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	91^65772-2	128851	Lelio R Paula	05/2017
3252	2^428022+43	128848	Lelio R Paula	05/2017
3253	2^427999-459397	128841	Enzo Doria	05/2015
3254	2^427993+76847	128839	Enzo Doria	05/2016
3255	31059^14060+14060^31059	128833	Hans Havermann	03/2021
3256	10^128805+152871	128806	Patrick De Geest	05/2021
3257	10^128805-10001	128805	Robert Price	02/2021
3258	2^427824-1851507	128788	Enzo Doria	08/2015
3259	2^427807-21469	128783	Enzo Doria	07/2013
3260	29082^26783+26783^29082	128772	Hans Havermann	04/2021
3261	40055^1638+1638^40055	128750	Hans Havermann	04/2021
3262	11^123594-240	128710	Enzo Doria	09/2012
3263	2^427504-21503	128692	Enzo Doria	07/2013
3264	37727^2574+2574^37727	128673	Hans Havermann	04/2021
3265	29686^21591+21591^29686	128668	Hans Havermann	04/2021
3266	10^128668-70000000001	128668	Robert Price	08/2021
3267	2^427420+91	128667	Lelio R Paula	05/2017
3268	(68*10^128645-257)/9	128646	Robert Price	07/2019
3269	2^427269-113635	128621	Enzo Doria	08/2014
3270	2^427130+1877569	128579	Enzo Doria	08/2016
3271	2^427016-115349	128545	Enzo Doria	07/2015
3272	(4*10^128510+137)/3	128511	Robert Price	03/2018
3273	2^426889-112879	128507	Enzo Doria	06/2014
3274	2^426804+1869931	128481	Enzo Doria	05/2016
3275	2^426750+77635	128465	Enzo Doria	05/2016
3276	36988^2969+2969^36988	128445	Hans Havermann	03/2021
3277	36664^3185+3185^36664	128439	Hans Havermann	03/2021
3278	32618^8649+8649^32618	128416	Hans Havermann	04/2021
3279	28883^27874+27874^28883	128391	Hans Havermann	04/2021
3280	2^426425-91	128367	Lelio R Paula	05/2017
3281	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
3282	2^426352+74971	128345	Enzo Doria	04/2016
3283	(199*10^128343-7)/3	128345	Robert Price	05/2020
3284	4*10^128343-21	128344	Robert Price	09/2018
3285	(65*10^128338+493)/9	128339	Robert Price	08/2021
3286	35632^3997+3997^35632	128337	Hans Havermann	04/2021
3287	2^426300-1863689	128330	Enzo Doria	03/2016
3288	2^426293+1881017	128327	Enzo Doria	11/2016
3289	(88*10^128324-637)/9	128325	Robert Price	11/2020
3290	39103^1908+1908^39103	128281	Hans Havermann	04/2021
3291	2^426043+35	128252	Robert Price	11/2015
3292	(4*10^128244-19)/3	128245	Robert Price	03/2018
3293	35489^4102+4102^35489	128222	Hans Havermann	04/2021
3294	34721^4926+4926^34721	128208	Hans Havermann	04/2021
3295	(305*10^128198+1)/9	128200	Robert Price	02/2020
3296	2^425808-459959	128181	Enzo Doria	06/2015
3297	30632^15291+15291^30632	128178	Hans Havermann	04/2021
3298	35981^3648+3648^35981	128167	Hans Havermann	04/2021
3299	2^425627-113605	128127	Enzo Doria	08/2014
3300	(4*10^128109+119)/3	128110	Robert Price	12/2021
3301	(22*10^128094+53)/3	128095	Robert Price	07/2019
3302	(86*10^128086-221)/9	128087	Robert Price	09/2019
3303	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
3304	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
3305	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
3306	2^425205+4911	128000	Marek Hubal	02/2017
3307	29241^23836+23836^29241	127995	Hans Havermann	04/2021
3308	2^425118-113663	127974	Enzo Doria	08/2014
3309	(86*10^127967-329)/9	127968	Robert Price	01/2020
3310	2^425061+1869761	127957	Enzo Doria	05/2016
3311	746^44541+44541^746	127955	Norbert Schneider	07/2019
3312	30236^17043+17043^30236	127946	Hans Havermann	03/2021
3313	2^424918-21141	127914	Enzo Doria	07/2013
3314	(62*10^127903+91)/9	127904	Robert Price	07/2021
3315	2^424864-29489	127897	Enzo Doria	08/2015
3316	30438^15893+15893^30438	127877	Hans Havermann	02/2021
3317	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
3318	28929^26258+26258^28929	127845	Hans Havermann	03/2021
3319	30563^15220+15220^30563	127828	Hans Havermann	03/2021
3320	2^424632-2786639	127827	Enzo Doria	03/2016
3321	10^127821-700001	127821	Robert Price	08/2021
3322	2^424577-113755	127811	Enzo Doria	09/2014
3323	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
3324	(56*10^127752+691)/9	127753	Robert Price	05/2019
3325	11^122629-720	127705	Enzo Doria	11/2012
3326	22*10^127645+3	127647	Robert Price	01/2020
3327	28715^27844+27844^28715	127631	Hans Havermann	03/2021
3328	(56*10^127612+187)/9	127613	Robert Price	10/2021
3329	(5*36^81995+821)/7	127609	Eric Chen	01/2021
3330	4*10^127562-39	127563	Robert Price	09/2020
3331	32595^8186+8186^32595	127547	Hans Havermann	03/2021
3332	2^423696-21429	127546	Enzo Doria	07/2013
3333	2^423664-1864559	127536	Enzo Doria	03/2016
3334	37889^2322+2322^37889	127530	Hans Havermann	03/2021
3335	37668^2429+2429^37668	127523	Hans Havermann	03/2021
3336	3^267267-4	127519	Henri Lifchitz	10/2014
3337	(103*10^127491+17)/3	127493	Robert Price	08/2020
3338	29376^21869+21869^29376	127487	Hans Havermann	03/2021
3339	31186^12241+12241^31186	127483	Hans Havermann	02/2021
3340	(19^99689+5^99689)/24	127477	Robert Price	09/2013
3341	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
3342	30594^14645+14645^30594	127446	Hans Havermann	03/2021
3343	2^423328-21537	127435	Enzo Doria	07/2013
3344	(67*10^127413-7)/3	127415	Robert Price	01/2020
3345	(2*10^127407+73)/3	127407	Robert Price	09/2020
3346	(2^423165-7)/25	127384	Lelio R Paula	05/2015
3347	(7726^32768+1)/13917994151414876602369	127379	Kellen Shenton	04/2021
3348	29512^20647+20647^29512	127341	Hans Havermann	03/2021
3349	(112*10^127324+17)/3	127326	Robert Price	03/2020
3350	29565^20252+20252^29565	127321	Hans Havermann	03/2021
3351	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
3352	(16*10^127259+197)/3	127260	Robert Price	04/2019
3353	(26*10^127240+61)/3	127241	Robert Price	10/2019
3354	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
3355	2^422515-114997	127190	Enzo Doria	06/2015
3356	5*10^127179-3	127180	Robert Price	07/2015
3357	31678^10343+10343^31678	127176	Hans Havermann	03/2021
3358	(44*10^127169-233)/9	127170	Robert Price	01/2019
3359	34947^4352+4352^34947	127162	Hans Havermann	03/2021
3360	6*10^127158+19	127159	Robert Price	11/2021
3361	30469^14902+14902^30469	127155	Hans Havermann	03/2021
3362	5*10^127153+77	127154	Robert Price	12/2018
3363	29941^17620+17620^29941	127130	Hans Havermann	02/2021
3364	31607^10516+10516^31607	127119	Hans Havermann	03/2021
3365	(19*10^127118-97)/3	127119	Robert Price	10/2021
3366	(29*10^127111+691)/9	127112	Robert Price	08/2021
3367	736^44335+44335^736	127104	Norbert Schneider	07/2019
3368	33040^7023+7023^33040	127090	Hans Havermann	03/2021
3369	29748^18661+18661^29748	127052	Hans Havermann	03/2021
3370	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
3371	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
3372	(14*10^127014-137)/3	127015	Robert Price	04/2021
3373	31436^10965+10965^31436	127002	Hans Havermann	03/2021
3374	28905^24758+24758^28905	127001	Hans Havermann	03/2021
3375	2^421860-113285	126993	Enzo Doria	07/2014
3376	(10^127030+7)/81234833/9230384921/6092460488946445358851	126991	Alfred Reich	07/2021
3377	(2^421827-7)/11	126982	Lelio R Paula	05/2015
3378	11^121910-840	126957	Enzo Doria	12/2012
3379	(56*10^126935+187)/9	126936	Robert Price	10/2021
3380	28915^24538+24538^28915	126933	Hans Havermann	03/2021
3381	(29*10^126928-77)/3	126929	Robert Price	02/2020
3382	(259*10^126919-1)/3	126921	Robert Price	12/2020
3383	10^126919+204567	126920	Patrick De Geest	05/2021
3384	10^126919-100001	126919	Robert Price	07/2020
3385	28340^28503+28503^28340	126907	Norbert Schneider	02/2021
3386	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
3387	(5*10^126871-119)/3	126872	Robert Price	03/2018
3388	331^50339-10004	126846	Enzo Doria	07/2012
3389	2^421363-2790757	126843	Enzo Doria	03/2016
3390	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
3391	37938^2203+2203^37938	126828	Hans Havermann	03/2021
3392	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
3393	(14*10^126784-83)/3	126785	Robert Price	12/2018
3394	2^421161-286183	126783	Enzo Doria	06/2015
3395	(106*10^126726+17)/3	126728	Robert Price	04/2021
3396	30718^13347+13347^30718	126724	Hans Havermann	03/2021
3397	2^420939-113935	126716	Enzo Doria	10/2014
3398	177^56363-2	126703	Lelio R Paula	10/2017
3399	2^420741-113659	126656	Enzo Doria	08/2014
3400	2^420694-21	126642	Lelio R Paula	05/2017
3401	(13*10^126638+437)/9	126639	Robert Price	04/2018
3402	(167*10^126637-17)/3	126639	Robert Price	03/2020
3403	4*10^126625+87	126626	Robert Price	08/2018
3404	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
3405	7*10^126600-99	126601	Robert Price	06/2019
3406	2^420424-59189	126561	Enzo Doria	10/2015
3407	28717^25534+25534^28717	126560	Hans Havermann	03/2021
3408	(86*10^126542+103)/9	126543	Robert Price	12/2021
3409	28922^23655+23655^28922	126503	Hans Havermann	03/2021
3410	2^420126+71893	126471	Enzo Doria	04/2016
3411	(43*10^126441+47)/9	126442	Robert Price	12/2018
3412	2^419866+1877059	126393	Enzo Doria	07/2016
3413	29315^20484+20484^29315	126390	Hans Havermann	03/2021
3414	29433^19676+19676^29433	126384	Hans Havermann	03/2021
3415	F(604711)	126377	Henri Lifchitz	02/2005
3416	2^419757+72707	126360	Enzo Doria	04/2016
3417	2^419720-21569	126349	Enzo Doria	07/2013
3418	2^419637+29	126324	Henri Lifchitz	02/2006
3419	31004^11865+11865^31004	126319	Hans Havermann	03/2021
3420	2^419612+1876741	126316	Enzo Doria	07/2016
3421	2^419520+2793271	126289	Enzo Doria	03/2016
3422	(2^419447-5)/369	126264	Lelio R Paula	05/2014
3423	2^419328-1859939	126231	Enzo Doria	03/2016
3424	2^419282-1851507	126217	Enzo Doria	08/2015
3425	(133*10^126212+17)/3	126214	Robert Price	11/2021
3426	2^419251+1866143	126208	Enzo Doria	03/2016
3427	11^121185+2	126202	Robert Price	05/2014
3428	28203^28352+28352^28203	126175	Norbert Schneider	01/2021
3429	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
3430	2^418851+23	126087	Robert Price	09/2015
3431	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
3432	2^418829+167	126081	Lelio R Paula	01/2012
3433	31037^11530+11530^31037	126067	Hans Havermann	03/2021
3434	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
3435	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
3436	(35*10^126048-323)/9	126049	Robert Price	10/2021
3437	33016^6551+6551^33016	126000	Hans Havermann	03/2021
3438	2^418548-111546435	125996	Paul Bourdelais	10/2021
3439	34736^4227+4227^34736	125954	Hans Havermann	03/2021
3440	2^418319-109501	125927	Enzo Doria	04/2014
3441	2^418316-112373	125926	Enzo Doria	06/2014
3442	40398^1309+1309^40398	125919	Hans Havermann	03/2021
3443	(8*10^125894-29)/3	125895	Robert Price	07/2018
3444	(26*10^125886-413)/9	125887	Robert Price	05/2018
3445	2^417968+1869811	125821	Enzo Doria	06/2016
3446	2^417902+63	125802	Lelio R Paula	09/2015
3447	(10^125792-91)/9	125792	Serge Batalov	12/2014
3448	30438^13573+13573^30438	125791	Hans Havermann	03/2021
3449	32867^6714+6714^32867	125782	Hans Havermann	03/2021
3450	31155^10892+10892^31155	125777	Hans Havermann	03/2021
3451	(35*10^125754-593)/9	125755	Robert Price	07/2018
3452	30455^13464+13464^30455	125754	Hans Havermann	03/2021
3453	(32*10^125751-77)/9	125752	Robert Price	06/2018
3454	2^417704+77011	125742	Enzo Doria	05/2016
3455	29755^16816+16816^29755	125737	Hans Havermann	03/2021
3456	(22*10^125734+203)/9	125735	Robert Price	10/2021
3457	29918^15915+15915^29918	125710	Hans Havermann	03/2021
3458	(10^125706+149)/3	125706	Serge Batalov	12/2014
3459	28531^25368+25368^28531	125659	Hans Havermann	03/2021
3460	2^417419-115309	125656	Enzo Doria	07/2015
3461	2^417300+77281	125620	Enzo Doria	05/2016
3462	30638^12537+12537^30638	125561	Hans Havermann	03/2021
3463	2^417095-1657	125559	Yves Minet	07/2014
3464	30162^14525+14525^30162	125538	Hans Havermann	03/2021
3465	(56*10^125535+583)/9	125536	Robert Price	08/2021
3466	(88*10^125492-637)/9	125493	Robert Price	11/2020
3467	28958^21525+21525^28958	125474	Hans Havermann	02/2021
3469	2^416773-25	125462	Lelio R Paula	09/2015
3468	(10^125482+7)/162685667/1639829194459	125462	Alfred Reich	07/2021
3470	33889^5032+5032^33889	125449	Hans Havermann	03/2021
3471	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
3472	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
3473	(289511#+1896)/(23^3797801939911849)	125434	Makoto Morimoto	06/2019
3474	2^416641-2*416641+1	125422	Robert Price	05/2018
3475	33392^5697+5697^33392	125409	Hans Havermann	03/2021
3476	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
3477	2^416530+1870429	125389	Enzo Doria	05/2016
3478	(56*10^125385+691)/9	125386	Robert Price	05/2019
3479	27953^28198+28198^27953	125381	Norbert Schneider	01/2021
3480	31074^10837+10837^31074	125381	Hans Havermann	03/2021
3481	33745^5194+5194^33745	125380	Hans Havermann	03/2021
3482	2^416490+1875109	125376	Enzo Doria	09/2016
3483	28360^26331+26331^28360	125365	Hans Havermann	03/2021
3484	2^416416-114929	125354	Enzo Doria	05/2015
3485	(77*10^125330-293)/9	125331	Robert Price	09/2019
3486	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
3487	2^416134+1865899	125269	Enzo Doria	03/2016
3488	153^57337-152	125264	Norbert Schneider	12/2018
3489	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
3490	30054^14657+14657^30054	125207	Hans Havermann	03/2021
3491	(23^91943-1)/22	125201	Robert Price	01/2012
3492	2^415884-933075	125194	Paul Bourdelais	06/2021
3493	43125^27010-106	125185	Enzo Doria	08/2012
3494	(38*10^125166+349)/9	125167	Robert Price	10/2018
3495	10^125166-5001	125166	Robert Price	12/2021
3496	2^415765-112603	125158	Enzo Doria	06/2014
3497	8*10^125088-13	125089	Robert Price	08/2019
3498	(25*10^125076-13)/3	125077	Robert Price	09/2019
3499	(11*10^125054+73)/3	125055	Robert Price	08/2021
3500	(29*10^125021-113)/3	125022	Robert Price	10/2019

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Probable Primes Top 10000

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