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	2^1036020-114539	311874	Enzo Doria	02/2015
252	2^1032240+1883431	310736	Enzo Doria	01/2017
253	2^1030352+1870021	310167	Enzo Doria	06/2016
254	2^1030046+1882843	310075	Enzo Doria	11/2016
255	(11^293831-1)/10	305993	Paul Bourdelais	03/2010
256	2^1015321-1015321	305643	Henri Lifchitz	08/2013
257	2^1014224-2791229	305312	Enzo Doria	01/2016
258	2^1010751-107709	304267	Enzo Doria	03/2014
259	(2^1010623-1)/12602017578957977	304212	Tony Prest / Never Odd Or Even	02/2014
260	2^1009577+1869587	303913	Enzo Doria	06/2016
261	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
262	2^1008301+1869377	303529	Enzo Doria	06/2016
263	(2^1007838+5)/3	303389	Serge Batalov	08/2015
264	2^1005326+383059	302634	Enzo Doria	12/2016
265	2^1004929+1877567	302514	Enzo Doria	08/2016
266	2^1003494+1874899	302082	Enzo Doria	06/2016
267	2^1003046+60529	301947	Enzo Doria	04/2016
268	2^1000647+1881353	301225	Enzo Doria	11/2016
269	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
270	2^999646+1874029	300924	Enzo Doria	06/2016
271	10^300476+3	300477	Ed Trice	10/2012
272	10^300476-530913	300476	Patrick De Geest	03/2016
273	2^998053+1879667	300444	Enzo Doria	09/2016
274	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
275	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
276	numbpart(72526161452)	299999	Serge Batalov	04/2017
277	2^996182-114431	299881	Enzo Doria	02/2015
278	2^995214-2788361	299590	Enzo Doria	12/2015
279	2^994791-114319	299462	Enzo Doria	01/2015
280	2^994490-1863791	299372	Enzo Doria	01/2016
281	2^993322+1885729	299020	Enzo Doria	03/2017
282	2^992711-2788807	298836	Enzo Doria	12/2015
283	2^992525-114199	298780	Enzo Doria	12/2014
284	2^992329+1884707	298721	Enzo Doria	02/2017
285	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
286	2^985217-114553	296580	Enzo Doria	03/2015
287	2^984131-1828009	296253	Enzo Doria	01/2015
288	2^983620+60451	296100	Phil Moore	03/2008
289	2^982721-2683	295829	Yves Minet	02/2016
290	2^981298-2788421	295401	Enzo Doria	12/2015
291	2^981163-2790967	295360	Enzo Doria	12/2015
292	2^979594+1865839	294888	Enzo Doria	02/2016
293	2^976760+1885021	294035	Enzo Doria	02/2017
294	2^974441+1878407	293336	Enzo Doria	08/2016
295	2^974180+1876831	293258	Enzo Doria	07/2016
296	2^974170+453319	293255	Enzo Doria	01/2017
297	2^972744-114419	292826	Enzo Doria	03/2015
298	CopelandErdos(292447)	292447	Mark Rodenkirch	12/2015
299	2^970911+1873373	292274	Enzo Doria	07/2016
300	2^970670+383059	292201	Enzo Doria	12/2016
301	2^970141-100363	292042	Enzo Doria	02/2014
302	2^969945+1874717	291983	Enzo Doria	06/2016
303	2^969384+1880701	291814	Enzo Doria	10/2016
304	(3^611333-2^611333)/(99035947*87109884549431)	291659	Mike Oakes	02/2017
305	2^962194+60139	289650	Enzo Doria	02/2016
306	2^959307-1861507	288781	Enzo Doria	11/2015
307	2^957372+283531	288198	Enzo Doria	02/2017
308	2^957192-1864049	288144	Enzo Doria	01/2016
309	2^956446+1875199	287919	Enzo Doria	06/2016
310	(17^233689+1)/18	287542	Paul Bourdelais	09/2013
311	2^955178+1883587	287538	Enzo Doria	12/2016
312	2^954001+1875257	287183	Enzo Doria	07/2016
313	(23891^65536+1)/2	286932	Serge Batalov	03/2018
314	2^952268+1878601	286662	Enzo Doria	09/2016
315	2^950801+81557	286220	Enzo Doria	08/2016
316	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
317	2^948510+782569	285530	Enzo Doria	10/2016
318	2^948374-114137	285490	Enzo Doria	01/2015
319	2^947739+1872923	285298	Enzo Doria	06/2016
320	2^942533+82067	283731	Enzo Doria	09/2016
321	2^940950+1874989	283255	Enzo Doria	06/2016
322	2^940426-2786141	283097	Enzo Doria	11/2015
323	2^939881-114115	282933	Enzo Doria	12/2014
324	10^282493+632551	282494	Patrick De Geest	02/2017
326	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
325	10^282493-132327	282493	Patrick De Geest	02/2017
327	3^591827-2^591827	282374	Mike Oakes	08/2009
328	Tau(509^18946)	282048	Nik Lygeros / Olivier Rozier	05/2015
329	2^936716-1835519	281980	Enzo Doria	04/2015
330	2^936588+79411	281942	Enzo Doria	06/2016
331	2^936047+1877423	281779	Enzo Doria	08/2016
332	2^935713+1869377	281678	Enzo Doria	05/2016
333	2^933082+1877059	280886	Enzo Doria	08/2016
334	(5*10^280710+1)/3	280711	Serge Batalov	10/2014
335	(10^279978+11)/3	279978	Serge Batalov	07/2015
336	2^929524-1864829	279815	Enzo Doria	01/2016
337	2^929152+60181	279703	Enzo Doria	02/2016
338	2^928621-2787883	279543	Enzo Doria	11/2015
339	(2^927763+lucasV(-1,2,927763)+1)/2	279285	Mike Oakes	04/2017
340	2^927429+1882277	279184	Enzo Doria	12/2016
341	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
342	2^925330-1301	278553	Yves Minet	06/2015
343	(21^210599+1)/22	278457	Paul Bourdelais	08/2013
344	2^923261-69175	277930	Enzo Doria	11/2015
345	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
346	((((((((((((((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
347	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
348	2^920318+2792299	277044	Enzo Doria	02/2016
349	2^918596-2786939	276525	Enzo Doria	11/2015
350	2^916639+60563	275936	Enzo Doria	04/2016
351	2^916385-2786383	275860	Enzo Doria	11/2015
352	2^915928+82081	275722	Enzo Doria	09/2016
353	2^915576-114137	275616	Enzo Doria	01/2015
354	2^914828+1876741	275391	Enzo Doria	07/2016
355	2^914757-2203	275370	Yves Minet	12/2015
356	2^911900+1871245	274510	Enzo Doria	05/2016
357	2^910490+283429	274085	Enzo Doria	01/2017
358	2^909988-1862249	273934	Enzo Doria	12/2015
359	2^909297+1879157	273726	Enzo Doria	08/2016
360	2^909257-1864423	273714	Enzo Doria	01/2016
361	2^908579-1861747	273510	Enzo Doria	12/2015
362	2^907635-2791597	273226	Enzo Doria	01/2016
363	2^906594-113201	272912	Enzo Doria	08/2014
364	2^904773+1872167	272364	Enzo Doria	06/2016
365	2^904149-1862473	272176	Enzo Doria	12/2015
366	(7*10^271757-61)/9	271757	Erik Branger	03/2012
367	2^902497+1880117	271679	Enzo Doria	09/2016
368	2^901858+77689	271487	Enzo Doria	06/2016
369	2^901372+1875301	271341	Enzo Doria	06/2016
370	2^899121-115033	270663	Enzo Doria	07/2015
371	2^898900+883021	270596	Enzo Doria	12/2016
372	2^898762-251511	270555	Enzo Doria	12/2013
373	2^898589+47	270503	Lelio R Paula	03/2016
374	187322*10^270343-187321	270349	Danilo Nitsche	09/2013
375	48358*10^270343-48357	270348	Danilo Nitsche	09/2013
376	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
377	2^897867-3217	270285	Yves Minet	12/2016
378	2^897849-115273	270280	Enzo Doria	07/2015
379	2^896616-114179	269909	Enzo Doria	12/2014
380	2^894928+583561	269401	Enzo Doria	04/2017
381	2^894673-39343	269324	Enzo Doria	08/2015
382	F(1285607)	268676	Henri Lifchitz	11/2008
383	2^892112+187663	268553	Enzo Doria	08/2016
384	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
385	2^890957-69583	268205	Enzo Doria	12/2015
386	32841!^2+32840!^2+...+2!^2+1!^2	268128	Serge Batalov	07/2017
387	2^890122-351401	267954	Enzo Doria	07/2015
388	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
389	2^886324+77791	266811	Enzo Doria	06/2016
390	2^884714+1880527	266326	Enzo Doria	10/2016
391	11^255426+255426^11	265999	Serge Batalov	05/2014
392	2^883462-343421	265949	Enzo Doria	07/2015
393	2^883442+1875019	265943	Enzo Doria	06/2016
394	2^883333-291583	265910	Enzo Doria	07/2015
395	2^880411+1882673	265031	Enzo Doria	12/2016
396	2^879530-2788031	264765	Enzo Doria	12/2015
397	2^878118+2793079	264340	Enzo Doria	02/2016
398	2^875748-461129	263627	Enzo Doria	07/2015
399	2^875181-2789923	263456	Enzo Doria	12/2015
400	2^875101-350083	263432	Enzo Doria	08/2015
401	2^874684+1883587	263307	Enzo Doria	01/2017
402	2^874616+1872211	263286	Enzo Doria	05/2016
403	2^874073+2792957	263123	Enzo Doria	02/2016
404	2^873628+1878751	262989	Enzo Doria	08/2016
405	2^873288-269	262886	Yves Minet	01/2015
406	2^871146-3173	262242	Yves Minet	07/2016
407	2^869601-163	261776	Yves Minet	01/2015
408	2^869326+282859	261694	Enzo Doria	11/2016
409	2^869035-114181	261606	Enzo Doria	12/2014
410	2^865715+80303	260607	Enzo Doria	07/2016
411	2^865048+1882411	260406	Enzo Doria	12/2016
412	2^864899-113871	260361	Enzo Doria	10/2014
413	(7*10^260198-61)/9	260198	Erik Branger	11/2011
414	2^864298-2788421	260180	Enzo Doria	12/2015
415	2^864039-2791357	260102	Enzo Doria	01/2016
416	2^863621-113833	259976	Enzo Doria	10/2014
417	2^862837+75767	259740	Enzo Doria	05/2016
418	2^862088+1874941	259515	Enzo Doria	06/2016
419	2^861987-134557	259484	Hans Havermann	10/2018
420	2^861516-1854029	259343	Enzo Doria	09/2015
421	2^860975-1853977	259180	Enzo Doria	09/2015
422	2^860625-1858843	259074	Enzo Doria	10/2015
423	2^860110+77689	258919	Enzo Doria	05/2016
424	2^859600+1880371	258766	Enzo Doria	10/2016
425	2^859433+494711	258716	Makoto Morimoto	10/2013
426	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
427	2^859240+1875271	258658	Enzo Doria	06/2016
428	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
429	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
430	2^857016-633113	257988	Enzo Doria	12/2013
431	2^855732-113969	257602	Enzo Doria	10/2014
432	2^853682-3911	256984	Enzo Doria	05/2014
433	11^246668-90	256879	Enzo Doria	12/2012
434	2^851904-113939	256449	Enzo Doria	10/2014
435	11^246167-90	256357	Enzo Doria	12/2012
436	2^850700-569049	256087	Enzo Doria	11/2013
437	21^193601-20^193601	255983	Jean-Louis Charton	02/2015
438	2^849177-114025	255628	Enzo Doria	12/2014
439	2^848502-3173	255425	Yves Minet	07/2016
440	2^848178-140291	255328	Enzo Doria	01/2014
441	2^847622-2441	255160	Yves Minet	02/2016
442	2^847291+182843	255061	Enzo Doria	11/2016
443	2^847174+1879429	255025	Enzo Doria	09/2016
444	24*29^174239+13361	254809	Curtis Bright	04/2015
445	2^845610-1868591	254554	Enzo Doria	04/2016
446	2^845484+81931	254517	Enzo Doria	08/2016
447	2^845402-114761	254492	Enzo Doria	05/2015
448	2^844334-2792441	254170	Enzo Doria	02/2016
449	11^243796-90	253888	Enzo Doria	12/2012
450	30^171733-29^171733	253671	Jean-Louis Charton	10/2018
451	2^842209+1876037	253531	Enzo Doria	07/2016
452	2^842123-59197	253505	Enzo Doria	10/2015
453	2^840716-2969	253081	Yves Minet	05/2016
454	2^840358-462491	252973	Enzo Doria	08/2015
455	2^840310+1878379	252959	Enzo Doria	08/2016
456	11^242579-60	252620	Enzo Doria	10/2012
457	45^152659+2	252378	Robert Price	09/2015
458	2^837725+1869377	252181	Enzo Doria	05/2016
459	2^837536-311039	252124	Enzo Doria	06/2015
460	21^190632-2	252058	Robert Price	07/2015
461	2^837242+1873297	252035	Enzo Doria	06/2016
462	2^836656-2787929	251859	Enzo Doria	11/2015
463	2^836380+1875541	251776	Enzo Doria	07/2016
464	(359^98327-1)/358	251233	Alexander Zhirkov	11/2017
465	tau(41^28288)	250924	Nik Lygeros / Olivier Rozier	10/2013
466	2^832511-461197	250611	Enzo Doria	07/2015
467	2^832505+1881137	250609	Enzo Doria	11/2016
468	2^832363+583295	250567	Enzo Doria	12/2016
469	2^832244-403635	250531	Enzo Doria	01/2014
470	2^831157+1880657	250204	Enzo Doria	11/2016
471	2^831088-7200899	250183	Enzo Doria	01/2015
472	2^830956-1349	250143	Yves Minet	07/2015
473	2^830037+282317	249867	Enzo Doria	09/2016
474	2^829589-113653	249732	Enzo Doria	09/2014
475	2^828281-3193	249338	Yves Minet	08/2016
476	2^828064-2785619	249273	Enzo Doria	10/2015
477	2^827602+60409	249134	Enzo Doria	03/2016
478	10^249010+348861	249011	Patrick De Geest	04/2016
479	10^249010-21	249010	Serge Batalov	12/2014
480	2^826733+1882907	248872	Enzo Doria	12/2016
481	2^825682+1876549	248556	Enzo Doria	07/2016
482	2^824991-114121	248348	Enzo Doria	12/2014
483	2^824642-362727	248242	Enzo Doria	12/2013
484	2^824565-114265	248219	Enzo Doria	01/2015
485	(73*10^248145-1)/9	248146	Robert Price	01/2015
486	(2^823337+1)/(3*362268281)	247841	Gord Palameta	08/2018
487	(2^822971-1)/6583769/28211445881/21255852651726486149207	247700	Robert Kinser	09/2016
488	2^822296+76501	247536	Enzo Doria	05/2016
489	2^821590-114167	247324	Enzo Doria	12/2014
490	2^821512-2790659	247300	Enzo Doria	12/2015
491	2^820077+382847	246868	Enzo Doria	11/2016
492	2^820001+81269	246845	Enzo Doria	07/2016
493	2^819463-59197	246683	Enzo Doria	10/2015
494	2^819296+80581	246633	Enzo Doria	07/2016
495	2^817160-350369	245990	Enzo Doria	06/2015
496	88093#+(653879#)/(88093#)	245374	Makoto Morimoto	11/2017
497	2^815111-113857	245373	Enzo Doria	10/2014
498	2^814914-4001	245314	Yves Minet	05/2017
499	846^83761-845^83761	245200	Jean-Louis Charton	12/2012
500	2^814356-2790449	245146	Enzo Doria	12/2015

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PRP Records

Probable Primes Top 10000

(252402 PRPs in the top)