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 ?
251	(83467^121801-1)/(83467^349-1)	597728	Ryan Propper	11/2023
252	(61448^124609-1)/(61448^353-1)	595001	Ryan Propper	11/2023
253	(15^505117-1)/14	594063	Paul Bourdelais	01/2015
254	81^310721-80^310721	593007	Paul Bourdelais	07/2023
255	(152^270217-1)/(152-1)	589570	Michael Stocker	06/2015
256	Phi(177147,94259)	587458	Anonymous	09/2022
257	2^1950002+1867369	587010	Enzo Doria	02/2018
258	116265^111218+111218^116265	586694	Ryan Propper	10/2023
259	2^1940812+3	584243	Paul Bourdelais	06/2020
260	1933695^2+2^1933695	582101	Ryan Propper	05/2023
261	(5^832151-2^832151)/3	581649	Jon Grantham	08/2023
262	(129810^113569-1)/(129810^337-1)	578991	Ryan Propper	11/2023
263	2^1923104+153	578912	Stefano Morozzi	07/2021
264	116761^87652+87652^116761	577122	Ryan Propper	10/2023
265	116395^87994+87994^116395	575510	Ryan Propper	10/2023
266	(3^1205459+1)/4	575150	Paul Bourdelais	08/2015
267	(160972^109561-1)/(160972^331-1)	568734	Ryan Propper	11/2023
268	(37015^124609-1)/(37015^353-1)	567649	Ryan Propper	11/2023
269	2^1882800+384541	566780	Enzo Doria	12/2017
270	(2^1882787-2^941394+1)/5	566775	Borys Jaworski	11/2012
271	2^1882474+71389	566682	Enzo Doria	04/2018
272	(6^727496-11)/5	566102	Paul Bourdelais	08/2019
273	2^1875552+3	564598	Paul Bourdelais	04/2020
274	(145373^109561-1)/(145373^331-1)	563899	Ryan Propper	11/2023
275	(10^563535-7)/3	563535	Rytis Slatkevicius	02/2023
276	3^1180181-2	563090	Jorge Coveiro	05/2020
277	(15063^134689-1)/(15063^367-1)	561186	Ryan Propper	11/2023
278	2^1852265+1890425	557588	Enzo Doria	11/2017
279	5^797390-2	557352	Paul Bourdelais	03/2021
280	(10^556441-7^556441)/3	556441	Jon Grantham	07/2023
281	8^615997-7^615997	556301	Jean-Louis Charton	07/2009
282	(5^795829-2^795829)/3	556261	Jon Grantham	08/2023
283	Tau(773^34960)	555339	Nik Lygeros / Olivier Rozier	09/2015
284	((((((((((1361^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840)^3+1623568	555154	Serge Batalov	08/2013
285	2^1835205+225197	552452	Enzo Doria	10/2024
286	2^1825513+32507	549535	Enzo Doria	07/2024
287	2^1823921+34937	549055	Enzo Doria	11/2024
288	(42^337081-1)/41	547165	Paul Bourdelais	09/2021
289	114868^57423+57423^114868	546667	Ryan Propper	10/2023
290	109092^100999+100999^109092	545931	Ryan Propper	10/2023
291	2^1812234+31879	545537	Enzo Doria	05/2024
292	(64814^113569-1)/(64814^337-1)	544835	Ryan Propper	11/2023
293	2^1804109+37007	543091	Enzo Doria	11/2024
294	(92170^109561-1)/(92170^331-1)	542283	Ryan Propper	11/2023
295	2^1797319+29693	541047	Enzo Doria	11/2024
296	(28262^121801-1)/(28262^349-1)	540608	Ryan Propper	11/2023
297	2^1791569+33587	539317	Enzo Doria	09/2024
298	(2^1790743-1)/(1468409271583589849773835546416767873*20752172271489035681)	539014	Dario Alpern	06/2015
299	10^538640-3	538640	Paul Bourdelais	01/2021
300	(10^538508+53)/9	538508	Rytis Slatkevicius	01/2023
301	2^1787653+224687	538138	Enzo Doria	10/2024
302	2^1787167+71963	537991	Enzo Doria	12/2018
303	(7^636043-5^636043)/2	537519	Jon Grantham	08/2023
304	108309^91610+91610^108309	537424	Ryan Propper	10/2023
305	(12^495953+1)/13	535223	Paul Bourdelais	11/2018
306	2^1774781+30197	534263	Enzo Doria	08/2024
307	2^1773644+72511	533921	Enzo Doria	10/2018
308	(92^271639-1)/91	533440	Paul Bourdelais	02/2022
309	2^1771408+223201	533247	Enzo Doria	07/2024
310	2^1770613+212597	533008	Enzo Doria	10/2023
311	(11559^131072+1)/2	532535	Serge Batalov	04/2018
312	(85^275881-1)/84	532289	Paul Bourdelais	02/2022
313	2^1767579+213683	532095	Enzo Doria	10/2023
314	2^1767218+25249	531986	Enzo Doria	02/2024
315	2^1762004-3	530417	Paul Bourdelais	04/2020
316	2^1754760+217465	528236	Enzo Doria	01/2024
317	2^1753261+25367	527785	Enzo Doria	11/2023
318	105006^105006-133^133	527258	Sergey Batalov	05/2024
319	2^1750727+213683	527022	Enzo Doria	10/2023
320	2^1750208+218371	526866	Enzo Doria	01/2024
321	2^1743981+28997	524991	Enzo Doria	03/2024
322	2^1737680+23161	523094	Enzo Doria	01/2024
323	(73^280697+1)/74	523028	Paul Bourdelais	02/2022
324	2^1737207+218153	522952	Enzo Doria	05/2024
325	2^1735354+227509	522394	Enzo Doria	11/2024
326	2^1734898+225529	522257	Enzo Doria	09/2024
327	(21^394579+1)/22	521719	Paul Bourdelais	10/2018
328	2^1730246+384439	520856	Enzo Doria	09/2017
329	2^1729303+34313	520573	Enzo Doria	11/2024
330	(55^299087+1)/56	520519	Paul Bourdelais	02/2022
331	5^744171-3^744171-1	520154	Jon Grantham	08/2023
332	2^1727856+31951	520137	Enzo Doria	04/2024
333	(18^414269-1)/17	520020	Paul Bourdelais	12/2014
334	2^1726522+30859	519735	Enzo Doria	06/2024
335	2^1717949+30077	517155	Enzo Doria	08/2024
336	2^1717612+31891	517053	Enzo Doria	04/2024
337	(144171^100489-1)/(144171^317-1)	516776	Ryan Propper	11/2023
338	2^1714462+217465	516105	Enzo Doria	01/2024
339	2^1714021+29777	515972	Enzo Doria	03/2024
340	2^1713855+220703	515922	Enzo Doria	03/2024
341	2^1712979+222143	515659	Enzo Doria	05/2024
342	20^396120-3	515365	Paul Bourdelais	01/2021
343	(136102^100489-1)/(136102^317-1)	514270	Ryan Propper	11/2023
344	2^1708341+221897	514262	Enzo Doria	09/2024
345	(7^608347-5^608347)/2	514113	Jon Grantham	08/2023
346	(62^286483+1)/63	513488	Paul Bourdelais	02/2022
347	(20^393257+1)/21	511638	Paul Bourdelais	12/2014
348	2^1698083+24743	511174	Enzo Doria	11/2023
349	2^1696453+219257	510684	Enzo Doria	06/2024
350	(124869^100489-1)/(124869^317-1)	510523	Ryan Propper	11/2023
351	(124292^100489-1)/(124292^317-1)	510321	Ryan Propper	11/2023
352	10^509546+3	509547	Paul Bourdelais	01/2021
353	101876^99207+99207^101876	509028	Gabor Levai	08/2023
354	2^1690434+213589	508872	Enzo Doria	12/2023
355	2^1688450+221989	508275	Enzo Doria	07/2024
356	2^1688111+217313	508173	Enzo Doria	04/2024
357	(118270^100489-1)/(118270^317-1)	508160	Ryan Propper	11/2023
358	105196^67205+67205^105196	507824	Miklos Levai	09/2023
359	2^1686452+220681	507673	Enzo Doria	04/2024
360	2^1685708+27781	507449	Enzo Doria	01/2024
361	(72^273149-1)/71	507327	Paul Bourdelais	02/2022
362	105154^66373+66373^105154	507052	Miklos Levai	09/2023
363	2^1683331+225413	506734	Enzo Doria	09/2024
364	107890^49423+49423^107890	506429	Miklos Levai	02/2022
365	(14^441697-1)/13	506241	Paul Bourdelais	12/2014
366	101645^94522+94522^101645	505739	Gabor Levai	02/2023
367	3^1059503-2^1059503	505512	Mike Oakes	04/2012
368	2^1678670+21529	505331	Enzo Doria	11/2023
369	101542^92885+92885^101542	504456	Gabor Levai	04/2022
370	105273^60238+60238^105273	503192	Miklos Levai	09/2023
371	105098^61113+61113^105098	503014	Miklos Levai	09/2022
372	2^1670703+60293	502932	Enzo Doria	11/2017
373	(2^1669219-2^834610+1)/5	502485	Borys Jaworski	01/2011
374	101311^90816+90816^101311	502317	Gabor Levai	12/2021
375	101643^87368+87368^101643	502254	Gabor Levai	11/2022
376	(161502^96721-1)/(161502^311-1)	502121	Ryan Propper	11/2023
377	101863^84922+84922^101863	502085	Gabor Levai	10/2022
378	2^1666440+212671	501649	Enzo Doria	09/2023
379	100291^100291+172^172	501582	Serge Batalov	04/2024
380	2^1666177+226697	501570	Enzo Doria	10/2024
381	100207^99856+99856^100207	500973	Gabor Levai	11/2021
382	101839^83028+83028^101839	500969	Gabor Levai	11/2022
383	100263^98600+98600^100263	500702	Gabor Levai	09/2021
384	2^1662045+37607	500326	Enzo Doria	11/2024
385	101761^82168+82168^101761	500126	Gabor Levai	03/2022
386	2^1661176+336631	500064	Tony Prest / Never Odd Or Even	09/2019
387	101070^88579+88579^101070	500027	Gabor Levai	01/2022
388	(85^259159-1)/84	500025	Paul Bourdelais	11/2021
389	2^1660973+368139	500003	Tony Prest / Never Odd Or Even	08/2020
390	2^1660964-382425	500000	Tony Prest / Never Odd Or Even	05/2020
391	(87^257689-1)/86	499791	Paul Bourdelais	01/2021
392	(64*10^499210+53)/9	499211	Serge Batalov	03/2015
393	Tau(631^32370)	498503	Nik Lygeros / Olivier Rozier	05/2015
394	29^339887-28^339887	497051	Jean-Louis Charton	05/2019
395	2^1650975+185225	496993	Stefano Morozzi	09/2024
396	2^1650959+198513	496989	Stefano Morozzi	09/2024
397	2^1650942+181575	496984	Stefano Morozzi	09/2024
398	2^1650905+193947	496972	Stefano Morozzi	09/2024
399	2^1650867+192615	496961	Stefano Morozzi	09/2024
400	2^1650819+198315	496947	Stefano Morozzi	07/2024
401	2^1650788+185823	496937	Stefano Morozzi	09/2024
402	2^1650749+185235	496925	Stefano Morozzi	06/2024
403	2^1650695+183141	496909	Stefano Morozzi	04/2024
404	2^1650640+185311	496893	Stefano Morozzi	03/2024
405	2^1650593+187871	496879	Stefano Morozzi	03/2024
406	2^1650538+196863	496862	Stefano Morozzi	03/2024
407	2^1650484+181413	496846	Stefano Morozzi	03/2024
408	2^1650473+193151	496842	Stefano Morozzi	03/2024
409	2^1650443+193613	496833	Stefano Morozzi	01/2024
410	2^1650426+183543	496828	Stefano Morozzi	01/2024
411	2^1650388+189741	496817	Stefano Morozzi	10/2023
412	2^1650267+193743	496780	Stefano Morozzi	09/2023
413	2^1650196+191835	496759	Stefano Morozzi	07/2023
414	2^1650190+185733	496757	Stefano Morozzi	07/2023
415	2^1650141+189525	496742	Stefano Morozzi	07/2023
416	2^1650103+189519	496731	Stefano Morozzi	05/2023
417	2^1648342+215029	496201	Enzo Doria	01/2024
418	2^1646078+36937	495519	Enzo Doria	10/2024
419	(136688^96721-1)/(136688^311-1)	495136	Ryan Propper	11/2023
420	2^1643411+26213	494717	Enzo Doria	03/2024
421	2^1642104+227491	494323	Enzo Doria	10/2024
422	2^1640056+216241	493707	Enzo Doria	02/2024
423	2^1636027+25763	492494	Enzo Doria	01/2024
424	2^1635235+227693	492255	Enzo Doria	10/2024
425	2^1632498+30397	491431	Enzo Doria	08/2024
426	2^1631030+73519	490989	Enzo Doria	08/2023
427	(2^1629469-1)/644908484660139264379223	490496	Gord Palameta	11/2017
428	2^1627834+225529	490027	Enzo Doria	08/2024
429	2^1626709+30407	489689	Enzo Doria	07/2024
430	2^1619885+28229	487634	Enzo Doria	04/2024
431	10^487291+7	487292	Alfred Reich	06/2021
432	2^1617677+227927	486970	Enzo Doria	10/2024
433	2^1617579+1889543	486940	Enzo Doria	09/2017
434	97481^97481-70^70	486325	Henri Lifchitz	10/2024
435	2^1613632+215011	485752	Enzo Doria	11/2023
436	2^1612600+27331	485441	Enzo Doria	03/2024
437	2^1610146+24739	484703	Enzo Doria	11/2023
438	L(2316773)	484177	Serge Batalov	06/2017
439	(57^275669-1)/56	484039	Paul Bourdelais	04/2021
440	2^1601964+215491	482240	Enzo Doria	11/2023
441	2^1600308+34051	481741	Enzo Doria	09/2024
442	2^1599624+20011	481535	Enzo Doria	07/2023
443	2^1599205+27047	481409	Enzo Doria	03/2024
444	2^1599120-5	481384	Stefano Morozzi	12/2022
445	10^480684-3	480684	Paul Bourdelais	01/2021
446	2^1595483+184133	480289	Enzo Doria	07/2017
447	2^1594947+3	480127	Paul Bourdelais	07/2019
448	2^1594420+36781	479969	Enzo Doria	10/2024
449	2^1594135+225893	479883	Enzo Doria	10/2024
450	2^1594129+22697	479881	Enzo Doria	11/2023
451	2^1593922+213289	479819	Enzo Doria	10/2023
452	2^1592677+228257	479444	Enzo Doria	11/2024
453	2^1592234+26809	479311	Enzo Doria	03/2024
454	2^1590797+34967	478878	Enzo Doria	10/2024
455	(94^241993-1)/93	477482	Paul Bourdelais	09/2020
456	2^1585195+1888373	477192	Enzo Doria	08/2017
457	(33^313553+1)/34	476134	Paul Bourdelais	02/2021
458	2^1581306+220309	476021	Enzo Doria	03/2024
459	2^1578654+215029	475223	Enzo Doria	01/2024
460	(84615^96721-1)/(84615^311-1)	475056	Ryan Propper	11/2023
461	3^994536+16	474515	Robert Price	10/2020
462	2^1575391+71483	474240	Enzo Doria	04/2018
463	(2^1572882+5)/3	473485	Serge Batalov	08/2015
464	(6^608099-1)/5	473193	Paul Bourdelais	05/2010
465	2^1569708+20371	472530	Enzo Doria	09/2023
466	2^1569375+29153	472429	Enzo Doria	05/2024
467	3^989124+16	471933	Robert Price	10/2020
468	2^1567006+1888099	471716	Enzo Doria	05/2017
469	2^1563067+1889813	470531	Enzo Doria	08/2017
470	2^1562428+215851	470338	Enzo Doria	02/2024
471	2^1557036+226321	468715	Enzo Doria	09/2024
472	2^1556730+222829	468623	Enzo Doria	07/2024
473	2^1551415+215813	467023	Enzo Doria	02/2024
474	2^1551411+212933	467022	Enzo Doria	09/2023
475	2^1550887+36743	466864	Enzo Doria	11/2024
476	2^1549797+60197	466536	Enzo Doria	02/2018
477	2^1549030+1887619	466305	Enzo Doria	05/2017
478	416^177481-415^177481	464840	Jean-Louis Charton	12/2016
479	2^1541374+226729	464000	Enzo Doria	09/2024
480	(78^245183-1)/77	463908	Paul Bourdelais	02/2021
481	93331^93331-90^90	463858	Henri Lifchitz	10/2024
482	2^1540117+31907	463622	Enzo Doria	04/2024
483	2^1537058+29839	462701	Enzo Doria	07/2024
484	2^1534770+20809	462012	Enzo Doria	08/2023
485	2^1531286+24799	460964	Enzo Doria	11/2023
486	2^1530725+38267	460795	Enzo Doria	10/2024
487	10^459480-11	459480	Mischa Rodermond	04/2023
488	(5^656657-2^656657)/3	458984	Jon Grantham	08/2023
489	2^1522569+71657	458339	Enzo Doria	04/2018
490	2^1520990+35257	457864	Enzo Doria	10/2024
491	2^1520920+38251	457843	Enzo Doria	11/2024
492	(55814^96721-1)/(55814^311-1)	457634	Ryan Propper	11/2023
493	2^1518191+75353	457022	Ben Maloney / Five or Bust	01/2009
494	2^1512733+227027	455379	Enzo Doria	10/2024
495	2^1510915+223463	454831	Enzo Doria	06/2024
496	6^584279-5	454658	Paul Bourdelais	02/2021
497	2^1509037-13	454266	Stefano Morozzi	12/2022
498	(52^264697-1)/51	454220	Paul Bourdelais	10/2021
499	2^1507169+29027	453704	Enzo Doria	05/2024
500	2^1506029+1890167	453360	Enzo Doria	02/2018

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Probable Primes Top 10000

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