2019
3488	2^342966-16995	103244	Lelio R Paula	11/2016
3489	(16*10^103214-31)/3	103215	Robert Price	03/2019
3490	(37*10^103211+611)/9	103212	Robert Price	11/2018
3491	5^147650+16	103203	Lelio R Paula	11/2016
3492	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
3493	2^342817+2707067	103199	Enzo Doria	03/2016
3494	43^63177-42	103198	Theodore Burton	02/2007
3495	2^342805-21025	103195	Enzo Doria	06/2013
3496	2^342714+12285	103168	Lelio R Paula	11/2016
3497	18^82178-4481	103156	Enzo Doria	03/2013
3498	2^342665-17349	103153	Enzo Doria	05/2013
3499	2^342612+175	103137	Lelio R Paula	08/2011
3500	5*2^342585-3	103130	Lelio R Paula	09/2014

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Probable Primes Top 10000

(255312 PRPs in the top)