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 ?
3501	8*10^128651-37	128652	Robert Price	03/2022
3502	(68*10^128645-257)/9	128646	Robert Price	07/2019
3503	2^427269-113635	128621	Enzo Doria	08/2014
3504	2^427130+1877569	128579	Enzo Doria	08/2016
3505	2^427016-115349	128545	Enzo Doria	07/2015
3506	(4*10^128510+137)/3	128511	Robert Price	03/2018
3507	2^426889-112879	128507	Enzo Doria	06/2014
3508	2^426804+1869931	128481	Enzo Doria	05/2016
3509	2^426750+77635	128465	Enzo Doria	05/2016
3510	36988^2969+2969^36988	128445	Hans Havermann	03/2021
3511	36664^3185+3185^36664	128439	Hans Havermann	03/2021
3512	32618^8649+8649^32618	128416	Hans Havermann	04/2021
3513	28883^27874+27874^28883	128391	Hans Havermann	04/2021
3514	2^426425-91	128367	Lelio R Paula	05/2017
3515	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
3516	2^426352+74971	128345	Enzo Doria	04/2016
3517	(199*10^128343-7)/3	128345	Robert Price	05/2020
3518	4*10^128343-21	128344	Robert Price	09/2018
3519	(65*10^128338+493)/9	128339	Robert Price	08/2021
3520	35632^3997+3997^35632	128337	Hans Havermann	04/2021
3521	2^426300-1863689	128330	Enzo Doria	03/2016
3522	2^426293+1881017	128327	Enzo Doria	11/2016
3523	(88*10^128324-637)/9	128325	Robert Price	11/2020
3524	(491*10^128285+31)/9	128287	Robert Price	04/2022
3525	39103^1908+1908^39103	128281	Hans Havermann	04/2021
3526	2^426043+35	128252	Robert Price	11/2015
3527	(4*10^128244-19)/3	128245	Robert Price	03/2018
3528	35489^4102+4102^35489	128222	Hans Havermann	04/2021
3529	34721^4926+4926^34721	128208	Hans Havermann	04/2021
3530	(305*10^128198+1)/9	128200	Robert Price	02/2020
3531	2^425808-459959	128181	Enzo Doria	06/2015
3532	30632^15291+15291^30632	128178	Hans Havermann	04/2021
3533	35981^3648+3648^35981	128167	Hans Havermann	04/2021
3534	2^425627-113605	128127	Enzo Doria	08/2014
3535	(4*10^128109+119)/3	128110	Robert Price	12/2021
3536	(22*10^128094+53)/3	128095	Robert Price	07/2019
3537	(86*10^128086-221)/9	128087	Robert Price	09/2019
3538	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
3539	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
3540	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
3541	Phi(149401,10)/30037901719561	128003	Makoto Kamada	07/2022
3542	2^425205+4911	128000	Marek Hubal	02/2017
3543	29241^23836+23836^29241	127995	Hans Havermann	04/2021
3544	2^425118-113663	127974	Enzo Doria	08/2014
3545	(86*10^127967-329)/9	127968	Robert Price	01/2020
3546	2^425061+1869761	127957	Enzo Doria	05/2016
3547	746^44541+44541^746	127955	Norbert Schneider	07/2019
3548	30236^17043+17043^30236	127946	Hans Havermann	03/2021
3549	2^424918-21141	127914	Enzo Doria	07/2013
3550	(62*10^127903+91)/9	127904	Robert Price	07/2021
3551	2^424864-29489	127897	Enzo Doria	08/2015
3552	30438^15893+15893^30438	127877	Hans Havermann	02/2021
3553	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
3554	28929^26258+26258^28929	127845	Hans Havermann	03/2021
3555	30563^15220+15220^30563	127828	Hans Havermann	03/2021
3556	2^424632-2786639	127827	Enzo Doria	03/2016
3557	10^127821-700001	127821	Robert Price	08/2021
3558	2^424577-113755	127811	Enzo Doria	09/2014
3559	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
3560	(56*10^127752+691)/9	127753	Robert Price	05/2019
3561	11^122629-720	127705	Enzo Doria	11/2012
3562	22*10^127645+3	127647	Robert Price	01/2020
3563	28715^27844+27844^28715	127631	Hans Havermann	03/2021
3564	(56*10^127612+187)/9	127613	Robert Price	10/2021
3565	(5*36^81995+821)/7	127609	Eric Chen	01/2021
3566	4*10^127562-39	127563	Robert Price	09/2020
3567	32595^8186+8186^32595	127547	Hans Havermann	03/2021
3568	2^423696-21429	127546	Enzo Doria	07/2013
3569	2^423664-1864559	127536	Enzo Doria	03/2016
3570	37889^2322+2322^37889	127530	Hans Havermann	03/2021
3571	37668^2429+2429^37668	127523	Hans Havermann	03/2021
3572	3^267267-4	127519	Henri Lifchitz	10/2014
3573	(103*10^127491+17)/3	127493	Robert Price	08/2020
3574	29376^21869+21869^29376	127487	Hans Havermann	03/2021
3575	31186^12241+12241^31186	127483	Hans Havermann	02/2021
3576	(19^99689+5^99689)/24	127477	Robert Price	09/2013
3577	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
3578	30594^14645+14645^30594	127446	Hans Havermann	03/2021
3579	2^423328-21537	127435	Enzo Doria	07/2013
3580	(67*10^127413-7)/3	127415	Robert Price	01/2020
3581	(2*10^127407+73)/3	127407	Robert Price	09/2020
3582	(2^423165-7)/25	127384	Lelio R Paula	05/2015
3583	(7726^32768+1)/13917994151414876602369	127379	Kellen Shenton	04/2021
3584	29512^20647+20647^29512	127341	Hans Havermann	03/2021
3585	(112*10^127324+17)/3	127326	Robert Price	03/2020
3586	29565^20252+20252^29565	127321	Hans Havermann	03/2021
3588	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
3587	(5^182099-3^182099)/2	127282	Kellen Shenton	05/2022
3589	(16*10^127259+197)/3	127260	Robert Price	04/2019
3590	(26*10^127240+61)/3	127241	Robert Price	10/2019
3591	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
3592	2^422515-114997	127190	Enzo Doria	06/2015
3593	5*10^127179-3	127180	Robert Price	07/2015
3594	31678^10343+10343^31678	127176	Hans Havermann	03/2021
3595	(44*10^127169-233)/9	127170	Robert Price	01/2019
3596	34947^4352+4352^34947	127162	Hans Havermann	03/2021
3597	6*10^127158+19	127159	Robert Price	11/2021
3598	30469^14902+14902^30469	127155	Hans Havermann	03/2021
3599	5*10^127153+77	127154	Robert Price	12/2018
3600	29941^17620+17620^29941	127130	Hans Havermann	02/2021
3601	31607^10516+10516^31607	127119	Hans Havermann	03/2021
3602	(19*10^127118-97)/3	127119	Robert Price	10/2021
3603	(29*10^127111+691)/9	127112	Robert Price	08/2021
3604	736^44335+44335^736	127104	Norbert Schneider	07/2019
3605	33040^7023+7023^33040	127090	Hans Havermann	03/2021
3606	(4*10^127081+167)/9	127081	Robert Price	03/2022
3607	29748^18661+18661^29748	127052	Hans Havermann	03/2021
3608	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
3609	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
3610	(14*10^127014-137)/3	127015	Robert Price	04/2021
3611	31436^10965+10965^31436	127002	Hans Havermann	03/2021
3612	28905^24758+24758^28905	127001	Hans Havermann	03/2021
3613	2^421860-113285	126993	Enzo Doria	07/2014
3614	(10^127030+7)/81234833/9230384921/6092460488946445358851	126991	Alfred Reich	07/2021
3615	(2^421827-7)/11	126982	Lelio R Paula	05/2015
3616	11^121910-840	126957	Enzo Doria	12/2012
3617	(56*10^126935+187)/9	126936	Robert Price	10/2021
3618	28915^24538+24538^28915	126933	Hans Havermann	03/2021
3619	(29*10^126928-77)/3	126929	Robert Price	02/2020
3620	(259*10^126919-1)/3	126921	Robert Price	12/2020
3621	10^126919+204567	126920	Patrick De Geest	05/2021
3622	(2^421617+100280245065)	126920	Paul Bourdelais	05/2022
3623	10^126919-100001	126919	Robert Price	07/2020
3624	28340^28503+28503^28340	126907	Norbert Schneider	02/2021
3625	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
3626	(5*10^126871-119)/3	126872	Robert Price	03/2018
3627	331^50339-10004	126846	Enzo Doria	07/2012
3628	2^421363-2790757	126843	Enzo Doria	03/2016
3629	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
3630	37938^2203+2203^37938	126828	Hans Havermann	03/2021
3631	(13*10^126819+77)/9	126820	Robert Price	07/2022
3632	(7*2^421243+1)/39	126807	Lelio R Paula	05/2014
3633	(14*10^126784-83)/3	126785	Robert Price	12/2018
3634	2^421161-286183	126783	Enzo Doria	06/2015
3635	(106*10^126726+17)/3	126728	Robert Price	04/2021
3636	30718^13347+13347^30718	126724	Hans Havermann	03/2021
3637	2^420939-113935	126716	Enzo Doria	10/2014
3638	177^56363-2	126703	Lelio R Paula	10/2017
3639	2^420741-113659	126656	Enzo Doria	08/2014
3640	2^420694-21	126642	Lelio R Paula	05/2017
3641	(13*10^126638+437)/9	126639	Robert Price	04/2018
3642	(167*10^126637-17)/3	126639	Robert Price	03/2020
3643	4*10^126625+87	126626	Robert Price	08/2018
3644	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
3645	7*10^126600-99	126601	Robert Price	06/2019
3646	2^420424-59189	126561	Enzo Doria	10/2015
3647	28717^25534+25534^28717	126560	Hans Havermann	03/2021
3648	(86*10^126542+103)/9	126543	Robert Price	12/2021
3649	28922^23655+23655^28922	126503	Hans Havermann	03/2021
3650	2^420126+71893	126471	Enzo Doria	04/2016
3651	(43*10^126441+47)/9	126442	Robert Price	12/2018
3652	8*10^126408+71	126409	Robert Price	05/2022
3653	2^419866+1877059	126393	Enzo Doria	07/2016
3654	29315^20484+20484^29315	126390	Hans Havermann	03/2021
3655	29433^19676+19676^29433	126384	Hans Havermann	03/2021
3656	F(604711)	126377	Henri Lifchitz	02/2005
3657	2^419757+72707	126360	Enzo Doria	04/2016
3658	2^419720-21569	126349	Enzo Doria	07/2013
3659	2^419637+29	126324	Henri Lifchitz	02/2006
3660	31004^11865+11865^31004	126319	Hans Havermann	03/2021
3661	2^419612+1876741	126316	Enzo Doria	07/2016
3662	2^419520+2793271	126289	Enzo Doria	03/2016
3663	(2^419447-5)/369	126264	Lelio R Paula	05/2014
3664	2^419328-1859939	126231	Enzo Doria	03/2016
3665	2^419282-1851507	126217	Enzo Doria	08/2015
3666	(133*10^126212+17)/3	126214	Robert Price	11/2021
3667	2^419251+1866143	126208	Enzo Doria	03/2016
3668	11^121185+2	126202	Robert Price	05/2014
3669	28203^28352+28352^28203	126175	Norbert Schneider	01/2021
3670	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
3671	2^418851+23	126087	Robert Price	09/2015
3672	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
3673	2^418829+167	126081	Lelio R Paula	01/2012
3674	31037^11530+11530^31037	126067	Hans Havermann	03/2021
3675	4*10^126064-69	126065	Robert Price	01/2022
3676	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
3677	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
3678	(35*10^126048-323)/9	126049	Robert Price	10/2021
3679	33016^6551+6551^33016	126000	Hans Havermann	03/2021
3680	2^418548-111546435	125996	Paul Bourdelais	10/2021
3681	34736^4227+4227^34736	125954	Hans Havermann	03/2021
3682	2^418319-109501	125927	Enzo Doria	04/2014
3683	2^418316-112373	125926	Enzo Doria	06/2014
3684	40398^1309+1309^40398	125919	Hans Havermann	03/2021
3685	(8*10^125894-29)/3	125895	Robert Price	07/2018
3686	(26*10^125886-413)/9	125887	Robert Price	05/2018
3687	55*10^125847+9	125849	Robert Price	03/2022
3688	4*10^125832+57	125833	Robert Price	05/2022
3689	2^417968+1869811	125821	Enzo Doria	06/2016
3690	2^417902+63	125802	Lelio R Paula	09/2015
3691	(10^125792-91)/9	125792	Serge Batalov	12/2014
3692	30438^13573+13573^30438	125791	Hans Havermann	03/2021
3693	32867^6714+6714^32867	125782	Hans Havermann	03/2021
3694	31155^10892+10892^31155	125777	Hans Havermann	03/2021
3695	(35*10^125754-593)/9	125755	Robert Price	07/2018
3696	30455^13464+13464^30455	125754	Hans Havermann	03/2021
3697	(32*10^125751-77)/9	125752	Robert Price	06/2018
3698	2^417704+77011	125742	Enzo Doria	05/2016
3699	29755^16816+16816^29755	125737	Hans Havermann	03/2021
3700	(22*10^125734+203)/9	125735	Robert Price	10/2021
3701	29918^15915+15915^29918	125710	Hans Havermann	03/2021
3702	(10^125706+149)/3	125706	Serge Batalov	12/2014
3703	28531^25368+25368^28531	125659	Hans Havermann	03/2021
3704	2^417419-115309	125656	Enzo Doria	07/2015
3705	(46*10^125642+593)/9	125643	Robert Price	04/2022
3706	2^417300+77281	125620	Enzo Doria	05/2016
3707	30638^12537+12537^30638	125561	Hans Havermann	03/2021
3708	2^417095-1657	125559	Yves Minet	07/2014
3709	30162^14525+14525^30162	125538	Hans Havermann	03/2021
3710	(56*10^125535+583)/9	125536	Robert Price	08/2021
3711	(23*10^125517-179)/3	125518	Robert Price	06/2022
3712	9*10^125516+29	125517	Robert Price	03/2022
3713	(88*10^125492-637)/9	125493	Robert Price	11/2020
3714	28958^21525+21525^28958	125474	Hans Havermann	02/2021
3716	2^416773-25	125462	Lelio R Paula	09/2015
3715	(10^125482+7)/162685667/1639829194459	125462	Alfred Reich	07/2021
3717	33889^5032+5032^33889	125449	Hans Havermann	03/2021
3718	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
3719	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
3720	(289511#+1896)/(23^3797801939911849)	125434	Makoto Morimoto	06/2019
3721	2^416641-2*416641+1	125422	Robert Price	05/2018
3722	33392^5697+5697^33392	125409	Hans Havermann	03/2021
3723	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
3724	2^416530+1870429	125389	Enzo Doria	05/2016
3725	(56*10^125385+691)/9	125386	Robert Price	05/2019
3726	27953^28198+28198^27953	125381	Norbert Schneider	01/2021
3727	31074^10837+10837^31074	125381	Hans Havermann	03/2021
3728	33745^5194+5194^33745	125380	Hans Havermann	03/2021
3729	2^416490+1875109	125376	Enzo Doria	09/2016
3730	28360^26331+26331^28360	125365	Hans Havermann	03/2021
3731	2^416416-114929	125354	Enzo Doria	05/2015
3732	(77*10^125330-293)/9	125331	Robert Price	09/2019
3733	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
3734	2^416134+1865899	125269	Enzo Doria	03/2016
3735	153^57337-152	125264	Norbert Schneider	12/2018
3736	(599*10^125224+13)/9	125226	Robert Price	02/2022
3737	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
3738	30054^14657+14657^30054	125207	Hans Havermann	03/2021
3739	(23^91943-1)/22	125201	Robert Price	01/2012
3740	2^415884-933075	125194	Paul Bourdelais	06/2021
3741	43125^27010-106	125185	Enzo Doria	08/2012
3742	(38*10^125166+349)/9	125167	Robert Price	10/2018
3743	10^125166-5001	125166	Robert Price	12/2021
3744	2^415765-112603	125158	Enzo Doria	06/2014
3745	8*10^125088-13	125089	Robert Price	08/2019
3746	(25*10^125076-13)/3	125077	Robert Price	09/2019
3747	(11*10^125054+73)/3	125055	Robert Price	08/2021
3748	(29*10^125021-113)/3	125022	Robert Price	10/2019
3749	2^415290-113591	125015	Enzo Doria	08/2014
3750	2^415276-460919	125011	Enzo Doria	06/2015

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Probable Primes Top 10000

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