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	2^1195093+1882577	359759	Enzo Doria	12/2016
252	(6^461108-11)/5	358812	Paul Bourdelais	04/2019
253	2^1191375+8543	358640	Phil Moore	06/2008
254	2^1190972+1880191	358519	Enzo Doria	11/2016
255	(45^216551-1)/44	358004	Paul Bourdelais	08/2020
256	(50^210319-1)/49	357324	Paul Bourdelais	08/2020
257	2^1179836+1885021	355167	Enzo Doria	02/2017
258	(63^195893-1)/62	352477	Paul Bourdelais	08/2020
259	numbpart(100000135540)	352269	Serge Batalov	04/2017
260	(10^352237-1)/9/10567111/950335427	352221	Maksym Voznyy	01/2015
261	2^1168554+783529	351770	Enzo Doria	01/2017
262	(2^1168183-1)/54763676838381762583	351639	Matthias Wurtinger	01/2011
263	2^1166152+1882411	351047	Enzo Doria	12/2016
264	2^1162154+1890207	349844	Enzo Doria	08/2017
265	(7*10^348724-61)/9	348724	Erik Branger	09/2016
266	(127^165601-1)/126	348390	Alexander Zhirkov	09/2015
267	2^1153083+1883693	347113	Enzo Doria	04/2017
268	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
269	2^1145882+80779	344945	Enzo Doria	09/2016
270	2^1136462+1887289	342110	Enzo Doria	05/2017
271	F(1636007)	341905	Henri Lifchitz	03/2009
272	2^1133678+782569	341272	Enzo Doria	11/2016
273	(11^327001+1)/12	340536	Paul Bourdelais	09/2013
274	(2^1127239+2^563620+1)/5	339333	Borys Jaworski	11/2006
275	Tau(907^20848)	339132	Nik Lygeros / Olivier Rozier	01/2016
276	2^1126380-3	339075	Paul Bourdelais	06/2019
277	2^1125446+1885099	338794	Enzo Doria	08/2017
278	2^1124549+143807	338523	Enzo Doria	10/2016
279	2^1121187+1886783	337511	Enzo Doria	04/2017
280	(48^200443-1)/47	336992	Paul Bourdelais	08/2020
281	(94^170371-1)/93	336162	Paul Bourdelais	09/2020
282	2^1116184+1883521	336005	Enzo Doria	02/2017
283	2^1114517+1880087	335504	Enzo Doria	10/2016
284	(3^700897+1)/4	334413	Paul Bourdelais	04/2010
285	2^1104408-114539	332460	Enzo Doria	03/2015
286	2^1101921+82085	331712	Enzo Doria	10/2016
287	2^1100655+683513	331331	Enzo Doria	01/2017
288	(10^330906+71)/9	330906	Serge Batalov	07/2015
289	2^1098346+482899	330636	Enzo Doria	11/2016
290	2^1095679+1878713	329833	Enzo Doria	09/2016
291	2^1094740-1851539	329550	Enzo Doria	08/2015
292	2^1091469-379369	328565	Enzo Doria	03/2014
293	(69^178093-1)/68	327485	Paul Bourdelais	08/2020
294	2^1085750+582349	326844	Enzo Doria	11/2016
295	2^1083596+483061	326195	Enzo Doria	12/2016
296	(2^541456-1)*10^162995+2^541455-1	325990	paolo galliani	01/2019
297	2^1082908+583561	325988	Enzo Doria	05/2017
298	30^220411-29^220411	325574	Jean-Louis Charton	10/2018
299	2^1078242+1881649	324584	Enzo Doria	11/2016
300	2^1077737+1880117	324432	Enzo Doria	10/2016
301	2^1075425+1880117	323736	Enzo Doria	10/2016
302	10^322999+187071	323000	Stefano Morozzi	03/2019
303	10^322999-143151	322999	Patrick De Geest	05/2020
304	2^1072146+1886869	322749	Enzo Doria	04/2017
305	2^1072118-7321953	322740	Enzo Doria	02/2015
306	2^1071026+1886869	322411	Enzo Doria	04/2017
307	2^1070539+1880633	322265	Enzo Doria	10/2016
308	2^1069293-1147195	321890	Enzo Doria	05/2015
309	2^1065968+1880941	320889	Enzo Doria	10/2016
310	2^1065897-1147195	320867	Enzo Doria	05/2015
311	2^1063427+1882103	320124	Enzo Doria	12/2016
312	2^1061095-1061095	319422	Henri Lifchitz	10/2013
313	2^1060950+653119	319378	Enzo Doria	12/2016
314	2^1060363+782753	319202	Enzo Doria	11/2016
315	(71^172259-1)/70	318895	Paul Bourdelais	08/2020
316	2^1054736+483061	317508	Enzo Doria	12/2016
317	2^1053965+1879667	317276	Enzo Doria	10/2016
318	(43^194119-1)/42	317086	Paul Bourdelais	08/2020
319	2^1052186-458165	316740	Enzo Doria	03/2015
320	2^1046613-114685	315062	Enzo Doria	04/2015
321	2^1045625-459373	314765	Enzo Doria	06/2015
322	(7*10^314564-61)/9	314564	Erik Branger	09/2016
323	(7^371669-1)/6	314096	Paul Bourdelais	02/2010
324	(53^181981-1)/52	313784	Paul Bourdelais	08/2020
325	2^1041944+283051	313657	Enzo Doria	12/2016
326	2^1041153-114391	313419	Enzo Doria	02/2015
327	2^1038871+1866983	312732	Enzo Doria	04/2016
328	(55^179573-1)/54	312521	Paul Bourdelais	08/2020
329	2^1037647+1881263	312363	Enzo Doria	11/2016
330	2^1037226+1879699	312237	Enzo Doria	10/2016
331	2^1036867+1865843	312129	Enzo Doria	02/2016
332	2^1036020-114539	311874	Enzo Doria	02/2015
333	(90^159463-1)/89	311628	Paul Bourdelais	08/2020
334	2^1032240+1883431	310736	Enzo Doria	01/2017
335	2^1030352+1870021	310167	Enzo Doria	06/2016
336	2^1030046+1882843	310075	Enzo Doria	11/2016
337	3^648872+16	309591	Robert Price	04/2020
338	(11^293831-1)/10	305993	Paul Bourdelais	03/2010
339	(67^167449-1)/66	305773	Paul Bourdelais	08/2020
340	2^1015321-1015321	305643	Henri Lifchitz	08/2013
341	2^1014224-2791229	305312	Enzo Doria	01/2016
342	2^1010751-107709	304267	Enzo Doria	03/2014
343	(2^1010623-1)/12602017578957977	304212	Tony Prest / Never Odd Or Even	02/2014
344	2^1009577+1869587	303913	Enzo Doria	06/2016
345	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
346	2^1008301+1869377	303529	Enzo Doria	06/2016
347	(2^1007838+5)/3	303389	Serge Batalov	08/2015
348	2^1005326+383059	302634	Enzo Doria	12/2016
349	2^1004929+1877567	302514	Enzo Doria	08/2016
350	2^1003494+1874899	302082	Enzo Doria	06/2016
351	2^1003046+60529	301947	Enzo Doria	04/2016
352	(23^221411-1)/22	301501	Paul Bourdelais	08/2020
353	2^1000647+1881353	301225	Enzo Doria	11/2016
354	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
355	2^999646+1874029	300924	Enzo Doria	06/2016
356	(59^169777-1)/58	300649	Paul Bourdelais	08/2020
357	10^300476+3	300477	Ed Trice	10/2012
358	10^300476-530913	300476	Patrick De Geest	03/2016
359	2^998053+1879667	300444	Enzo Doria	09/2016
360	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
361	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
362	10^300000+287389	300001	Patrick De Geest	10/2019
363	10^300000-83657	300000	Patrick De Geest	10/2019
364	numbpart(72526161452)	299999	Serge Batalov	04/2017
365	2^996182-114431	299881	Enzo Doria	02/2015
366	2^995214-2788361	299590	Enzo Doria	12/2015
367	2^994791-114319	299462	Enzo Doria	01/2015
368	2^994490-1863791	299372	Enzo Doria	01/2016
369	2^993322+1885729	299020	Enzo Doria	03/2017
370	2^992711-2788807	298836	Enzo Doria	12/2015
371	2^992525-114199	298780	Enzo Doria	12/2014
372	2^992329+1884707	298721	Enzo Doria	02/2017
373	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
374	2^985217-114553	296580	Enzo Doria	03/2015
375	(76^157649-1)/75	296507	Paul Bourdelais	07/2019
376	2^984131-1828009	296253	Enzo Doria	01/2015
377	2^983620+60451	296100	Phil Moore	03/2008
378	2^982721-2683	295829	Yves Minet	02/2016
379	2^981298-2788421	295401	Enzo Doria	12/2015
380	2^981163-2790967	295360	Enzo Doria	12/2015
381	2^979594+1865839	294888	Enzo Doria	02/2016
382	2^976760+1885021	294035	Enzo Doria	02/2017
383	2^974441+1878407	293336	Enzo Doria	08/2016
384	2^974180+1876831	293258	Enzo Doria	07/2016
385	2^974170+453319	293255	Enzo Doria	01/2017
386	2^972744-114419	292826	Enzo Doria	03/2015
387	CopelandErdos(292447)	292447	Mark Rodenkirch	12/2015
388	2^970911+1873373	292274	Enzo Doria	07/2016
389	2^970670+383059	292201	Enzo Doria	12/2016
390	2^970141-100363	292042	Enzo Doria	02/2014
391	2^969945+1874717	291983	Enzo Doria	06/2016
392	2^969384+1880701	291814	Enzo Doria	10/2016
393	(3^611333-2^611333)/(99035947*87109884549431)	291659	Mike Oakes	02/2017
394	2^962194+60139	289650	Enzo Doria	02/2016
395	2^959307-1861507	288781	Enzo Doria	11/2015
396	2^957372+283531	288198	Enzo Doria	02/2017
397	2^957192-1864049	288144	Enzo Doria	01/2016
398	2^956446+1875199	287919	Enzo Doria	06/2016
399	(17^233689+1)/18	287542	Paul Bourdelais	09/2013
400	2^955178+1883587	287538	Enzo Doria	12/2016
401	2^954001+1875257	287183	Enzo Doria	07/2016
402	(23891^65536+1)/2	286932	Serge Batalov	03/2018
403	2^952268+1878601	286662	Enzo Doria	09/2016
404	2^950801+81557	286220	Enzo Doria	08/2016
405	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
406	(54^164839+1)/55	285565	Paul Bourdelais	07/2019
407	2^948510+782569	285530	Enzo Doria	10/2016
408	2^948374-114137	285490	Enzo Doria	01/2015
409	2^947739+1872923	285298	Enzo Doria	06/2016
410	2^942533+82067	283731	Enzo Doria	09/2016
411	2^940950+1874989	283255	Enzo Doria	06/2016
412	2^940426-2786141	283097	Enzo Doria	11/2015
413	2^939881-114115	282933	Enzo Doria	12/2014
414	10^282493+632551	282494	Patrick De Geest	02/2017
416	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
415	10^282493-132327	282493	Patrick De Geest	02/2017
417	3^591827-2^591827	282374	Mike Oakes	08/2009
418	Tau(509^18946)	282048	Nik Lygeros / Olivier Rozier	05/2015
419	2^936716-1835519	281980	Enzo Doria	04/2015
420	2^936588+79411	281942	Enzo Doria	06/2016
421	2^936047+1877423	281779	Enzo Doria	08/2016
422	2^935713+1869377	281678	Enzo Doria	05/2016
423	2^933082+1877059	280886	Enzo Doria	08/2016
424	(5*10^280710+1)/3	280711	Serge Batalov	10/2014
425	(42^172663+1)/43	280274	Paul Bourdelais	07/2019
426	(10^279978+11)/3	279978	Serge Batalov	07/2015
427	2^929524-1864829	279815	Enzo Doria	01/2016
428	2^929152+60181	279703	Enzo Doria	02/2016
429	2^928621-2787883	279543	Enzo Doria	11/2015
430	(2^927763+lucasV(-1,2,927763)+1)/2	279285	Mike Oakes	04/2017
431	2^927429+1882277	279184	Enzo Doria	12/2016
432	(71^150697-1)/70	278978	Paul Bourdelais	07/2019
433	(33^183661-1)/32	278891	Paul Bourdelais	12/2018
434	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
435	2^925330-1301	278553	Yves Minet	06/2015
436	(21^210599+1)/22	278457	Paul Bourdelais	08/2013
437	2^923261-69175	277930	Enzo Doria	11/2015
438	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
439	((((((((((((((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
440	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
441	2^920318+2792299	277044	Enzo Doria	02/2016
442	2^918596-2786939	276525	Enzo Doria	11/2015
443	2^916639+60563	275936	Enzo Doria	04/2016
444	2^916385-2786383	275860	Enzo Doria	11/2015
445	2^915928+82081	275722	Enzo Doria	09/2016
446	2^915576-114137	275616	Enzo Doria	01/2015
447	2^914828+1876741	275391	Enzo Doria	07/2016
448	2^914757-2203	275370	Yves Minet	12/2015
449	2^911900+1871245	274510	Enzo Doria	05/2016
450	2^910490+283429	274085	Enzo Doria	01/2017
451	2^909988-1862249	273934	Enzo Doria	12/2015
452	2^909297+1879157	273726	Enzo Doria	08/2016
453	2^909257-1864423	273714	Enzo Doria	01/2016
454	2^908579-1861747	273510	Enzo Doria	12/2015
455	2^907635-2791597	273226	Enzo Doria	01/2016
456	(53^158341+1)/54	273022	Paul Bourdelais	07/2019
457	2^906594-113201	272912	Enzo Doria	08/2014
458	2^904773+1872167	272364	Enzo Doria	06/2016
459	2^904149-1862473	272176	Enzo Doria	12/2015
460	(7*10^271757-61)/9	271757	Erik Branger	03/2012
461	2^902497+1880117	271679	Enzo Doria	09/2016
462	2^901858+77689	271487	Enzo Doria	06/2016
463	2^901372+1875301	271341	Enzo Doria	06/2016
464	2^899121-115033	270663	Enzo Doria	07/2015
465	2^898900+883021	270596	Enzo Doria	12/2016
466	2^898762-251511	270555	Enzo Doria	12/2013
467	2^898589+47	270503	Lelio R Paula	03/2016
468	187322*10^270343-187321	270349	Danilo Nitsche	09/2013
469	48358*10^270343-48357	270348	Danilo Nitsche	09/2013
470	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
471	2^897867-3217	270285	Yves Minet	12/2016
472	2^897849-115273	270280	Enzo Doria	07/2015
473	2^896616-114179	269909	Enzo Doria	12/2014
474	2^894928+583561	269401	Enzo Doria	04/2017
475	2^894673-39343	269324	Enzo Doria	08/2015
476	F(1285607)	268676	Henri Lifchitz	11/2008
477	2^892112+187663	268553	Enzo Doria	08/2016
478	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
479	2^890957-69583	268205	Enzo Doria	12/2015
480	32841!^2+32840!^2+...+2!^2+1!^2	268128	Serge Batalov	07/2017
481	2^890122-351401	267954	Enzo Doria	07/2015
482	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
483	(85^138647+1)/86	267507	Paul Bourdelais	07/2019
484	(485^99523-1)/484	267291	Michael Stocker	05/2020
485	2^886324+77791	266811	Enzo Doria	06/2016
486	2^884714+1880527	266326	Enzo Doria	10/2016
487	11^255426+255426^11	265999	Serge Batalov	05/2014
488	2^883462-343421	265949	Enzo Doria	07/2015
489	2^883442+1875019	265943	Enzo Doria	06/2016
490	2^883333-291583	265910	Enzo Doria	07/2015
491	2^880411+1882673	265031	Enzo Doria	12/2016
492	2^879530-2788031	264765	Enzo Doria	12/2015
493	2^878118+2793079	264340	Enzo Doria	02/2016
494	(37^168527-1)/36	264283	Paul Bourdelais	08/2019
495	2^875748-461129	263627	Enzo Doria	07/2015
496	2^875181-2789923	263456	Enzo Doria	12/2015
497	2^875101-350083	263432	Enzo Doria	08/2015
498	2^874684+1883587	263307	Enzo Doria	01/2017
499	2^874616+1872211	263286	Enzo Doria	05/2016
500	3^551491+16	263129	Robert Price	04/2020

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PRP Records

Probable Primes Top 10000

(271019 PRPs in the top)