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	(20^472709-1)/19	615008	Paul Bourdelais	01/2015
252	PIPrime(613373)	613373	Adrian Bondrescu	05/2016
253	124452^80465+80465^124452	610513	Ryan Propper	10/2023
254	11^586020-2	610277	Paul Bourdelais	11/2021
255	(19^476929+1)/20	609874	Paul Bourdelais	03/2015
256	(7^720497-2^720497)/5	608890	Jon Grantham	08/2023
257	2^2020893-25	608350	Boyan Hu	01/2025
258	2^2019811+1867211	608024	Enzo Doria	04/2018
259	F(2904353)	606974	Henri Lifchitz	07/2014
260	2^2014720+71893	606492	Enzo Doria	04/2018
261	(5^866029-3^866029)/2	605328	Jon Grantham	08/2023
262	L(2894561)	604928	Ryan Propper	06/2022
263	(18^481147+1)/19	603970	Paul Bourdelais	07/2011
264	200^262144+119^262144	603202	Kellen Shenton	08/2022
265	(20^463511+1)/21	603041	Paul Bourdelais	03/2025
266	(70^326437-1)/69	602307	Paul Bourdelais	02/2025
267	(83467^121801-1)/(83467^349-1)	597728	Ryan Propper	11/2023
268	(61448^124609-1)/(61448^353-1)	595001	Ryan Propper	11/2023
269	(15^505117-1)/14	594063	Paul Bourdelais	01/2015
270	2^1971190+43819	593388	Enzo Doria	04/2025
271	81^310721-80^310721	593007	Paul Bourdelais	07/2023
272	(152^270217-1)/(152-1)	589570	Michael Stocker	06/2015
273	2^1951707+234041	587523	Enzo Doria	04/2025
274	Phi(177147,94259)	587458	Anonymous	09/2022
275	2^1950002+1867369	587010	Enzo Doria	02/2018
276	116265^111218+111218^116265	586694	Ryan Propper	10/2023
277	2^1940812+3	584243	Paul Bourdelais	06/2020
278	1933695^2+2^1933695	582101	Ryan Propper	05/2023
279	(5^832151-2^832151)/3	581649	Jon Grantham	08/2023
280	2^1930263+229883	581068	Enzo Doria	01/2025
281	(129810^113569-1)/(129810^337-1)	578991	Ryan Propper	11/2023
282	2^1923104+153	578912	Stefano Morozzi	07/2021
283	(48^343901-1)/47	578179	Paul Bourdelais	03/2025
284	116761^87652+87652^116761	577122	Ryan Propper	10/2023
285	116395^87994+87994^116395	575510	Ryan Propper	10/2023
286	(3^1205459+1)/4	575150	Paul Bourdelais	08/2015
287	2^1910103+231413	574999	Enzo Doria	07/2025
288	2^1904743+42713	573385	Enzo Doria	06/2025
289	2^1904054+49999	573178	Enzo Doria	09/2025
290	2^1900703+49853	572169	Enzo Doria	09/2025
291	2^1900633-18099	572148	Stefano Morozzi	09/2025
292	2^1900634-9131	572148	Stefano Morozzi	09/2025
293	2^1900622-141095	572145	Stefano Morozzi	09/2025
294	2^1900610-193031	572141	Stefano Morozzi	08/2025
295	2^1900611-167967	572141	Stefano Morozzi	08/2025
296	2^1900607-47727	572140	Stefano Morozzi	07/2025
297	2^1900604-7659	572139	Stefano Morozzi	07/2025
298	2^1900059-153039	571975	Stefano Morozzi	09/2025
299	2^1900055-192841	571974	Stefano Morozzi	09/2025
300	2^1900056-190077	571974	Stefano Morozzi	09/2025
301	2^1900044-179669	571971	Stefano Morozzi	09/2025
302	2^1900035-5485	571968	Stefano Morozzi	08/2025
303	2^1900027-131409	571966	Stefano Morozzi	08/2025
304	2^1900021-14971	571964	Stefano Morozzi	08/2025
305	2^1900022-15353	571964	Stefano Morozzi	08/2025
306	2^1900023-177499	571964	Stefano Morozzi	08/2025
307	2^1900017-176593	571963	Stefano Morozzi	08/2025
308	2^1900012-162405	571961	Stefano Morozzi	07/2025
309	2^1900005-101625	571959	Stefano Morozzi	07/2025
310	2^1900005-101713	571959	Stefano Morozzi	07/2025
311	2^1900002-24945	571958	Stefano Morozzi	07/2025
312	2^1895562+229729	570622	Enzo Doria	02/2025
313	(160972^109561-1)/(160972^331-1)	568734	Ryan Propper	11/2023
314	2^1887092+38191	568072	Enzo Doria	01/2025
315	(37015^124609-1)/(37015^353-1)	567649	Ryan Propper	11/2023
316	2^1882800+384541	566780	Enzo Doria	12/2017
317	(2^1882787-2^941394+1)/5	566775	Borys Jaworski	11/2012
318	2^1882474+71389	566682	Enzo Doria	04/2018
319	(6^727496-11)/5	566102	Paul Bourdelais	08/2019
320	2^1875552+3	564598	Paul Bourdelais	04/2020
321	(145373^109561-1)/(145373^331-1)	563899	Ryan Propper	11/2023
322	(10^563535-7)/3	563535	Rytis Slatkevicius	02/2023
323	3^1180181-2	563090	Jorge Coveiro	05/2020
324	(15063^134689-1)/(15063^367-1)	561186	Ryan Propper	11/2023
325	2^1852265+1890425	557588	Enzo Doria	11/2017
326	5^797390-2	557352	Paul Bourdelais	03/2021
327	2^1851447+38573	557342	Enzo Doria	02/2025
328	(10^556441-7^556441)/3	556441	Jon Grantham	07/2023
329	8^615997-7^615997	556301	Jean-Louis Charton	07/2009
330	(5^795829-2^795829)/3	556261	Jon Grantham	08/2023
331	Tau(773^34960)	555339	Nik Lygeros / Olivier Rozier	09/2015
332	((((((((((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
333	2^1835428+227221	552519	Enzo Doria	01/2025
334	2^1835205+225197	552452	Enzo Doria	10/2024
335	2^1827961+43427	550272	Enzo Doria	05/2025
336	2^1825513+32507	549535	Enzo Doria	07/2024
337	2^1823921+34937	549055	Enzo Doria	11/2024
338	2^1822728+228991	548696	Enzo Doria	02/2025
339	2^1819810+42727	547818	Enzo Doria	03/2025
340	(42^337081-1)/41	547165	Paul Bourdelais	09/2021
341	114868^57423+57423^114868	546667	Ryan Propper	10/2023
342	2^1815834+231799	546621	Enzo Doria	05/2025
343	2^1814913+37607	546344	Enzo Doria	12/2024
344	109092^100999+100999^109092	545931	Ryan Propper	10/2023
345	2^1812446+34789	545601	Enzo Doria	02/2025
346	2^1812234+31879	545537	Enzo Doria	05/2024
347	(64814^113569-1)/(64814^337-1)	544835	Ryan Propper	11/2023
348	2^1809045+225641	544577	Enzo Doria	12/2024
349	2^1806435+42683	543792	Enzo Doria	05/2025
350	2^1804650+230149	543254	Enzo Doria	02/2025
351	2^1804109+37007	543091	Enzo Doria	11/2024
352	(92170^109561-1)/(92170^331-1)	542283	Ryan Propper	11/2023
353	2^1799578+36883	541727	Enzo Doria	03/2025
354	2^1797319+29693	541047	Enzo Doria	11/2024
355	(28262^121801-1)/(28262^349-1)	540608	Ryan Propper	11/2023
356	(68^294947+1)/69	540492	Paul Bourdelais	03/2025
357	2^1792175+230543	539499	Enzo Doria	01/2025
358	2^1791569+33587	539317	Enzo Doria	09/2024
359	(2^1790743-1)/(1468409271583589849773835546416767873*20752172271489035681)	539014	Dario Alpern	06/2015
360	10^538640-3	538640	Paul Bourdelais	01/2021
361	(10^538508+53)/9	538508	Rytis Slatkevicius	01/2023
362	2^1787653+224687	538138	Enzo Doria	10/2024
363	2^1787167+71963	537991	Enzo Doria	12/2018
364	(7^636043-5^636043)/2	537519	Jon Grantham	08/2023
365	108309^91610+91610^108309	537424	Ryan Propper	10/2023
366	2^1777975+233603	535224	Enzo Doria	04/2025
367	(12^495953+1)/13	535223	Paul Bourdelais	11/2018
368	2^1774781+30197	534263	Enzo Doria	08/2024
369	2^1773644+72511	533921	Enzo Doria	10/2018
370	(92^271639-1)/91	533440	Paul Bourdelais	02/2022
371	2^1771408+223201	533247	Enzo Doria	07/2024
372	2^1770613+212597	533008	Enzo Doria	10/2023
373	(11559^131072+1)/2	532535	Serge Batalov	04/2018
374	(85^275881-1)/84	532289	Paul Bourdelais	02/2022
375	2^1767579+213683	532095	Enzo Doria	10/2023
376	2^1767218+25249	531986	Enzo Doria	02/2024
377	2^1762004-3	530417	Paul Bourdelais	04/2020
378	2^1761634+48019	530305	Enzo Doria	06/2025
379	2^1754760+217465	528236	Enzo Doria	01/2024
380	2^1753261+25367	527785	Enzo Doria	11/2023
381	105006^105006-133^133	527258	Sergey Batalov	05/2024
382	2^1750727+213683	527022	Enzo Doria	10/2023
383	2^1750208+218371	526866	Enzo Doria	01/2024
384	2^1743981+28997	524991	Enzo Doria	03/2024
385	2^1740587+40493	523969	Enzo Doria	02/2025
386	2^1737680+23161	523094	Enzo Doria	01/2024
387	(73^280697+1)/74	523028	Paul Bourdelais	02/2022
388	2^1737207+218153	522952	Enzo Doria	05/2024
389	2^1735354+227509	522394	Enzo Doria	11/2024
390	2^1734898+225529	522257	Enzo Doria	09/2024
391	2^1733867+231383	521946	Enzo Doria	03/2025
392	(21^394579+1)/22	521719	Paul Bourdelais	10/2018
393	2^1732919+43553	521661	Enzo Doria	04/2025
394	2^1732565+226757	521555	Enzo Doria	12/2024
395	2^1730246+384439	520856	Enzo Doria	09/2017
396	2^1729303+34313	520573	Enzo Doria	11/2024
397	(55^299087+1)/56	520519	Paul Bourdelais	02/2022
398	2^1728446+41629	520315	Enzo Doria	02/2025
399	5^744171-3^744171-1	520154	Jon Grantham	08/2023
400	2^1727856+31951	520137	Enzo Doria	04/2024
401	(18^414269-1)/17	520020	Paul Bourdelais	12/2014
402	2^1727029+228257	519888	Enzo Doria	12/2024
403	2^1726522+30859	519735	Enzo Doria	06/2024
404	2^1724695+228353	519185	Enzo Doria	01/2025
405	2^1717949+30077	517155	Enzo Doria	08/2024
406	2^1717612+31891	517053	Enzo Doria	04/2024
407	(144171^100489-1)/(144171^317-1)	516776	Ryan Propper	11/2023
408	2^1714462+217465	516105	Enzo Doria	01/2024
409	2^1714021+29777	515972	Enzo Doria	03/2024
410	2^1713855+220703	515922	Enzo Doria	03/2024
411	2^1712979+222143	515659	Enzo Doria	05/2024
412	20^396120-3	515365	Paul Bourdelais	01/2021
413	2^1709785+36557	514697	Enzo Doria	02/2025
414	(136102^100489-1)/(136102^317-1)	514270	Ryan Propper	11/2023
415	2^1708341+221897	514262	Enzo Doria	09/2024
416	(7^608347-5^608347)/2	514113	Jon Grantham	08/2023
417	(62^286483+1)/63	513488	Paul Bourdelais	02/2022
418	155630^1971+1971^155630	512753	Henri Lifchitz	11/2024
419	2^1702747+230873	512578	Enzo Doria	01/2025
420	2^1701757+47207	512280	Enzo Doria	06/2025
421	2^1701350+48019	512158	Enzo Doria	08/2025
422	(20^393257+1)/21	511638	Paul Bourdelais	12/2014
423	2^1699164+40141	511500	Enzo Doria	01/2025
424	2^1698083+24743	511174	Enzo Doria	11/2023
425	2^1696453+219257	510684	Enzo Doria	06/2024
426	(124869^100489-1)/(124869^317-1)	510523	Ryan Propper	11/2023
427	(124292^100489-1)/(124292^317-1)	510321	Ryan Propper	11/2023
428	10^509546+3	509547	Paul Bourdelais	01/2021
429	101876^99207+99207^101876	509028	Gabor Levai	08/2023
430	2^1690808+237151	508984	Enzo Doria	08/2025
431	2^1690434+213589	508872	Enzo Doria	12/2023
432	2^1688450+221989	508275	Enzo Doria	07/2024
433	2^1688360+233581	508248	Enzo Doria	05/2025
434	2^1688111+217313	508173	Enzo Doria	04/2024
435	(118270^100489-1)/(118270^317-1)	508160	Ryan Propper	11/2023
436	2^1687922+40849	508116	Enzo Doria	01/2025
437	2^1687521+230267	507995	Enzo Doria	01/2025
438	105196^67205+67205^105196	507824	Miklos Levai	09/2023
439	2^1686452+220681	507673	Enzo Doria	04/2024
440	2^1685708+27781	507449	Enzo Doria	01/2024
441	(72^273149-1)/71	507327	Paul Bourdelais	02/2022
442	2^1685092+227191	507264	Enzo Doria	12/2024
443	105154^66373+66373^105154	507052	Miklos Levai	09/2023
444	2^1683331+225413	506734	Enzo Doria	09/2024
445	107890^49423+49423^107890	506429	Miklos Levai	02/2022
446	(14^441697-1)/13	506241	Paul Bourdelais	12/2014
447	101645^94522+94522^101645	505739	Gabor Levai	02/2023
448	3^1059503-2^1059503	505512	Mike Oakes	04/2012
449	2^1678670+21529	505331	Enzo Doria	11/2023
450	101542^92885+92885^101542	504456	Gabor Levai	04/2022
451	2^1675306+227839	504318	Enzo Doria	12/2024
452	2^1674819+42683	504171	Enzo Doria	04/2025
453	2^1673623+42983	503811	Enzo Doria	03/2025
454	105273^60238+60238^105273	503192	Miklos Levai	09/2023
455	105098^61113+61113^105098	503014	Miklos Levai	09/2022
456	2^1670703+60293	502932	Enzo Doria	11/2017
457	(2^1669219-2^834610+1)/5	502485	Borys Jaworski	01/2011
458	101311^90816+90816^101311	502317	Gabor Levai	12/2021
459	101643^87368+87368^101643	502254	Gabor Levai	11/2022
460	(161502^96721-1)/(161502^311-1)	502121	Ryan Propper	11/2023
461	101863^84922+84922^101863	502085	Gabor Levai	10/2022
462	2^1666440+212671	501649	Enzo Doria	09/2023
463	100291^100291+172^172	501582	Serge Batalov	04/2024
464	2^1666177+226697	501570	Enzo Doria	10/2024
465	100207^99856+99856^100207	500973	Gabor Levai	11/2021
466	101839^83028+83028^101839	500969	Gabor Levai	11/2022
467	100263^98600+98600^100263	500702	Gabor Levai	09/2021
468	2^1662045+37607	500326	Enzo Doria	11/2024
469	2^1661503+43553	500163	Enzo Doria	04/2025
470	101761^82168+82168^101761	500126	Gabor Levai	03/2022
471	2^1661176+336631	500064	Tony Prest / Never Odd Or Even	09/2019
472	8603^127088-127088^8603	500047	Norbert Schneider	06/2025
473	101070^88579+88579^101070	500027	Gabor Levai	01/2022
474	(85^259159-1)/84	500025	Paul Bourdelais	11/2021
475	2^1660973+368139	500003	Tony Prest / Never Odd Or Even	08/2020
476	100000^100000+85707^85707	500001	Henri Lifchitz	01/2025
477	2^1660964-382425	500000	Tony Prest / Never Odd Or Even	05/2020
478	2^1660328+226951	499809	Enzo Doria	04/2025
479	(87^257689-1)/86	499791	Paul Bourdelais	01/2021
480	(64*10^499210+53)/9	499211	Serge Batalov	03/2015
481	2^1656126+223227	498544	Enzo Doria	03/2025
482	Tau(631^32370)	498503	Nik Lygeros / Olivier Rozier	05/2015
483	2^1653321+49217	497700	Enzo Doria	09/2025
484	29^339887-28^339887	497051	Jean-Louis Charton	05/2019
485	2^1650975+185225	496993	Stefano Morozzi	09/2024
486	2^1650959+198513	496989	Stefano Morozzi	09/2024
487	2^1650942+181575	496984	Stefano Morozzi	09/2024
488	2^1650905+193947	496972	Stefano Morozzi	09/2024
489	2^1650877+186537	496964	Stefano Morozzi	01/2025
490	2^1650867+192615	496961	Stefano Morozzi	09/2024
491	2^1650854+188973	496957	Stefano Morozzi	01/2025
492	2^1650837+199641	496952	Stefano Morozzi	01/2025
493	2^1650819+198315	496947	Stefano Morozzi	07/2024
494	2^1650788+185823	496937	Stefano Morozzi	09/2024
495	2^1650749+185235	496925	Stefano Morozzi	06/2024
496	2^1650695+183141	496909	Stefano Morozzi	04/2024
497	2^1650640+185311	496893	Stefano Morozzi	03/2024
498	2^1650593+187871	496879	Stefano Morozzi	03/2024
499	2^1650538+196863	496862	Stefano Morozzi	03/2024
500	2^1650484+181413	496846	Stefano Morozzi	03/2024

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