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 (> 30000)	Who ?	When ?
251	2^950801+81557	286220	Enzo Doria	08/2016
252	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
253	2^948510+782569	285530	Enzo Doria	10/2016
254	2^948374-114137	285490	Enzo Doria	01/2015
255	2^947739+1872923	285298	Enzo Doria	06/2016
256	2^942533+82067	283731	Enzo Doria	09/2016
257	2^940950+1874989	283255	Enzo Doria	06/2016
258	2^940426-2786141	283097	Enzo Doria	11/2015
259	2^939881-114115	282933	Enzo Doria	12/2014
260	10^282493+632551	282494	Patrick De Geest	02/2017
262	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
261	10^282493-132327	282493	Patrick De Geest	02/2017
263	3^591827-2^591827	282374	Mike Oakes	08/2009
264	Tau(509^18946)	282048	Nik Lygeros / Olivier Rozier	05/2015
265	2^936716-1835519	281980	Enzo Doria	04/2015
266	2^936588+79411	281942	Enzo Doria	06/2016
267	2^936047+1877423	281779	Enzo Doria	08/2016
268	2^935713+1869377	281678	Enzo Doria	05/2016
269	2^933082+1877059	280886	Enzo Doria	08/2016
270	(5*10^280710+1)/3	280711	Serge Batalov	10/2014
271	(10^279978+11)/3	279978	Serge Batalov	07/2015
272	2^929524-1864829	279815	Enzo Doria	01/2016
273	2^929152+60181	279703	Enzo Doria	02/2016
274	2^928621-2787883	279543	Enzo Doria	11/2015
275	(2^927763+lucasV(-1,2,927763)+1)/2	279285	Mike Oakes	04/2017
276	2^927429+1882277	279184	Enzo Doria	12/2016
277	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
278	2^925330-1301	278553	Yves Minet	06/2015
279	(21^210599+1)/22	278457	Paul Bourdelais	08/2013
280	2^923261-69175	277930	Enzo Doria	11/2015
281	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
282	((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	277369	Serge Batalov	07/2016
283	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
284	2^920318+2792299	277044	Enzo Doria	02/2016
285	2^918596-2786939	276525	Enzo Doria	11/2015
286	2^916639+60563	275936	Enzo Doria	04/2016
287	2^916385-2786383	275860	Enzo Doria	11/2015
288	2^915928+82081	275722	Enzo Doria	09/2016
289	2^915576-114137	275616	Enzo Doria	01/2015
290	2^914828+1876741	275391	Enzo Doria	07/2016
291	2^914757-2203	275370	Yves Minet	12/2015
292	2^911900+1871245	274510	Enzo Doria	05/2016
293	2^910490+283429	274085	Enzo Doria	01/2017
294	2^909988-1862249	273934	Enzo Doria	12/2015
295	2^909297+1879157	273726	Enzo Doria	08/2016
296	2^909257-1864423	273714	Enzo Doria	01/2016
297	2^908579-1861747	273510	Enzo Doria	12/2015
298	2^907635-2791597	273226	Enzo Doria	01/2016
299	2^906594-113201	272912	Enzo Doria	08/2014
300	2^904773+1872167	272364	Enzo Doria	06/2016
301	2^904149-1862473	272176	Enzo Doria	12/2015
302	(7*10^271757-61)/9	271757	Erik Branger	03/2012
303	2^902497+1880117	271679	Enzo Doria	09/2016
304	2^901858+77689	271487	Enzo Doria	06/2016
305	2^901372+1875301	271341	Enzo Doria	06/2016
306	2^899121-115033	270663	Enzo Doria	07/2015
307	2^898900+883021	270596	Enzo Doria	12/2016
308	2^898762-251511	270555	Enzo Doria	12/2013
309	2^898589+47	270503	Lelio R Paula	03/2016
310	187322*10^270343-187321	270349	Danilo Nitsche	09/2013
311	48358*10^270343-48357	270348	Danilo Nitsche	09/2013
312	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
313	2^897867-3217	270285	Yves Minet	12/2016
314	2^897849-115273	270280	Enzo Doria	07/2015
315	2^896616-114179	269909	Enzo Doria	12/2014
316	2^894928+583561	269401	Enzo Doria	04/2017
317	2^894673-39343	269324	Enzo Doria	08/2015
318	F(1285607)	268676	Henri Lifchitz	11/2008
319	2^892112+187663	268553	Enzo Doria	08/2016
320	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
321	2^890957-69583	268205	Enzo Doria	12/2015
322	2^890122-351401	267954	Enzo Doria	07/2015
323	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
324	2^886324+77791	266811	Enzo Doria	06/2016
325	2^884714+1880527	266326	Enzo Doria	10/2016
326	11^255426+255426^11	265999	Serge Batalov	05/2014
327	2^883462-343421	265949	Enzo Doria	07/2015
328	2^883442+1875019	265943	Enzo Doria	06/2016
329	2^883333-291583	265910	Enzo Doria	07/2015
330	2^880411+1882673	265031	Enzo Doria	12/2016
331	2^879530-2788031	264765	Enzo Doria	12/2015
332	2^878118+2793079	264340	Enzo Doria	02/2016
333	2^875748-461129	263627	Enzo Doria	07/2015
334	2^875181-2789923	263456	Enzo Doria	12/2015
335	2^875101-350083	263432	Enzo Doria	08/2015
336	2^874684+1883587	263307	Enzo Doria	01/2017
337	2^874616+1872211	263286	Enzo Doria	05/2016
338	2^874073+2792957	263123	Enzo Doria	02/2016
339	2^873628+1878751	262989	Enzo Doria	08/2016
340	2^873288-269	262886	Yves Minet	01/2015
341	2^871146-3173	262242	Yves Minet	07/2016
342	2^869601-163	261776	Yves Minet	01/2015
343	2^869326+282859	261694	Enzo Doria	11/2016
344	2^869035-114181	261606	Enzo Doria	12/2014
345	2^865715+80303	260607	Enzo Doria	07/2016
346	2^865048+1882411	260406	Enzo Doria	12/2016
347	2^864899-113871	260361	Enzo Doria	10/2014
348	(7*10^260198-61)/9	260198	Erik Branger	11/2011
349	2^864298-2788421	260180	Enzo Doria	12/2015
350	2^864039-2791357	260102	Enzo Doria	01/2016
351	2^863621-113833	259976	Enzo Doria	10/2014
352	2^862837+75767	259740	Enzo Doria	05/2016
353	2^862088+1874941	259515	Enzo Doria	06/2016
354	2^861516-1854029	259343	Enzo Doria	09/2015
355	2^860975-1853977	259180	Enzo Doria	09/2015
356	2^860625-1858843	259074	Enzo Doria	10/2015
357	2^860110+77689	258919	Enzo Doria	05/2016
358	2^859600+1880371	258766	Enzo Doria	10/2016
359	2^859433+494711	258716	Makoto Morimoto	10/2013
360	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
361	2^859240+1875271	258658	Enzo Doria	06/2016
362	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
363	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
364	2^857016-633113	257988	Enzo Doria	12/2013
365	2^855732-113969	257602	Enzo Doria	10/2014
366	2^853682-3911	256984	Enzo Doria	05/2014
367	11^246668-90	256879	Enzo Doria	12/2012
368	2^851904-113939	256449	Enzo Doria	10/2014
369	11^246167-90	256357	Enzo Doria	12/2012
370	2^850700-569049	256087	Enzo Doria	11/2013
371	21^193601-20^193601	255983	Jean-Louis Charton	02/2015
372	2^849177-114025	255628	Enzo Doria	12/2014
373	2^848502-3173	255425	Yves Minet	07/2016
374	2^848178-140291	255328	Enzo Doria	01/2014
375	2^847622-2441	255160	Yves Minet	02/2016
376	2^847291+182843	255061	Enzo Doria	11/2016
377	2^847174+1879429	255025	Enzo Doria	09/2016
378	24*29^174239+13361	254809	Curtis Bright	04/2015
379	2^845610-1868591	254554	Enzo Doria	04/2016
380	2^845484+81931	254517	Enzo Doria	08/2016
381	2^845402-114761	254492	Enzo Doria	05/2015
382	2^844334-2792441	254170	Enzo Doria	02/2016
383	11^243796-90	253888	Enzo Doria	12/2012
384	2^842209+1876037	253531	Enzo Doria	07/2016
385	2^842123-59197	253505	Enzo Doria	10/2015
386	2^840716-2969	253081	Yves Minet	05/2016
387	2^840358-462491	252973	Enzo Doria	08/2015
388	2^840310+1878379	252959	Enzo Doria	08/2016
389	11^242579-60	252620	Enzo Doria	10/2012
390	45^152659+2	252378	Robert Price	09/2015
391	2^837725+1869377	252181	Enzo Doria	05/2016
392	2^837536-311039	252124	Enzo Doria	06/2015
393	21^190632-2	252058	Robert Price	07/2015
394	2^837242+1873297	252035	Enzo Doria	06/2016
395	2^836656-2787929	251859	Enzo Doria	11/2015
396	2^836380+1875541	251776	Enzo Doria	07/2016
397	tau(41^28288)	250924	Nik Lygeros / Olivier Rozier	10/2013
398	2^832511-461197	250611	Enzo Doria	07/2015
399	2^832505+1881137	250609	Enzo Doria	11/2016
400	2^832363+583295	250567	Enzo Doria	12/2016
401	2^832244-403635	250531	Enzo Doria	01/2014
402	2^831157+1880657	250204	Enzo Doria	11/2016
403	2^831088-7200899	250183	Enzo Doria	01/2015
404	2^830956-1349	250143	Yves Minet	07/2015
405	2^830037+282317	249867	Enzo Doria	09/2016
406	2^829589-113653	249732	Enzo Doria	09/2014
407	2^828281-3193	249338	Yves Minet	08/2016
408	2^828064-2785619	249273	Enzo Doria	10/2015
409	2^827602+60409	249134	Enzo Doria	03/2016
410	10^249010+348861	249011	Patrick De Geest	04/2016
411	10^249010-21	249010	Serge Batalov	12/2014
412	2^826733+1882907	248872	Enzo Doria	12/2016
413	2^825682+1876549	248556	Enzo Doria	07/2016
414	2^824991-114121	248348	Enzo Doria	12/2014
415	2^824642-362727	248242	Enzo Doria	12/2013
416	2^824565-114265	248219	Enzo Doria	01/2015
417	(73*10^248145-1)/9	248146	Robert Price	01/2015
418	(2^822971-1)/6583769/28211445881/21255852651726486149207	247700	Robert Kinser	09/2016
419	2^822296+76501	247536	Enzo Doria	05/2016
420	2^821590-114167	247324	Enzo Doria	12/2014
421	2^821512-2790659	247300	Enzo Doria	12/2015
422	2^820077+382847	246868	Enzo Doria	11/2016
423	2^820001+81269	246845	Enzo Doria	07/2016
424	2^819463-59197	246683	Enzo Doria	10/2015
425	2^819296+80581	246633	Enzo Doria	07/2016
426	2^817160-350369	245990	Enzo Doria	06/2015
427	2^815111-113857	245373	Enzo Doria	10/2014
428	2^814914-4001	245314	Yves Minet	05/2017
429	846^83761-845^83761	245200	Jean-Louis Charton	12/2012
430	2^814356-2790449	245146	Enzo Doria	12/2015
431	2^814276-459029	245122	Enzo Doria	04/2015
432	2^814023+180923	245046	Enzo Doria	07/2016
433	(3^513059-2^513059)/(1026119*5430216457)	244776	Mike Oakes	03/2017
434	2^811842-113675	244389	Enzo Doria	09/2014
435	2^811132-2787929	244176	Enzo Doria	11/2015
436	2^809746-2790971	243758	Enzo Doria	01/2016
437	2^808767-3295	243464	Yves Minet	12/2016
438	2^808621-113809	243420	Enzo Doria	09/2014
439	2^807724+1879621	243150	Enzo Doria	09/2016
440	2^805843-113611	242583	Enzo Doria	08/2014
441	2^805745-459763	242554	Enzo Doria	05/2015
442	2^805353+782687	242436	Enzo Doria	11/2016
443	2^804277-417933	242112	Enzo Doria	01/2014
444	2^803468-269039	241868	Enzo Doria	10/2013
445	2^803172+80851	241779	Enzo Doria	07/2016
446	3^506233-2	241535	Robert Price	11/2013
447	2^802025-25999	241434	Enzo Doria	10/2013
448	(3^505823+3^252912+1)/7	241339	Serge Batalov	03/2014
449	2^801303+1872923	241217	Enzo Doria	05/2016
450	2^800579-1862947	240999	Enzo Doria	12/2015
451	2^798973-26283	240515	Enzo Doria	10/2013
452	2^798671-69487	240424	Enzo Doria	12/2015
453	2^797220+79831	239988	Enzo Doria	06/2016
454	2^796910-26001	239894	Enzo Doria	10/2013
455	2^796598+653119	239800	Enzo Doria	12/2016
456	2^796432-1859729	239750	Enzo Doria	11/2015
457	2^796002-1852211	239621	Enzo Doria	08/2015
458	2^795709+75767	239533	Enzo Doria	04/2016
459	2^795708+81721	239532	Enzo Doria	08/2016
460	2^795468-2786249	239460	Enzo Doria	10/2015
461	2^795442+80779	239452	Enzo Doria	07/2016
462	2^795075-1852057	239342	Enzo Doria	08/2015
463	2^794043+1875023	239031	Enzo Doria	06/2016
464	2^793347-69577	238822	Enzo Doria	01/2016
465	2^792988-344429	238714	Enzo Doria	08/2015
466	2^792700-2786369	238627	Enzo Doria	11/2015
467	2^792663-1844797	238616	Enzo Doria	06/2015
468	2^792605-291943	238598	Enzo Doria	07/2015
469	(2^792061-2^396031+1)/5	238434	Thomas Ritschel	03/2014
470	2^789373+1869377	237625	Enzo Doria	05/2016
471	((10^59387+1)^3(10^59387+1+10^29694)-(10^118774+10^59387)(10^29694-1)+10^178161)/27961	237544	Serge Batalov	04/2015
472	2^788942+1866409	237496	Enzo Doria	02/2016
473	2^788844-114329	237466	Enzo Doria	01/2015
474	2^788705-1859713	237424	Enzo Doria	11/2015
475	2^786180+1871971	236664	Enzo Doria	05/2016
476	11^227092-90	236492	Enzo Doria	11/2012
477	2^785260+1866361	236387	Enzo Doria	02/2016
478	2^785220+1880611	236375	Enzo Doria	10/2016
479	19^184650-2	236122	Robert Price	10/2014
480	10^236059+216513	236060	Patrick De Geest	04/2016
481	10^236059-20909	236059	Robert Price	09/2015
482	2^782634-113981	235597	Enzo Doria	11/2014
483	2^782423+1879733	235533	Enzo Doria	09/2016
484	2^781682-2789543	235310	Enzo Doria	12/2015
485	2^780408-113453	234927	Enzo Doria	08/2014
486	2^780368-1864829	234915	Enzo Doria	01/2016
487	2^779593-1836559	234681	Enzo Doria	05/2015
488	(5^335429+1)/6	234455	Paul Bourdelais	08/2010
489	2^778395-113617	234321	Enzo Doria	08/2014
490	2^776245-2792353	233674	Enzo Doria	02/2016
491	2^776060-114029	233618	Enzo Doria	11/2014
492	2^775987-2789557	233596	Enzo Doria	12/2015
493	2^775672+1866721	233501	Enzo Doria	03/2016
494	(11^223999+1)/12	233270	Paul Bourdelais	02/2010
495	2^774118+1885789	233033	Enzo Doria	04/2017
496	21^176191-20^176191	232964	Jean-Louis Charton	01/2015
497	2^773679-113425	232901	Enzo Doria	08/2014
498	10^232599+192489	232600	Patrick De Geest	12/2013
499	10^232599-3	232599	Markus Tervooren	10/2010
500	2^772552-458879	232562	Enzo Doria	04/2015

Find by discoverer :

PRP Records

Probable Primes Top 10000

(177649 PRPs in the top)