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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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 ?
501	2^1373111+1884833	413348	Enzo Doria	02/2017
502	2^1372996+15	413313	Stefano Morozzi	10/2022
503	2^1369171+216593	412162	Enzo Doria	01/2024
504	2^1368632+1889731	412000	Enzo Doria	10/2017
505	(65245^85849-1)/(65245^293-1)	411914	Ryan Propper	11/2023
506	(89*10^411590+1)/9	411591	Serge Batalov	09/2014
507	F(1968721)	411439	Henri Lifchitz	11/2009
508	2^1366066+683749	411227	Enzo Doria	02/2017
509	2^1364401+217727	410726	Enzo Doria	02/2024
510	2^1364303+219533	410697	Enzo Doria	03/2024
511	2^1363434+27589	410435	Enzo Doria	02/2024
512	2^1359550+25819	409266	Enzo Doria	12/2023
513	2^1355826+15	408145	Stefano Morozzi	10/2022
514	2^1355790+1888939	408134	Enzo Doria	07/2017
515	2^1355635+1884203	408087	Enzo Doria	01/2017
516	(22071^94249-1)/(22071^307-1)	408068	Ryan Propper	11/2023
517	2^1349535+218783	406251	Enzo Doria	03/2024
518	(55766^85849-1)/(55766^293-1)	406081	Ryan Propper	11/2023
519	2^1348956+24241	406077	Enzo Doria	11/2023
520	(88^208739+1)/89	405888	Paul Bourdelais	12/2020
521	(2^1347781-2^673891+1)/5	405722	Borys Jaworski	10/2008
522	2^1347744-3	405712	Paul Bourdelais	07/2019
523	9*10^404644-11	404645	Mischa Rodermond	04/2023
524	1215^131072+242^131072	404302	Kellen Shenton	08/2022
525	2^1341908+212911	403955	Enzo Doria	09/2023
526	1196^131072+595^131072	403405	Kellen Shenton	08/2022
527	2^1339302+29389	403171	Enzo Doria	04/2024
528	2^1330371+28313	400482	Enzo Doria	03/2024
529	10^400000+1415223	400001	Patrick De Geest	10/2020
530	10^400000-339233	400000	Patrick De Geest	10/2020
531	2^1323373+27317	398375	Enzo Doria	01/2024
532	Tau(863^24630)	397727	Nik Lygeros / Olivier Rozier	01/2016
533	2^1320423+24293	397487	Enzo Doria	11/2023
534	2^1320057+211517	397377	Enzo Doria	08/2023
535	2^1319770+1884949	397291	Enzo Doria	06/2017
536	2^1317657+31367	396655	Enzo Doria	04/2024
537	2^1314741+219257	395777	Enzo Doria	03/2024
538	2^1313062+1888849	395272	Enzo Doria	08/2017
539	(1073516^81920+1)/(1073516^16384+1)	395236	Serge Batalov	01/2017
540	2^1312349+221177	395057	Enzo Doria	04/2024
541	(1059995^81920+1)/(1059995^16384+1)	394875	Serge Batalov	01/2017
542	2^1311618+783529	394837	Enzo Doria	01/2017
543	2^1308992+28111	394046	Enzo Doria	02/2024
544	2^1308000+1883521	393748	Enzo Doria	02/2017
545	2^1307262+28759	393526	Enzo Doria	02/2024
546	(1009565^81920+1)/(1009565^16384+1)	393487	Serge Batalov	01/2017
547	(995042^81920+1)/(995042^16384+1)	393075	Serge Batalov	01/2017
548	(988945^81920+1)/(988945^16384+1)	392900	Serge Batalov	01/2017
549	(988823^81920+1)/(988823^16384+1)	392897	Serge Batalov	01/2017
550	(2^1304983-1)/52199321	392832	Tony Prest / Never Odd Or Even	03/2014
551	(978970^81920+1)/(978970^16384+1)	392612	Serge Batalov	01/2017
552	2^1303102+1866409	392273	Enzo Doria	09/2017
553	2^1302818+283429	392188	Enzo Doria	01/2017
554	2^1301430+22669	391770	Enzo Doria	10/2023
555	(934422^81920+1)/(934422^16384+1)	391286	Serge Batalov	01/2017
556	2^1299181+1886867	391093	Enzo Doria	04/2017
557	(37^249341-1)/36	391016	Paul Bourdelais	08/2020
558	2^1298304+1882891	390829	Enzo Doria	01/2017
559	95196^12497+12497^95196	390000	Hans Havermann	12/2021
560	86206^33381+33381^86206	389953	Hans Havermann	05/2023
561	2^1294324+25171	389631	Enzo Doria	12/2023
562	(874207^81920+1)/(874207^16384+1)	389390	Serge Batalov	01/2017
563	(7^457871-5^457871)/2	386946	Jon Grantham	08/2023
564	79455^73828+73828^79455	386805	Hans Havermann	03/2023
565	81650^54369+54369^81650	386642	Yusuf AttarBashi	06/2021
566	80565^62824+62824^80565	386561	Hans Havermann	08/2021
567	83747^41272+41272^83747	386548	Hans Havermann	08/2021
568	15^328574+328574^15	386434	Serge Batalov	05/2014
569	2^1280078+1885099	385342	Enzo Doria	08/2017
570	2^1279921+17	385295	Stefano Morozzi	10/2022
571	2^1276977+71657	384409	Enzo Doria	08/2023
572	(76803^78961-1)/(76803^281-1)	384382	Ryan Propper	11/2023
573	2^1276571+26213	384287	Enzo Doria	12/2023
574	2^1274941+1880717	383796	Enzo Doria	10/2016
575	2^1272632+383431	383101	Enzo Doria	01/2017
576	2^1271346+1889839	382714	Enzo Doria	08/2017
577	2^1271173+219587	382662	Enzo Doria	03/2024
578	5*3^798534-2^798534	380999	Jon Grantham	08/2023
579	(10^380976-7)/3	380976	Leonid Durman	01/2012
580	2^1264748+23221	380728	Enzo Doria	11/2023
581	(4*10^380056+11)/3	380057	Tyler Busby	03/2023
582	2^1257787+1447761	378632	Makoto Morimoto	10/2013
583	(2^1257787+32270)/(223328122073011)	378620	Makoto Morimoto	12/2016
584	2^1257728+20851	378614	Enzo Doria	08/2023
585	(77^200657-1)/76	378536	Paul Bourdelais	08/2020
586	(98^189619+1)/99	377573	Paul Bourdelais	02/2021
587	F(1803059)	376817	Henri Lifchitz	06/2009
588	2^1250590+29389	376466	Enzo Doria	03/2024
589	(10^376417-3^376417)/7	376417	Jon Grantham	08/2023
590	2^1246724+213961	375302	Enzo Doria	10/2023
591	2^1245230+19	374852	Stefano Morozzi	10/2022
592	7^442674+4	374103	Paul Bourdelais	02/2021
593	(97^187393-1)/96	372306	Paul Bourdelais	09/2020
594	10^371696+7	371697	Alfred Reich	05/2021
595	2^1234709+883127	371685	Enzo Doria	12/2016
596	2^1234119+21803	371507	Enzo Doria	09/2023
597	(67^203431+1)/68	371479	Paul Bourdelais	09/2021
598	2^1233971+216593	371463	Enzo Doria	12/2023
599	2^1233212+27301	371234	Enzo Doria	12/2023
600	2^1231466+283819	370709	Enzo Doria	07/2017
601	2^1229766+26659	370197	Enzo Doria	12/2023
602	2^1228899+30713	369936	Enzo Doria	03/2024
603	(49627^78961-1)/(49627^281-1)	369460	Ryan Propper	11/2023
604	2^1226987+28163	369360	Enzo Doria	02/2024
605	2^1226569+30857	369235	Enzo Doria	03/2024
606	73^197880+197880	368715	Kellen Shenton	06/2023
607	5*3^771723-2^771723	368207	Jon Grantham	08/2023
608	2^1222473+221597	368002	Enzo Doria	04/2024
609	2^1222211+22703	367923	Enzo Doria	11/2023
610	(2^1222097+19)/3	367888	Stefano Morozzi	09/2022
611	2^1220335+1881263	367358	Enzo Doria	11/2016
612	2^1218344+215641	366759	Enzo Doria	12/2023
613	2^1217510+220039	366508	Enzo Doria	03/2024
614	2^1216694+1884769	366262	Enzo Doria	02/2017
615	2^1215889-3	366020	Paul Bourdelais	06/2019
616	2^1215296+1885441	365841	Enzo Doria	03/2017
617	(80^192133+1)/81	365645	Paul Bourdelais	01/2021
618	2^1214307+1888115	365543	Enzo Doria	05/2017
619	2^1213815+3	365395	Paul Bourdelais	06/2019
620	(80^191953+1)/81	365302	Paul Bourdelais	01/2021
621	2^1213313+215837	365244	Enzo Doria	11/2023
622	2^1208276+22201	363728	Enzo Doria	09/2023
623	2^1207345+1882577	363448	Enzo Doria	12/2016
624	2^1207336+217801	363445	Enzo Doria	03/2024
625	2^1207073+883727	363366	Enzo Doria	03/2017
626	3^761457-2	363308	Ryan Propper	07/2015
627	(10^363030+7)/337/443	363025	Alfred Reich	12/2021
628	2^1200972+141811	361529	Stefano Morozzi	10/2022
629	(2^1200924+324730)/2	361514	Stefano Morozzi	06/2021
630	(2^1200912+274110)/2	361511	Stefano Morozzi	01/2021
631	2^1200906+165249	361509	Stefano Morozzi	07/2022
632	2^1200890+166339	361504	Stefano Morozzi	01/2023
633	(2^1200887+344126)/2	361503	Stefano Morozzi	10/2020
634	2^1200877+186755	361500	Stefano Morozzi	09/2022
635	2^1200861+198521	361495	Stefano Morozzi	11/2021
636	(2^1200856+305790)/2	361494	Stefano Morozzi	10/2020
637	(2^1200853+372822)/2	361493	Stefano Morozzi	06/2021
638	2^1200812+324178)/2	361481	Stefano Morozzi	06/2021
639	(2^1200768+380458)/2	361467	Stefano Morozzi	01/2021
640	2^1200756+140917	361464	Stefano Morozzi	05/2022
641	2^1200741+184781	361460	Stefano Morozzi	09/2022
642	(2^1200741+293402)/2	361459	Stefano Morozzi	07/2021
643	2^1200734+142653	361457	Stefano Morozzi	02/2023
645	2^1200672+1880881	361439	Enzo Doria	10/2016
644	2^1200672+141535	361439	Stefano Morozzi	09/2022
646	2^1200669+178805	361438	Stefano Morozzi	11/2022
647	2^1200660+198555	361435	Stefano Morozzi	12/2021
648	2^1200657+164837	361434	Stefano Morozzi	05/2022
649	2^1200631+166431	361426	Stefano Morozzi	02/2023
650	2^1200627+150669	361425	Stefano Morozzi	02/2023
651	(2^1200603+356030)/2	361418	Stefano Morozzi	10/2020
652	(2^1200590+275854)/2	361414	Stefano Morozzi	03/2021
653	2^1200550+139297	361402	Stefano Morozzi	10/2021
654	2^1200486+172855	361383	Stefano Morozzi	01/2023
655	(2^1200456+320526)/2	361373	Stefano Morozzi	10/2020
656	2^1200443+142121	361370	Stefano Morozzi	01/2023
657	2^1200416+164065	361362	Stefano Morozzi	01/2022
658	2^1200331+155429	361336	Stefano Morozzi	10/2021
660	(2^1200289+348366)/2	361323	Stefano Morozzi	10/2020
659	2^1200289+141885	361323	Stefano Morozzi	11/2022
661	(2^1200284+273162)/2	361322	Stefano Morozzi	10/2020
662	2^1200252+194535	361312	Stefano Morozzi	11/2021
663	(2^1200250+364230)/2	361311	Stefano Morozzi	10/2020
664	2^1200227+156881	361305	Stefano Morozzi	05/2022
665	(2^1200209+305990)/2	361299	Stefano Morozzi	10/2020
666	(2^1200210+376278)/2	361299	Stefano Morozzi	10/2020
667	2^1200202+216499	361297	Enzo Doria	12/2023
668	(2^1200182+274462)/2	361291	Stefano Morozzi	01/2021
669	2^1200178+149193	361290	Stefano Morozzi	07/2022
670	2^1200168+140403	361287	Stefano Morozzi	03/2022
671	(2^1200162+275910)/2	361285	Stefano Morozzi	03/2021
672	2^1200157+168927	361284	Stefano Morozzi	02/2023
673	2^1200134+141385	361277	Stefano Morozzi	08/2022
674	(2^1200131+360150)/2	361276	Stefano Morozzi	10/2020
675	(2^1200118+290718)/2	361272	Stefano Morozzi	01/2021
676	2^1200022+192777	361243	Stefano Morozzi	09/2022
677	2^1200021+149777	361243	Stefano Morozzi	10/2022
678	(64*10^360173-1)/243	360173	Serge Batalov	09/2014
679	(59^203309+1)/60	360029	Paul Bourdelais	09/2021
680	(2*10^359860-11)/9	359860	Rytis Slatkevicius	01/2023
681	2^1195093+1882577	359759	Enzo Doria	12/2016
682	3^753451+5*2^753451	359488	Jon Grantham	08/2023
683	(6^461108-11)/5	358812	Paul Bourdelais	04/2019
684	2^1191375+8543	358640	Phil Moore	06/2008
685	2^1190972+1880191	358519	Enzo Doria	11/2016
686	2^1189930+28549	358205	Enzo Doria	03/2024
687	(45^216551-1)/44	358004	Paul Bourdelais	08/2020
688	(50^210319-1)/49	357324	Paul Bourdelais	08/2020
689	(531^131072+25^131072)/2	357184	Kellen Shenton	03/2021
690	2^1184565+21227	356590	Enzo Doria	08/2023
691	2^1180159+22823	355264	Enzo Doria	11/2023
692	2^1179836+1885021	355167	Enzo Doria	02/2017
693	2^1177053+28607	354329	Enzo Doria	02/2024
694	(19*10^353884-91)/9	353885	Alfred Reich	02/2023
695	(10^353884*19-91)/9	353885	Alfred Reich	10/2023
696	20^271951+3	353817	Paul Bourdelais	01/2021
697	72722^72722+7^7	353551	Serge Batalov	04/2024
698	2^1173095+21	353137	Stefano Morozzi	10/2022
699	2^1170959+218945	352494	Enzo Doria	03/2024
700	(63^195893-1)/62	352477	Paul Bourdelais	08/2020
701	2^1170331+27293	352305	Enzo Doria	01/2024
702	2^1170326+7	352304	Stefano Morozzi	10/2022
703	numbpart(100000135540)	352269	Serge Batalov	04/2017
704	(10^352237-1)/9/10567111/950335427	352221	Maksym Voznyy	01/2015
705	5*3^737931-2^737931	352084	Jon Grantham	08/2023
706	2^1168554+783529	351770	Enzo Doria	01/2017
707	(2^1168183-1)/54763676838381762583	351639	Matthias Wurtinger	01/2011
708	2^1166950+30409	351287	Enzo Doria	03/2024
709	2^1166152+1882411	351047	Enzo Doria	12/2016
710	2^1163972+20971	350391	Enzo Doria	08/2023
711	2^1163272+22411	350180	Enzo Doria	10/2023
712	10^350071+7	350072	Alfred Reich	05/2021
713	2^1162154+1890207	349844	Enzo Doria	08/2017
714	(7*10^348724-61)/9	348724	Erik Branger	09/2016
715	(4*10^348453+41)/9	348453	Serge Batalov	11/2022
716	(127^165601-1)/126	348390	Alexander Zhirkov	09/2015
717	2^1155085+213377	347716	Enzo Doria	09/2023
718	2^1153083+1883693	347113	Enzo Doria	04/2017
719	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
720	2^1145882+80779	344945	Enzo Doria	09/2016
721	2^1143425+221177	344206	Enzo Doria	03/2024
722	2^1141813+27047	343720	Enzo Doria	12/2023
723	2^1141114+221869	343510	Enzo Doria	04/2024
724	2^1138296+27541	342662	Enzo Doria	01/2024
725	2^1136462+1887289	342110	Enzo Doria	05/2017
726	F(1636007)	341905	Henri Lifchitz	03/2009
727	(2^1135567+13)/3	341840	Stefano Morozzi	09/2022
728	2^1133678+782569	341272	Enzo Doria	11/2016
729	(11^327001+1)/12	340536	Paul Bourdelais	09/2013
730	2^1129361+221597	339972	Enzo Doria	04/2024
731	2^1128621+25919	339749	Enzo Doria	12/2023
732	(2^1127239+2^563620+1)/5	339333	Borys Jaworski	11/2006
733	Tau(907^20848)	339132	Nik Lygeros / Olivier Rozier	01/2016
734	2^1126380-3	339075	Paul Bourdelais	06/2019
735	2^1125784+24331	338895	Enzo Doria	10/2023
736	2^1125446+1885099	338794	Enzo Doria	08/2017
737	(63^188147+1)/64	338539	Paul Bourdelais	12/2020
738	2^1124549+143807	338523	Enzo Doria	10/2016
739	(4*10^338476+23)/9	338476	Serge Batalov	11/2022
740	2^1121187+1886783	337511	Enzo Doria	04/2017
741	(48^200443-1)/47	336992	Paul Bourdelais	08/2020
742	(2*10^336405+43)/9	336405	Rytis Slatkevicius	01/2023
743	(94^170371-1)/93	336162	Paul Bourdelais	09/2020
744	2^1116184+1883521	336005	Enzo Doria	02/2017
745	2^1115727+27683	335868	Enzo Doria	01/2024
746	2^1114974+28759	335641	Enzo Doria	02/2024
747	2^1114517+1880087	335504	Enzo Doria	10/2016
748	(5*10^335480+31)/9	335480	Serge Batalov	11/2022
749	5*3^701688+2^701688	334791	Jon Grantham	08/2023
750	(101^166849+1)/102	334418	Paul Bourdelais	12/2020

Find by discoverer :

PRP Records

Probable Primes Top 10000

(295036 PRPs in the top)