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	(14^441697-1)/13	506241	Paul Bourdelais	12/2014
252	101645^94522+94522^101645	505739	Gabor Levai	02/2023
253	3^1059503-2^1059503	505512	Mike Oakes	04/2012
254	101542^92885+92885^101542	504465	Gabor Levai	04/2022
255	105273^60238+60238^105273	503192	Miklos Levai	09/2023
256	105098^61113+61113^105098	503014	Miklos Levai	09/2022
257	2^1670703+60293	502932	Enzo Doria	11/2017
258	(2^1669219-2^834610+1)/5	502485	Borys Jaworski	01/2011
259	101311^90816+90816^101311	502317	Gabor Levai	12/2021
260	101643^87368+87368^101643	502254	Gabor Levai	11/2022
261	101863^84922+84922^101863	502085	Gabor Levai	10/2022
262	2^1666440+212671	501649	Enzo Doria	09/2023
263	100207^99856+99856^100207	500973	Gabor Levai	11/2021
264	101839^83028+83028^101839	500969	Gabor Levai	11/2022
265	100263^98600+98600^100263	500702	Gabor Levai	09/2021
266	101761^82168+82168^101761	500126	Gabor Levai	03/2022
267	2^1661176+336631	500064	Tony Prest / Never Odd Or Even	09/2019
268	101070^88579+88579^101070	500027	Gabor Levai	01/2022
269	(85^259159-1)/84	500025	Paul Bourdelais	11/2021
270	2^1660973+368139	500003	Tony Prest / Never Odd Or Even	08/2020
271	2^1660964-382425	500000	Tony Prest / Never Odd Or Even	05/2020
272	(87^257689-1)/86	499791	Paul Bourdelais	01/2021
273	(64*10^499210+53)/9	499211	Serge Batalov	03/2015
274	Tau(631^32370)	498503	Nik Lygeros / Olivier Rozier	05/2015
275	29^339887-28^339887	497051	Jean-Louis Charton	05/2019
276	2^1650267+193743	496780	Stefano Morozzi	09/2023
277	2^1650196+191835	496759	Stefano Morozzi	07/2023
278	2^1650190+185733	496757	Stefano Morozzi	07/2023
279	2^1650141+189525	496742	Stefano Morozzi	07/2023
280	2^1650103+189519	496731	Stefano Morozzi	05/2023
281	2^1631030+73519	490989	Enzo Doria	08/2023
282	(2^1629469-1)/644908484660139264379223	490496	Gord Palameta	11/2017
283	10^487291+7	487292	Alfred Reich	06/2021
284	2^1617579+1889543	486940	Enzo Doria	09/2017
285	L(2316773)	484177	Serge Batalov	06/2017
286	(57^275669-1)/56	484039	Paul Bourdelais	04/2021
287	2^1599624+20011	481535	Enzo Doria	07/2023
288	2^1599120-5	481384	Stefano Morozzi	12/2022
289	10^480684-3	480684	Paul Bourdelais	01/2021
290	2^1595483+184133	480289	Enzo Doria	07/2017
291	2^1594947+3	480127	Paul Bourdelais	07/2019
292	(94^241993-1)/93	477482	Paul Bourdelais	09/2020
293	2^1585195+1888373	477192	Enzo Doria	08/2017
294	(33^313553+1)/34	476134	Paul Bourdelais	02/2021
295	3^994536+16	474515	Robert Price	10/2020
296	2^1575391+71483	474240	Enzo Doria	04/2018
297	(2^1572882+5)/3	473485	Serge Batalov	08/2015
298	(6^608099-1)/5	473193	Paul Bourdelais	05/2010
299	2^1569708+20371	472530	Enzo Doria	09/2023
300	3^989124+16	471933	Robert Price	10/2020
301	2^1567006+1888099	471716	Enzo Doria	05/2017
302	2^1563067+1889813	470531	Enzo Doria	08/2017
303	2^1549797+60197	466536	Enzo Doria	02/2018
304	2^1549030+1887619	466305	Enzo Doria	05/2017
305	416^177481-415^177481	464840	Jean-Louis Charton	12/2016
306	(78^245183-1)/77	463908	Paul Bourdelais	02/2021
307	2^1534770+20809	462012	Enzo Doria	08/2023
308	10^459480-11	459480	Mischa Rodermond	04/2023
309	(5^656657-2^656657)/3	458984	Jon Grantham	08/2023
310	2^1522569+71657	458339	Enzo Doria	04/2018
311	2^1518191+75353	457022	Ben Maloney / Five or Bust	01/2009
312	6^584279-5	454658	Paul Bourdelais	02/2021
313	2^1509037-13	454266	Stefano Morozzi	12/2022
314	(52^264697-1)/51	454220	Paul Bourdelais	10/2021
315	2^1506029+1890167	453360	Enzo Doria	02/2018
316	(34^294277+1)/35	450678	Paul Bourdelais	06/2018
317	2^1495434+1890439	450171	Enzo Doria	12/2017
318	2^1494634+7	449930	Stefano Morozzi	10/2022
319	2^1493170+784129	449489	Enzo Doria	08/2017
320	2^1489873+1888277	448497	Enzo Doria	06/2017
321	2^1485203+71663	447091	Enzo Doria	09/2023
322	2^1484671+1888463	446931	Enzo Doria	06/2017
323	2^1482867+1886783	446388	Enzo Doria	04/2017
324	2^1482148+284011	446172	Enzo Doria	04/2017
325	2^1479356+1888291	445331	Enzo Doria	06/2017
326	2^1473184+212671	443473	Enzo Doria	09/2023
327	2^1466432+20371	441441	Enzo Doria	08/2023
328	14^384558+3	440753	Paul Bourdelais	01/2021
329	2^1461244+784531	439879	Enzo Doria	10/2017
330	3^919094+5*2^919094	438520	Jon Grantham	08/2023
331	(67^239053+1)/68	436527	Paul Bourdelais	09/2021
332	2^1448122+74209	435929	Enzo Doria	08/2023
333	2^1446263+74333	435369	Enzo Doria	08/2023
334	(80^228419+1)/81	434701	Paul Bourdelais	02/2021
335	2^1443089+60227	434414	Enzo Doria	10/2017
336	(21^328129-1)/20	433858	Paul Bourdelais	06/2014
337	(35^280979+1)/36	433850	Paul Bourdelais	09/2021
338	2^1434400+3	431798	Paul Bourdelais	06/2019
339	2^1432308+1888801	431168	Enzo Doria	10/2017
340	(2^1430131+1)/(335646873253736519993971459)	430487	Gord Palameta	12/2018
341	(7^508867-2^508867)/5	430042	Jon Grantham	08/2023
342	2^1425483+1886813	429114	Enzo Doria	04/2017
343	(63^238481+1)/64	429107	Paul Bourdelais	12/2020
344	(17^348259+1)/18	428514	Paul Bourdelais	05/2014
345	(10^427912+89)/9	427912	Serge Batalov	12/2014
346	2^1421089+1890167	427791	Enzo Doria	09/2017
347	20^326600+3	424917	Paul Bourdelais	01/2021
348	(10^424861-7)/3	424861	Leonid Durman	01/2012
349	10^424821-11	424821	Mischa Rodermond	04/2023
350	(2^1411200+13)/7	424813	Stefano Morozzi	09/2022
351	1+3^605376+5^605376	423140	Jon Grantham	08/2023
352	2^1404213+184217	422711	Enzo Doria	09/2017
353	2^1401872+1884385	422006	Enzo Doria	04/2017
354	2^1401257+6077	421821	Enzo Doria	09/2017
355	138^196873-137^196873	421285	Jean-Louis Charton	12/2009
356	2^1398726+7	421059	Stefano Morozzi	10/2022
357	2^1398269+131595	420921	Makoto Morimoto	10/2013
358	2^1397071+684443	420561	Enzo Doria	07/2017
359	953^141023-952^141023	420121	Jean-Louis Charton	10/2016
360	2^1393111+1867211	419369	Enzo Doria	09/2023
361	(3^877843-1)/2	418838	Paul Bourdelais	07/2010
362	2^1386321+60299	417325	Enzo Doria	02/2018
363	2^1386320+184531	417324	Enzo Doria	09/2017
364	2^1382074+1883587	416046	Enzo Doria	01/2017
365	2^1379907+1885223	415394	Enzo Doria	03/2017
366	2^1375574+1886719	414090	Enzo Doria	04/2017
367	2^1373111+1884833	413348	Enzo Doria	02/2017
368	2^1372996+15	413313	Stefano Morozzi	10/2022
369	2^1368632+1889731	412000	Enzo Doria	10/2017
370	(89*10^411590+1)/9	411591	Serge Batalov	09/2014
371	F(1968721)	411439	Henri Lifchitz	11/2009
372	2^1366066+683749	411227	Enzo Doria	02/2017
373	2^1355826+15	408145	Stefano Morozzi	10/2022
374	2^1355790+1888939	408134	Enzo Doria	07/2017
375	2^1355635+1884203	408087	Enzo Doria	01/2017
376	(88^208739+1)/89	405888	Paul Bourdelais	12/2020
377	(2^1347781-2^673891+1)/5	405722	Borys Jaworski	10/2008
378	2^1347744-3	405712	Paul Bourdelais	07/2019
379	9*10^404644-11	404645	Mischa Rodermond	04/2023
380	1215^131072+242^131072	404302	Kellen Shenton	08/2022
381	1196^131072+595^131072	403405	Kellen Shenton	08/2022
382	10^400000+1415223	400001	Patrick De Geest	10/2020
383	10^400000-339233	400000	Patrick De Geest	10/2020
384	Tau(863^24630)	397727	Nik Lygeros / Olivier Rozier	01/2016
385	2^1320057+211517	397377	Enzo Doria	08/2023
386	2^1319770+1884949	397291	Enzo Doria	06/2017
387	2^1313062+1888849	395272	Enzo Doria	08/2017
388	(1073516^81920+1)/(1073516^16384+1)	395236	Serge Batalov	01/2017
389	(1059995^81920+1)/(1059995^16384+1)	394875	Serge Batalov	01/2017
390	2^1311618+783529	394837	Enzo Doria	01/2017
391	2^1308000+1883521	393748	Enzo Doria	02/2017
392	(1009565^81920+1)/(1009565^16384+1)	393487	Serge Batalov	01/2017
393	(995042^81920+1)/(995042^16384+1)	393075	Serge Batalov	01/2017
394	(988945^81920+1)/(988945^16384+1)	392900	Serge Batalov	01/2017
395	(988823^81920+1)/(988823^16384+1)	392897	Serge Batalov	01/2017
396	(2^1304983-1)/52199321	392832	Tony Prest / Never Odd Or Even	03/2014
397	(978970^81920+1)/(978970^16384+1)	392612	Serge Batalov	01/2017
398	2^1303102+1866409	392273	Enzo Doria	09/2017
399	2^1302818+283429	392188	Enzo Doria	01/2017
400	(934422^81920+1)/(934422^16384+1)	391286	Serge Batalov	01/2017
401	2^1299181+1886867	391093	Enzo Doria	04/2017
402	(37^249341-1)/36	391016	Paul Bourdelais	08/2020
403	2^1298304+1882891	390829	Enzo Doria	01/2017
404	95196^12497+12497^95196	390000	Hans Havermann	12/2021
405	86206^33381+33381^86206	389953	Hans Havermann	05/2023
406	(874207^81920+1)/(874207^16384+1)	389390	Serge Batalov	01/2017
407	(7^457871-5^457871)/2	386946	Jon Grantham	08/2023
408	79455^73828+73828^79455	386805	Hans Havermann	03/2023
409	81650^54369+54369^81650	386642	Yusuf AttarBashi	06/2021
410	80565^62824+62824^80565	386561	Hans Havermann	08/2021
411	83747^41272+41272^83747	386548	Hans Havermann	08/2021
412	15^328574+328574^15	386434	Serge Batalov	05/2014
413	2^1280078+1885099	385342	Enzo Doria	08/2017
414	2^1279921+17	385295	Stefano Morozzi	10/2022
415	2^1276977+71657	384409	Enzo Doria	08/2023
416	2^1274941+1880717	383796	Enzo Doria	10/2016
417	2^1272632+383431	383101	Enzo Doria	01/2017
418	2^1271346+1889839	382714	Enzo Doria	08/2017
419	5*3^798534-2^798534	380999	Jon Grantham	08/2023
420	(10^380976-7)/3	380976	Leonid Durman	01/2012
421	(4*10^380056+11)/3	380057	Tyler Busby	03/2023
422	2^1257787+1447761	378632	Makoto Morimoto	10/2013
423	(2^1257787+32270)/(223328122073011)	378620	Makoto Morimoto	12/2016
424	2^1257728+20851	378614	Enzo Doria	08/2023
425	(77^200657-1)/76	378536	Paul Bourdelais	08/2020
426	(98^189619+1)/99	377573	Paul Bourdelais	02/2021
427	F(1803059)	376817	Henri Lifchitz	06/2009
428	(10^376417-3^376417)/7	376417	Jon Grantham	08/2023
429	2^1245230+19	374852	Stefano Morozzi	10/2022
430	7^442674+4	374103	Paul Bourdelais	02/2021
431	(97^187393-1)/96	372306	Paul Bourdelais	09/2020
432	10^371696+7	371697	Alfred Reich	05/2021
433	2^1234709+883127	371685	Enzo Doria	12/2016
434	2^1234119+21803	371507	Enzo Doria	09/2023
435	(67^203431+1)/68	371479	Paul Bourdelais	09/2021
436	2^1231466+283819	370709	Enzo Doria	07/2017
437	73^197880+197880	368715	Kellen Shenton	06/2023
438	5*3^771723-2^771723	368207	Jon Grantham	08/2023
439	(2^1222097+19)/3	367888	Stefano Morozzi	09/2022
440	2^1220335+1881263	367358	Enzo Doria	11/2016
441	2^1216694+1884769	366262	Enzo Doria	02/2017
442	2^1215889-3	366020	Paul Bourdelais	06/2019
443	2^1215296+1885441	365841	Enzo Doria	03/2017
444	(80^192133+1)/81	365645	Paul Bourdelais	01/2021
445	2^1214307+1888115	365543	Enzo Doria	05/2017
446	2^1213815+3	365395	Paul Bourdelais	06/2019
447	(80^191953+1)/81	365302	Paul Bourdelais	01/2021
448	2^1208276+22201	363728	Enzo Doria	09/2023
449	2^1207345+1882577	363448	Enzo Doria	12/2016
450	2^1207073+883727	363366	Enzo Doria	03/2017
451	3^761457-2	363308	Ryan Propper	07/2015
452	(10^363030+7)/337/443	363025	Alfred Reich	12/2021
453	2^1200972+141811	361529	Stefano Morozzi	10/2022
454	(2^1200924+324730)/2	361514	Stefano Morozzi	06/2021
455	(2^1200912+274110)/2	361511	Stefano Morozzi	01/2021
456	2^1200906+165249	361509	Stefano Morozzi	07/2022
457	2^1200890+166339	361504	Stefano Morozzi	01/2023
458	(2^1200887+344126)/2	361503	Stefano Morozzi	10/2020
459	2^1200877+186755	361500	Stefano Morozzi	09/2022
460	2^1200861+198521	361495	Stefano Morozzi	11/2021
461	(2^1200856+305790)/2	361494	Stefano Morozzi	10/2020
462	(2^1200853+372822)/2	361493	Stefano Morozzi	06/2021
463	2^1200812+324178)/2	361481	Stefano Morozzi	06/2021
464	(2^1200768+380458)/2	361467	Stefano Morozzi	01/2021
465	2^1200756+140917	361464	Stefano Morozzi	05/2022
466	2^1200741+184781	361460	Stefano Morozzi	09/2022
467	(2^1200741+293402)/2	361459	Stefano Morozzi	07/2021
468	2^1200734+142653	361457	Stefano Morozzi	02/2023
470	2^1200672+1880881	361439	Enzo Doria	10/2016
469	2^1200672+141535	361439	Stefano Morozzi	09/2022
471	2^1200669+178805	361438	Stefano Morozzi	11/2022
472	2^1200660+198555	361435	Stefano Morozzi	12/2021
473	2^1200657+164837	361434	Stefano Morozzi	05/2022
474	2^1200631+166431	361426	Stefano Morozzi	02/2023
475	2^1200627+150669	361425	Stefano Morozzi	02/2023
476	(2^1200603+356030)/2	361418	Stefano Morozzi	10/2020
477	(2^1200590+275854)/2	361414	Stefano Morozzi	03/2021
478	2^1200550+139297	361402	Stefano Morozzi	10/2021
479	2^1200486+172855	361383	Stefano Morozzi	01/2023
480	(2^1200456+320526)/2	361373	Stefano Morozzi	10/2020
481	2^1200443+142121	361370	Stefano Morozzi	01/2023
482	2^1200416+164065	361362	Stefano Morozzi	01/2022
483	2^1200331+155429	361336	Stefano Morozzi	10/2021
485	(2^1200289+348366)/2	361323	Stefano Morozzi	10/2020
484	2^1200289+141885	361323	Stefano Morozzi	11/2022
486	(2^1200284+273162)/2	361322	Stefano Morozzi	10/2020
487	2^1200252+194535	361312	Stefano Morozzi	11/2021
488	(2^1200250+364230)/2	361311	Stefano Morozzi	10/2020
489	2^1200227+156881	361305	Stefano Morozzi	05/2022
490	(2^1200209+305990)/2	361299	Stefano Morozzi	10/2020
491	(2^1200210+376278)/2	361299	Stefano Morozzi	10/2020
492	(2^1200182+274462)/2	361291	Stefano Morozzi	01/2021
493	2^1200178+149193	361290	Stefano Morozzi	07/2022
494	2^1200168+140403	361287	Stefano Morozzi	03/2022
495	(2^1200162+275910)/2	361285	Stefano Morozzi	03/2021
496	2^1200157+168927	361284	Stefano Morozzi	02/2023
497	2^1200134+141385	361277	Stefano Morozzi	08/2022
498	(2^1200131+360150)/2	361276	Stefano Morozzi	10/2020
499	(2^1200118+290718)/2	361272	Stefano Morozzi	01/2021
500	2^1200022+192777	361243	Stefano Morozzi	09/2022

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