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 (> 50000)	Who ?	When ?
251	2^1563067+1889813	470531	Enzo Doria	08/2017
252	2^1549797+60197	466536	Enzo Doria	02/2018
253	2^1549030+1887619	466305	Enzo Doria	05/2017
254	416^177481-415^177481	464840	Jean-Louis Charton	12/2016
255	(78^245183-1)/77	463908	Paul Bourdelais	02/2021
256	2^1522569+71657	458339	Enzo Doria	04/2018
257	2^1518191+75353	457022	Ben Maloney / Five or Bust	01/2009
258	6^584279-5	454658	Paul Bourdelais	02/2021
259	2^1509037-13	454266	Stefano Morozzi	12/2022
260	(52^264697-1)/51	454220	Paul Bourdelais	10/2021
261	2^1506029+1890167	453360	Enzo Doria	02/2018
262	(34^294277+1)/35	450678	Paul Bourdelais	06/2018
263	2^1495434+1890439	450171	Enzo Doria	12/2017
264	2^1494634+7	449930	Stefano Morozzi	10/2022
265	2^1493170+784129	449489	Enzo Doria	08/2017
266	2^1489873+1888277	448497	Enzo Doria	06/2017
267	2^1484671+1888463	446931	Enzo Doria	06/2017
268	2^1482867+1886783	446388	Enzo Doria	04/2017
269	2^1482148+284011	446172	Enzo Doria	04/2017
270	2^1479356+1888291	445331	Enzo Doria	06/2017
271	14^384558+3	440753	Paul Bourdelais	01/2021
272	2^1461244+784531	439879	Enzo Doria	10/2017
273	(67^239053+1)/68	436527	Paul Bourdelais	09/2021
274	(80^228419+1)/81	434701	Paul Bourdelais	02/2021
275	2^1443089+60227	434414	Enzo Doria	10/2017
276	(21^328129-1)/20	433858	Paul Bourdelais	06/2014
277	(35^280979+1)/36	433850	Paul Bourdelais	09/2021
278	2^1434400+3	431798	Paul Bourdelais	06/2019
279	2^1432308+1888801	431168	Enzo Doria	10/2017
280	(2^1430131+1)/(335646873253736519993971459)	430487	Gord Palameta	12/2018
281	2^1425483+1886813	429114	Enzo Doria	04/2017
282	(63^238481+1)/64	429107	Paul Bourdelais	12/2020
283	(17^348259+1)/18	428514	Paul Bourdelais	05/2014
284	(10^427912+89)/9	427912	Serge Batalov	12/2014
285	2^1421089+1890167	427791	Enzo Doria	09/2017
286	20^326600+3	424917	Paul Bourdelais	01/2021
287	(10^424861-7)/3	424861	Leonid Durman	01/2012
288	(2^1411200+13)/7	424813	Stefano Morozzi	09/2022
289	2^1404213+184217	422711	Enzo Doria	09/2017
290	2^1401872+1884385	422006	Enzo Doria	04/2017
291	2^1401257+6077	421821	Enzo Doria	09/2017
292	138^196873-137^196873	421285	Jean-Louis Charton	12/2009
293	2^1398726+7	421059	Stefano Morozzi	10/2022
294	2^1398269+131595	420921	Makoto Morimoto	10/2013
295	2^1397071+684443	420561	Enzo Doria	07/2017
296	953^141023-952^141023	420121	Jean-Louis Charton	10/2016
297	(3^877843-1)/2	418838	Paul Bourdelais	07/2010
298	2^1386321+60299	417325	Enzo Doria	02/2018
299	2^1386320+184531	417324	Enzo Doria	09/2017
300	2^1382074+1883587	416046	Enzo Doria	01/2017
301	2^1379907+1885223	415394	Enzo Doria	03/2017
302	2^1375574+1886719	414090	Enzo Doria	04/2017
303	2^1373111+1884833	413348	Enzo Doria	02/2017
304	2^1372996+15	413313	Stefano Morozzi	10/2022
305	2^1368632+1889731	412000	Enzo Doria	10/2017
306	(89*10^411590+1)/9	411591	Serge Batalov	09/2014
307	F(1968721)	411439	Henri Lifchitz	11/2009
308	2^1366066+683749	411227	Enzo Doria	02/2017
309	2^1355826+15	408145	Stefano Morozzi	10/2022
310	2^1355790+1888939	408134	Enzo Doria	07/2017
311	2^1355635+1884203	408087	Enzo Doria	01/2017
312	(88^208739+1)/89	405888	Paul Bourdelais	12/2020
313	(2^1347781-2^673891+1)/5	405722	Borys Jaworski	10/2008
314	2^1347744-3	405712	Paul Bourdelais	07/2019
315	1215^131072+242^131072	404302	Kellen Shenton	08/2022
316	1196^131072+595^131072	403405	Kellen Shenton	08/2022
317	10^400000+1415223	400001	Patrick De Geest	10/2020
318	10^400000-339233	400000	Patrick De Geest	10/2020
319	Tau(863^24630)	397727	Nik Lygeros / Olivier Rozier	01/2016
320	2^1319770+1884949	397291	Enzo Doria	06/2017
321	2^1313062+1888849	395272	Enzo Doria	08/2017
322	(1073516^81920+1)/(1073516^16384+1)	395236	Serge Batalov	01/2017
323	(1059995^81920+1)/(1059995^16384+1)	394875	Serge Batalov	01/2017
324	2^1311618+783529	394837	Enzo Doria	01/2017
325	2^1308000+1883521	393748	Enzo Doria	02/2017
326	(1009565^81920+1)/(1009565^16384+1)	393487	Serge Batalov	01/2017
327	(995042^81920+1)/(995042^16384+1)	393075	Serge Batalov	01/2017
328	(988945^81920+1)/(988945^16384+1)	392900	Serge Batalov	01/2017
329	(988823^81920+1)/(988823^16384+1)	392897	Serge Batalov	01/2017
330	(2^1304983-1)/52199321	392832	Tony Prest / Never Odd Or Even	03/2014
331	(978970^81920+1)/(978970^16384+1)	392612	Serge Batalov	01/2017
332	2^1303102+1866409	392273	Enzo Doria	09/2017
333	2^1302818+283429	392188	Enzo Doria	01/2017
334	(934422^81920+1)/(934422^16384+1)	391286	Serge Batalov	01/2017
335	2^1299181+1886867	391093	Enzo Doria	04/2017
336	(37^249341-1)/36	391016	Paul Bourdelais	08/2020
337	2^1298304+1882891	390829	Enzo Doria	01/2017
338	95196^12497+12497^95196	390000	Hans Havermann	12/2021
339	(874207^81920+1)/(874207^16384+1)	389390	Serge Batalov	01/2017
340	81650^54369+54369^81650	386642	Yusuf AttarBashi	06/2021
341	80565^62824+62824^80565	386561	Hans Havermann	08/2021
342	83747^41272+41272^83747	386548	Hans Havermann	08/2021
343	15^328574+328574^15	386434	Serge Batalov	05/2014
344	2^1280078+1885099	385342	Enzo Doria	08/2017
345	2^1279921+17	385295	Stefano Morozzi	10/2022
346	2^1274941+1880717	383796	Enzo Doria	10/2016
347	2^1272632+383431	383101	Enzo Doria	01/2017
348	2^1271346+1889839	382714	Enzo Doria	08/2017
349	(10^380976-7)/3	380976	Leonid Durman	01/2012
350	2^1257787+1447761	378632	Makoto Morimoto	10/2013
351	(2^1257787+32270)/(223328122073011)	378620	Makoto Morimoto	12/2016
352	(77^200657-1)/76	378536	Paul Bourdelais	08/2020
353	(98^189619+1)/99	377573	Paul Bourdelais	02/2021
354	F(1803059)	376817	Henri Lifchitz	06/2009
355	2^1245230+19	374852	Stefano Morozzi	10/2022
356	7^442674+4	374103	Paul Bourdelais	02/2021
357	(97^187393-1)/96	372306	Paul Bourdelais	09/2020
358	10^371696+7	371697	Alfred Reich	05/2021
359	2^1234709+883127	371685	Enzo Doria	12/2016
360	(67^203431+1)/68	371479	Paul Bourdelais	09/2021
361	2^1231466+283819	370709	Enzo Doria	07/2017
362	(2^1222097+19)/3	367888	Stefano Morozzi	09/2022
363	2^1220335+1881263	367358	Enzo Doria	11/2016
364	2^1216694+1884769	366262	Enzo Doria	02/2017
365	2^1215889-3	366020	Paul Bourdelais	06/2019
366	2^1215296+1885441	365841	Enzo Doria	03/2017
367	(80^192133+1)/81	365645	Paul Bourdelais	01/2021
368	2^1214307+1888115	365543	Enzo Doria	05/2017
369	2^1213815+3	365395	Paul Bourdelais	06/2019
370	(80^191953+1)/81	365302	Paul Bourdelais	01/2021
371	2^1207345+1882577	363448	Enzo Doria	12/2016
372	2^1207073+883727	363366	Enzo Doria	03/2017
373	3^761457-2	363308	Ryan Propper	07/2015
374	(10^363030+7)/337/443	363025	Alfred Reich	12/2021
375	2^1200972+141811	361529	Stefano Morozzi	10/2022
376	(2^1200924+324730)/2	361514	Stefano Morozzi	06/2021
377	(2^1200912+274110)/2	361511	Stefano Morozzi	01/2021
378	2^1200906+165249	361509	Stefano Morozzi	07/2022
379	2^1200890+166339	361504	Stefano Morozzi	01/2023
380	(2^1200887+344126)/2	361503	Stefano Morozzi	10/2020
381	2^1200877+186755	361500	Stefano Morozzi	09/2022
382	2^1200861+198521	361495	Stefano Morozzi	11/2021
383	(2^1200856+305790)/2	361494	Stefano Morozzi	10/2020
384	(2^1200853+372822)/2	361493	Stefano Morozzi	06/2021
385	2^1200812+324178)/2	361481	Stefano Morozzi	06/2021
386	(2^1200768+380458)/2	361467	Stefano Morozzi	01/2021
387	2^1200756+140917	361464	Stefano Morozzi	05/2022
388	2^1200741+184781	361460	Stefano Morozzi	09/2022
389	(2^1200741+293402)/2	361459	Stefano Morozzi	07/2021
391	2^1200672+1880881	361439	Enzo Doria	10/2016
390	2^1200672+141535	361439	Stefano Morozzi	09/2022
392	2^1200669+178805	361438	Stefano Morozzi	11/2022
393	2^1200660+198555	361435	Stefano Morozzi	12/2021
394	2^1200657+164837	361434	Stefano Morozzi	05/2022
395	(2^1200603+356030)/2	361418	Stefano Morozzi	10/2020
396	(2^1200590+275854)/2	361414	Stefano Morozzi	03/2021
397	2^1200550+139297	361402	Stefano Morozzi	10/2021
398	2^1200486+172855	361383	Stefano Morozzi	01/2023
399	(2^1200456+320526)/2	361373	Stefano Morozzi	10/2020
400	2^1200443+142121	361370	Stefano Morozzi	01/2023
401	2^1200416+164065	361362	Stefano Morozzi	01/2022
402	2^1200331+155429	361336	Stefano Morozzi	10/2021
404	(2^1200289+348366)/2	361323	Stefano Morozzi	10/2020
403	2^1200289+141885	361323	Stefano Morozzi	11/2022
405	(2^1200284+273162)/2	361322	Stefano Morozzi	10/2020
406	2^1200252+194535	361312	Stefano Morozzi	11/2021
407	(2^1200250+364230)/2	361311	Stefano Morozzi	10/2020
408	2^1200227+156881	361305	Stefano Morozzi	05/2022
409	(2^1200209+305990)/2	361299	Stefano Morozzi	10/2020
410	(2^1200210+376278)/2	361299	Stefano Morozzi	10/2020
411	(2^1200182+274462)/2	361291	Stefano Morozzi	01/2021
412	2^1200178+149193	361290	Stefano Morozzi	07/2022
413	2^1200168+140403	361287	Stefano Morozzi	03/2022
414	(2^1200162+275910)/2	361285	Stefano Morozzi	03/2021
415	2^1200134+141385	361277	Stefano Morozzi	08/2022
416	(2^1200131+360150)/2	361276	Stefano Morozzi	10/2020
417	(2^1200118+290718)/2	361272	Stefano Morozzi	01/2021
418	2^1200022+192777	361243	Stefano Morozzi	09/2022
419	2^1200021+149777	361243	Stefano Morozzi	10/2022
420	(64*10^360173-1)/243	360173	Serge Batalov	09/2014
421	(59^203309+1)/60	360029	Paul Bourdelais	09/2021
422	(2*10^359860-11)/9	359860	Rytis Slatkevicius	01/2023
423	2^1195093+1882577	359759	Enzo Doria	12/2016
424	(6^461108-11)/5	358812	Paul Bourdelais	04/2019
425	2^1191375+8543	358640	Phil Moore	06/2008
426	2^1190972+1880191	358519	Enzo Doria	11/2016
427	(45^216551-1)/44	358004	Paul Bourdelais	08/2020
428	(50^210319-1)/49	357324	Paul Bourdelais	08/2020
429	(531^131072+25^131072)/2	357184	Kellen Shenton	03/2021
430	2^1179836+1885021	355167	Enzo Doria	02/2017
431	20^271951+3	353817	Paul Bourdelais	01/2021
432	2^1173095+21	353137	Stefano Morozzi	10/2022
433	(63^195893-1)/62	352477	Paul Bourdelais	08/2020
434	2^1170326+7	352304	Stefano Morozzi	10/2022
435	numbpart(100000135540)	352269	Serge Batalov	04/2017
436	(10^352237-1)/9/10567111/950335427	352221	Maksym Voznyy	01/2015
437	2^1168554+783529	351770	Enzo Doria	01/2017
438	(2^1168183-1)/54763676838381762583	351639	Matthias Wurtinger	01/2011
439	2^1166152+1882411	351047	Enzo Doria	12/2016
440	10^350071+7	350072	Alfred Reich	05/2021
441	2^1162154+1890207	349844	Enzo Doria	08/2017
442	(7*10^348724-61)/9	348724	Erik Branger	09/2016
443	(4*10^348453+41)/9	348453	Serge Batalov	11/2022
444	(127^165601-1)/126	348390	Alexander Zhirkov	09/2015
445	2^1153083+1883693	347113	Enzo Doria	04/2017
446	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
447	2^1145882+80779	344945	Enzo Doria	09/2016
448	2^1136462+1887289	342110	Enzo Doria	05/2017
449	F(1636007)	341905	Henri Lifchitz	03/2009
450	(2^1135567+13)/3	341840	Stefano Morozzi	09/2022
451	2^1133678+782569	341272	Enzo Doria	11/2016
452	(11^327001+1)/12	340536	Paul Bourdelais	09/2013
453	(2^1127239+2^563620+1)/5	339333	Borys Jaworski	11/2006
454	Tau(907^20848)	339132	Nik Lygeros / Olivier Rozier	01/2016
455	2^1126380-3	339075	Paul Bourdelais	06/2019
456	2^1125446+1885099	338794	Enzo Doria	08/2017
457	(63^188147+1)/64	338539	Paul Bourdelais	12/2020
458	2^1124549+143807	338523	Enzo Doria	10/2016
459	(4*10^338476+23)/9	338476	Serge Batalov	11/2022
460	2^1121187+1886783	337511	Enzo Doria	04/2017
461	(48^200443-1)/47	336992	Paul Bourdelais	08/2020
462	(2*10^336405+43)/9	336405	Rytis Slatkevicius	01/2023
463	(94^170371-1)/93	336162	Paul Bourdelais	09/2020
464	2^1116184+1883521	336005	Enzo Doria	02/2017
465	2^1114517+1880087	335504	Enzo Doria	10/2016
466	(5*10^335480+31)/9	335480	Serge Batalov	11/2022
467	(101^166849+1)/102	334418	Paul Bourdelais	12/2020
468	(3^700897+1)/4	334413	Paul Bourdelais	04/2010
469	2^1104408-114539	332460	Enzo Doria	03/2015
470	2^1101921+82085	331712	Enzo Doria	10/2016
471	2^1100655+683513	331331	Enzo Doria	01/2017
472	(10^330906+71)/9	330906	Serge Batalov	07/2015
473	2^1098346+482899	330636	Enzo Doria	11/2016
474	(2^1096212+19)/5	329992	Stefano Morozzi	09/2022
475	2^1095679+1878713	329833	Enzo Doria	09/2016
476	2^1094740-1851539	329550	Enzo Doria	08/2015
477	2^1092242+19	328798	Stefano Morozzi	10/2022
478	2^1091469-379369	328565	Enzo Doria	03/2014
479	(69^178093-1)/68	327485	Paul Bourdelais	08/2020
480	(10^326884+7)/421	326882	Alfred Reich	12/2021
481	2^1085750+582349	326844	Enzo Doria	11/2016
482	2^1083596+483061	326195	Enzo Doria	12/2016
483	(2^541456-1)*10^162995+2^541455-1	325990	paolo galliani	01/2019
484	2^1082908+583561	325988	Enzo Doria	05/2017
485	30^220411-29^220411	325574	Jean-Louis Charton	10/2018
486	2^1081308+7	325507	Stefano Morozzi	10/2022
487	2^1078242+1881649	324584	Enzo Doria	11/2016
488	2^1077737+1880117	324432	Enzo Doria	10/2016
489	2^1075425+1880117	323736	Enzo Doria	10/2016
490	(28^223381+1)/29	323267	Paul Bourdelais	12/2020
491	10^322999+187071	323000	Stefano Morozzi	03/2019
492	10^322999-143151	322999	Patrick De Geest	05/2020
493	2^1072146+1886869	322749	Enzo Doria	04/2017
494	2^1072118-7321953	322740	Enzo Doria	02/2015
495	2^1071026+1886869	322411	Enzo Doria	04/2017
496	2^1070539+1880633	322265	Enzo Doria	10/2016
497	2^1069293-1147195	321890	Enzo Doria	05/2015
498	2^1065968+1880941	320889	Enzo Doria	10/2016
499	2^1065897-1147195	320867	Enzo Doria	05/2015
500	2^1063427+1882103	320124	Enzo Doria	12/2016

Find by discoverer :

PRP Records

Probable Primes Top 10000

(291910 PRPs in the top)