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	5*10^139945+81	139946	Robert Price	03/2019
3502	32648^19335+19335^32648	139941	Hans Havermann	05/2021
3503	2^464864-17	139939	Lelio R Paula	09/2017
3504	8*10^139920+51	139921	Robert Price	08/2019
3505	(85*10^139913-1)/3	139915	Robert Price	02/2020
3506	31203^30436+30436^31203	139896	Hans Havermann	04/2021
3507	2^464642+22189	139872	Enzo Doria	09/2023
3508	(16^116139+619)/5	139845	Anonymous	08/2022
3509	(2^464556+619)/5	139845	Eric Chen	10/2023
3510	4*10^139839-27	139840	Robert Price	08/2021
3511	33582^14573+14573^33582	139821	Hans Havermann	05/2021
3512	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
3514	2*10^139800-21	139801	Robert Price	09/2020
3513	32628^19261+19261^32628	139801	Hans Havermann	04/2021
3515	(13*10^139782+191)/3	139783	Robert Price	11/2018
3516	(64*10^139776+791)/9	139777	Robert Price	01/2022
3517	(695*10^139772+7)/9	139774	Robert Price	12/2021
3518	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
3519	(74*10^139723+133)/9	139724	Robert Price	06/2019
3520	3*10^139722+13	139723	Robert Price	07/2018
3521	31577^26592+26592^31577	139721	Hans Havermann	05/2021
3522	77*10^139692+3	139694	Robert Price	06/2020
3523	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
3524	(18203^(2^15)+(18201)^(2^15))/2	139597	Robert Price	05/2018
3525	39640^3321+3321^39640	139584	Hans Havermann	05/2021
3526	36663^6410+6410^36663	139571	Hans Havermann	05/2021
3527	2^463633-2788423	139568	Enzo Doria	11/2015
3528	33659^13978+13978^33659	139532	Hans Havermann	05/2021
3529	31811^24318+24318^31811	139521	Hans Havermann	04/2021
3530	34149^12172+12172^34149	139512	Hans Havermann	04/2021
3531	(29*10^139476+313)/9	139477	Robert Price	04/2021
3532	31721^24940+24940^31721	139474	Hans Havermann	05/2021
3533	32833^17698+17698^32833	139473	Hans Havermann	05/2021
3534	2^463271-109501	139459	Enzo Doria	04/2014
3535	(5*10^139457+79)/3	139458	Robert Price	03/2018
3536	2^463237-99	139449	Lelio R Paula	09/2017
3537	(49*10^139442+383)/9	139443	Robert Price	04/2019
3538	31155^29902+29902^31155	139441	Hans Havermann	05/2021
3539	(7*10^139417-547)/9	139417	Robert Price	01/2018
3540	(10^139398+191)/3	139398	Robert Price	02/2018
3541	23*10^139386-3	139388	Robert Price	10/2021
3542	2^463019+79463	139383	Enzo Doria	06/2016
3543	3^292129-112756	139381	Enzo Doria	07/2014
3544	(15*2^462951+1)/527	139361	Lelio R Paula	08/2015
3545	31922^23205+23205^31922	139359	Hans Havermann	05/2021
3546	(19*10^139336+503)/9	139337	Alfred Reich	11/2023
3548	2^462855-1865707	139334	Enzo Doria	02/2016
3547	31237^28876+28876^31237	139334	Hans Havermann	05/2021
3549	(86*10^139315+121)/9	139316	Robert Price	08/2019
3550	2^462786-292043	139313	Enzo Doria	08/2015
3551	38915^3798+3798^38915	139299	Hans Havermann	05/2021
3553	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
3552	(17*10^139289+7)/3	139290	Robert Price	06/2023
3554	34065^12248+12248^34065	139260	Hans Havermann	05/2021
3555	36425^6654+6654^36425	139256	Hans Havermann	05/2021
3556	39252^3527+3527^39252	139243	Hans Havermann	05/2021
3557	(17*10^139239+67)/3	139240	Robert Price	01/2019
3558	31887^23248+23248^31887	139231	Hans Havermann	05/2021
3559	(25*10^139210-97)/9	139211	Robert Price	01/2022
3560	2^462238-935	139148	Yves Minet	02/2014
3561	(29*10^139134-119)/9	139135	Robert Price	12/2021
3562	(109*10^139100-7)/3	139102	Robert Price	03/2021
3563	38744^3885+3885^38744	139068	Hans Havermann	05/2021
3564	31112^29499+29499^31112	139065	Hans Havermann	05/2021
3565	2*10^139043-63	139044	Robert Price	01/2022
3566	36390^6613+6613^36390	139025	Hans Havermann	04/2021
3567	2*10^138975+33	138976	Robert Price	11/2021
3568	42437^1882+1882^42437	138966	Hans Havermann	05/2021
3569	32151^20990+20990^32151	138958	Hans Havermann	05/2021
3570	32154^20933+20933^32154	138933	Hans Havermann	04/2021
3571	31082^29499+29499^31082	138931	Hans Havermann	04/2021
3572	2^461228+1870441	138844	Enzo Doria	05/2016
3573	2^461204-113675	138837	Enzo Doria	08/2014
3574	(2^461139-7)/47	138815	Lelio R Paula	08/2015
3575	(17*10^138812-521)/9	138813	Robert Price	04/2018
3576	3*10^138811-11	138812	Robert Price	07/2018
3577	(28*10^138768+173)/3	138769	Robert Price	12/2019
3578	(17*2^460963+1)/124051613	138757	Lelio R Paula	08/2015
3579	(379*10^138737-1)/9	138739	Robert Price	02/2020
3580	(43*10^138648+101)/9	138649	Robert Price	11/2018
3581	2^460567-113541	138645	Enzo Doria	08/2014
3582	(10^138622+161)/9	138622	Robert Price	09/2021
3583	7*10^138604+3	138605	Robert Price	08/2015
3584	(133*10^138600+17)/3	138602	Robert Price	11/2021
3585	33912^12203+12203^33912	138581	Hans Havermann	05/2021
3586	2^460330+69	138574	Lelio R Paula	09/2017
3587	(17*10^138569-77)/3	138570	Robert Price	08/2019
3588	31186^27725+27725^31186	138556	Hans Havermann	05/2021
3589	(16*10^138545+89)/3	138546	Robert Price	03/2021
3590	39753^3056+3056^39753	138546	Hans Havermann	05/2021
3591	31282^26847+26847^31282	138545	Hans Havermann	05/2021
3592	6*10^138520-37	138521	Robert Price	02/2021
3594	2^460078-69581	138498	Enzo Doria	12/2015
3593	31830^22447+22447^31830	138498	Hans Havermann	05/2021
3595	37384^5065+5065^37384	138492	Hans Havermann	05/2021
3596	34774^9585+9585^34774	138456	Hans Havermann	05/2021
3597	10^138444-5001	138444	Robert Price	12/2021
3598	2^459768+1531	138404	Lelio R Paula	06/2012
3599	(266*10^138328-17)/3	138330	Robert Price	07/2020
3600	32963^15696+15696^32963	138306	Hans Havermann	05/2021
3601	2^459343-113611	138277	Enzo Doria	08/2014
3602	(28*10^138240+113)/3	138241	Robert Price	03/2020
3603	2^459199+1874393	138233	Enzo Doria	06/2016
3604	33339^14002+14002^33339	138230	Hans Havermann	05/2021
3605	2^459063-345307	138192	Enzo Doria	06/2015
3606	2*10^138162-43	138163	Robert Price	04/2018
3607	2^458927-112747	138151	Enzo Doria	06/2014
3608	2^458927-69217	138151	Enzo Doria	11/2015
3609	30907^29458+29458^30907	138130	Hans Havermann	05/2021
3610	32882^15837+15837^32882	138094	Hans Havermann	05/2021
3611	39252^3295+3295^39252	138083	Hans Havermann	05/2021
3612	33789^12190+12190^33789	138062	Hans Havermann	06/2021
3613	555555*2^458524+1513	138036	Darren Bedwell	08/2009
3614	30931^29002+29002^30931	138028	Hans Havermann	05/2021
3615	2^458465+2^32+1	138012	T. D. Noe	06/2007
3616	32206^19275+19275^32206	138003	Hans Havermann	05/2021
3617	2^458321-113053	137969	Enzo Doria	07/2014
3618	6^177298+323	137965	Riley Fisher	03/2023
3619	2^458298+79459	137962	Enzo Doria	06/2016
3620	2^458248-21815	137947	Enzo Doria	07/2013
3621	2^458194+1876549	137931	Enzo Doria	07/2016
3622	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
3623	(318259#+2625)/(3^257^5*22965193)	137899	Makoto Morimoto	06/2019
3624	(793*10^137887+53)/9	137889	Robert Price	01/2022
3625	2^457937+57	137853	Lelio R Paula	09/2017
3626	(8*10^137845+13)/3	137846	Robert Price	06/2018
3627	2^457822+105	137819	Donovan Johnson	06/2006
3628	2^457754-113711	137798	Enzo Doria	09/2014
3629	11^132315-360	137792	Enzo Doria	09/2012
3630	32072^19689+19689^32072	137725	Hans Havermann	06/2021
3631	44592^1225+1225^44592	137707	Hans Havermann	05/2021
3632	2^457347-37	137676	Lelio R Paula	09/2017
3633	2^457322-2786393	137668	Enzo Doria	10/2015
3634	gcd(Phi(699340,10),(10^34967+1)^3(10^34967+1+10^17484)-(10^69934+10^34967)(10^17484-1)+10^104901)	137664	Serge Batalov	04/2015
3635	34015^11134+11134^34015	137647	Hans Havermann	06/2021
3636	2^457240-59939	137643	Enzo Doria	10/2015
3637	(856*10^137633-1)/9	137635	Robert Price	03/2020
3638	36232^6289+6289^36232	137631	Hans Havermann	05/2021
3639	2^457120-21575	137607	Enzo Doria	07/2013
3640	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
3641	30963^27722+27722^30963	137564	Hans Havermann	04/2021
3642	33722^12003+12003^33722	137562	Hans Havermann	06/2021
3643	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
3644	41901^1918+1918^41901	137555	Hans Havermann	06/2021
3645	(7*10^137551-1)/3	137552	Robert Price	08/2022
3646	32930^15021+15021^32930	137539	Hans Havermann	05/2021
3647	31178^25785+25785^31178	137538	Hans Havermann	05/2021
3648	419^52446+52446^419	137525	Norbert Schneider	11/2020
3649	2^456813+214175	137515	Enzo Doria	10/2023
3650	2^456796-113513	137510	Enzo Doria	08/2014
3651	31788^21137+21137^31788	137485	Hans Havermann	04/2021
3652	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
3653	2^456503-114361	137422	Enzo Doria	01/2015
3654	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
3655	36248^6147+6147^36248	137332	Hans Havermann	05/2021
3656	31986^19651+19651^31986	137329	Hans Havermann	05/2021
3657	2^456167+22313	137320	Enzo Doria	09/2023
3658	31817^20656+20656^31817	137292	Hans Havermann	05/2021
3659	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
3660	2^455922+76249	137247	Enzo Doria	05/2016
3661	31310^24171+24171^31310	137241	Hans Havermann	05/2021
3662	14^119741-119741^14	137239	Serge Batalov	04/2016
3663	35014^8297+8297^35014	137218	Hans Havermann	05/2021
3664	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
3666	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
3665	124^65536+57^65536	137195	Serge Batalov	03/2018
3667	2^455689+72677	137177	Enzo Doria	04/2016
3668	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
3669	31287^24128+24128^31287	137116	Hans Havermann	05/2021
3670	(37^87421-1)/36	137093	Robert Price	03/2012
3671	36233^6070+6070^36233	137077	Hans Havermann	05/2021
3672	(8*10^137073-17)/9	137073	Serge Batalov	11/2022
3673	38418^3697+3697^38418	137070	Hans Havermann	04/2021
3674	2^455323-57	137066	Lelio R Paula	09/2017
3675	(56*10^137019+583)/9	137020	Robert Price	08/2021
3676	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
3677	2^455025-112723	136977	Enzo Doria	06/2014
3678	33876^11039+11039^33876	136959	Hans Havermann	05/2021
3679	(19860^32041-1)/(19860^179-1)	136943	Ryan Propper	11/2023
3680	35142^7873+7873^35142	136919	Hans Havermann	05/2021
3681	66*10^136894+7	136896	Robert Price	07/2020
3682	2^454675-1777	136871	Yves Minet	10/2011
3683	31676^20931+20931^31676	136866	Hans Havermann	05/2021
3684	3*10^136829+29	136830	Robert Price	05/2018
3685	4*10^136813-57	136814	Robert Price	10/2018
3686	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
3687	fibonacci(654572)-2	136798	Jon Grantham	08/2023
3688	37359^4588+4588^37359	136795	Hans Havermann	05/2021
3689	2^454348-53	136773	Lelio R Paula	09/2017
3690	31^91680-2	136729	Lelio R Paula	05/2017
3691	2^454199-113697	136728	Enzo Doria	09/2014
3692	30785^27622+27622^30785	136725	Hans Havermann	05/2021
3693	32973^14014+14014^32973	136725	Hans Havermann	05/2021
3695	7*10^136716+69	136717	Robert Price	07/2019
3694	36002^6273+6273^36002	136717	Hans Havermann	05/2021
3696	6*10^136692+53	136693	Robert Price	05/2020
3697	(13*10^136687+47)/3	136688	Robert Price	10/2018
3698	2^453935-2791357	136649	Enzo Doria	01/2016
3699	2^453906-69131	136640	Enzo Doria	11/2015
3700	33232^12915+12915^33232	136620	Hans Havermann	05/2021
3701	2^453791+1873913	136605	Enzo Doria	06/2016
3702	34166^9951+9951^34166	136592	Hans Havermann	05/2021
3703	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
3704	31102^24635+24635^31102	136587	Hans Havermann	05/2021
3705	580^49413+49413^580	136550	Norbert Schneider	02/2019
3706	2^453503-2788297	136519	Enzo Doria	11/2015
3707	34989^7958+7958^34989	136486	Hans Havermann	12/2020
3708	(2*10^136484+187)/9	136484	Robert Price	06/2022
3709	31007^25158+25158^31007	136452	Hans Havermann	11/2020
3710	2^453267-113827	136447	Enzo Doria	09/2014
3711	32234^17085+17085^32234	136435	Hans Havermann	12/2020
3712	2^453102+1877629	136398	Enzo Doria	08/2016
3713	31016^24981+24981^31016	136397	Hans Havermann	12/2020
3714	(62*10^136384-791)/9	136385	Robert Price	06/2019
3715	34171^9798+9798^34171	136382	Hans Havermann	12/2020
3716	(17*10^136354-113)/3	136355	Robert Price	06/2021
3717	32756^14541+14541^32756	136350	Hans Havermann	11/2020
3718	32205^17086+17086^32205	136313	Hans Havermann	12/2020
3719	(25*10^136303+161)/3	136304	Robert Price	09/2019
3720	35337^7196+7196^35337	136299	Hans Havermann	12/2020
3721	(182*10^136291+1)/3	136293	Robert Price	02/2020
3722	(88*10^136234+83)/9	136235	Robert Price	03/2022
3723	23*10^136225-7	136227	Robert Price	02/2020
3724	L(651821)	136223	Henri Lifchitz	09/2008
3725	2^452460+77701	136205	Enzo Doria	05/2016
3726	2^452440-114755	136199	Enzo Doria	04/2015
3727	32286^16489+16489^32286	136157	Hans Havermann	11/2020
3728	(47*10^136141+493)/9	136142	Robert Price	03/2019
3729	40392^2339+2339^40392	136082	Hans Havermann	12/2020
3730	2*10^136057-43	136058	Robert Price	04/2018
3731	2^451971+21563	136057	Enzo Doria	08/2023
3732	(2^451956-5)/181	136051	Lelio R Paula	07/2015
3733	2^451947-22165	136050	Enzo Doria	07/2013
3734	2^451787-21805	136002	Enzo Doria	07/2013
3735	2^451734-112817	135986	Enzo Doria	06/2014
3736	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
3737	2^451705-21879	135977	Enzo Doria	07/2013
3738	(4666^37249-1)/(4666^193-1)	135957	Ryan Propper	11/2023
3739	2^451560-112349	135934	Enzo Doria	06/2014
3740	2^451530+45	135925	Lelio R Paula	08/2017
3741	31622^19875+19875^31622	135922	Hans Havermann	11/2020
3742	(25*10^135906-73)/3	135907	Robert Price	09/2019
3743	2^451450-21743	135900	Enzo Doria	07/2013
3744	(7*10^135879+11)/9	135879	Tyler Busby	01/2023
3745	35218^7199+7199^35218	135846	Hans Havermann	11/2020
3746	35661^6446+6446^35661	135844	Hans Havermann	11/2020
3747	31869^18248+18248^31869	135801	Hans Havermann	12/2020
3748	(77*10^135789+157)/9	135790	Robert Price	05/2022
3749	2^450958+60529	135752	Enzo Doria	08/2023
3750	2^450805+65	135706	Lelio R Paula	08/2017

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Probable Primes Top 10000

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