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
Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
251 | 2^1575391+71483 | 474240 | Enzo Doria | 04/2018 |
252 | (2^1572882+5)/3 | 473485 | Serge Batalov | 08/2015 |
253 | (6^608099-1)/5 | 473193 | Paul Bourdelais | 05/2010 |
254 | 3^989124+16 | 471933 | Robert Price | 10/2020 |
255 | 2^1567006+1888099 | 471716 | Enzo Doria | 05/2017 |
256 | 2^1563067+1889813 | 470531 | Enzo Doria | 08/2017 |
257 | 2^1549797+60197 | 466536 | Enzo Doria | 02/2018 |
258 | 2^1549030+1887619 | 466305 | Enzo Doria | 05/2017 |
259 | 416^177481-415^177481 | 464840 | Jean-Louis Charton | 12/2016 |
260 | (78^245183-1)/77 | 463908 | Paul Bourdelais | 02/2021 |
261 | 2^1522569+71657 | 458339 | Enzo Doria | 04/2018 |
262 | 2^1518191+75353 | 457022 | Ben Maloney / Five or Bust | 01/2009 |
263 | 6^584279-5 | 454658 | Paul Bourdelais | 02/2021 |
264 | 2^1509037-13 | 454266 | Stefano Morozzi | 12/2022 |
265 | (52^264697-1)/51 | 454220 | Paul Bourdelais | 10/2021 |
266 | 2^1506029+1890167 | 453360 | Enzo Doria | 02/2018 |
267 | (34^294277+1)/35 | 450678 | Paul Bourdelais | 06/2018 |
268 | 2^1495434+1890439 | 450171 | Enzo Doria | 12/2017 |
269 | 2^1494634+7 | 449930 | Stefano Morozzi | 10/2022 |
270 | 2^1493170+784129 | 449489 | Enzo Doria | 08/2017 |
271 | 2^1489873+1888277 | 448497 | Enzo Doria | 06/2017 |
272 | 2^1484671+1888463 | 446931 | Enzo Doria | 06/2017 |
273 | 2^1482867+1886783 | 446388 | Enzo Doria | 04/2017 |
274 | 2^1482148+284011 | 446172 | Enzo Doria | 04/2017 |
275 | 2^1479356+1888291 | 445331 | Enzo Doria | 06/2017 |
276 | 14^384558+3 | 440753 | Paul Bourdelais | 01/2021 |
277 | 2^1461244+784531 | 439879 | Enzo Doria | 10/2017 |
278 | (67^239053+1)/68 | 436527 | Paul Bourdelais | 09/2021 |
279 | (80^228419+1)/81 | 434701 | Paul Bourdelais | 02/2021 |
280 | 2^1443089+60227 | 434414 | Enzo Doria | 10/2017 |
281 | (21^328129-1)/20 | 433858 | Paul Bourdelais | 06/2014 |
282 | (35^280979+1)/36 | 433850 | Paul Bourdelais | 09/2021 |
283 | 2^1434400+3 | 431798 | Paul Bourdelais | 06/2019 |
284 | 2^1432308+1888801 | 431168 | Enzo Doria | 10/2017 |
285 | (2^1430131+1)/(3*356468732537*36519993971459) | 430487 | Gord Palameta | 12/2018 |
286 | 2^1425483+1886813 | 429114 | Enzo Doria | 04/2017 |
287 | (63^238481+1)/64 | 429107 | Paul Bourdelais | 12/2020 |
288 | (17^348259+1)/18 | 428514 | Paul Bourdelais | 05/2014 |
289 | (10^427912+89)/9 | 427912 | Serge Batalov | 12/2014 |
290 | 2^1421089+1890167 | 427791 | Enzo Doria | 09/2017 |
291 | 20^326600+3 | 424917 | Paul Bourdelais | 01/2021 |
292 | (10^424861-7)/3 | 424861 | Leonid Durman | 01/2012 |
293 | (2^1411200+13)/7 | 424813 | Stefano Morozzi | 09/2022 |
294 | 2^1404213+184217 | 422711 | Enzo Doria | 09/2017 |
295 | 2^1401872+1884385 | 422006 | Enzo Doria | 04/2017 |
296 | 2^1401257+6077 | 421821 | Enzo Doria | 09/2017 |
297 | 138^196873-137^196873 | 421285 | Jean-Louis Charton | 12/2009 |
298 | 2^1398726+7 | 421059 | Stefano Morozzi | 10/2022 |
299 | 2^1398269+131595 | 420921 | Makoto Morimoto | 10/2013 |
300 | 2^1397071+684443 | 420561 | Enzo Doria | 07/2017 |
301 | 953^141023-952^141023 | 420121 | Jean-Louis Charton | 10/2016 |
302 | (3^877843-1)/2 | 418838 | Paul Bourdelais | 07/2010 |
303 | 2^1386321+60299 | 417325 | Enzo Doria | 02/2018 |
304 | 2^1386320+184531 | 417324 | Enzo Doria | 09/2017 |
305 | 2^1382074+1883587 | 416046 | Enzo Doria | 01/2017 |
306 | 2^1379907+1885223 | 415394 | Enzo Doria | 03/2017 |
307 | 2^1375574+1886719 | 414090 | Enzo Doria | 04/2017 |
308 | 2^1373111+1884833 | 413348 | Enzo Doria | 02/2017 |
309 | 2^1372996+15 | 413313 | Stefano Morozzi | 10/2022 |
310 | 2^1368632+1889731 | 412000 | Enzo Doria | 10/2017 |
311 | (89*10^411590+1)/9 | 411591 | Serge Batalov | 09/2014 |
312 | F(1968721) | 411439 | Henri Lifchitz | 11/2009 |
313 | 2^1366066+683749 | 411227 | Enzo Doria | 02/2017 |
314 | 2^1355826+15 | 408145 | Stefano Morozzi | 10/2022 |
315 | 2^1355790+1888939 | 408134 | Enzo Doria | 07/2017 |
316 | 2^1355635+1884203 | 408087 | Enzo Doria | 01/2017 |
317 | (88^208739+1)/89 | 405888 | Paul Bourdelais | 12/2020 |
318 | (2^1347781-2^673891+1)/5 | 405722 | Borys Jaworski | 10/2008 |
319 | 2^1347744-3 | 405712 | Paul Bourdelais | 07/2019 |
320 | 1215^131072+242^131072 | 404302 | Kellen Shenton | 08/2022 |
321 | 1196^131072+595^131072 | 403405 | Kellen Shenton | 08/2022 |
322 | 10^400000+1415223 | 400001 | Patrick De Geest | 10/2020 |
323 | 10^400000-339233 | 400000 | Patrick De Geest | 10/2020 |
324 | Tau(863^24630) | 397727 | Nik Lygeros / Olivier Rozier | 01/2016 |
325 | 2^1319770+1884949 | 397291 | Enzo Doria | 06/2017 |
326 | 2^1313062+1888849 | 395272 | Enzo Doria | 08/2017 |
327 | (1073516^81920+1)/(1073516^16384+1) | 395236 | Serge Batalov | 01/2017 |
328 | (1059995^81920+1)/(1059995^16384+1) | 394875 | Serge Batalov | 01/2017 |
329 | 2^1311618+783529 | 394837 | Enzo Doria | 01/2017 |
330 | 2^1308000+1883521 | 393748 | Enzo Doria | 02/2017 |
331 | (1009565^81920+1)/(1009565^16384+1) | 393487 | Serge Batalov | 01/2017 |
332 | (995042^81920+1)/(995042^16384+1) | 393075 | Serge Batalov | 01/2017 |
333 | (988945^81920+1)/(988945^16384+1) | 392900 | Serge Batalov | 01/2017 |
334 | (988823^81920+1)/(988823^16384+1) | 392897 | Serge Batalov | 01/2017 |
335 | (2^1304983-1)/52199321 | 392832 | Tony Prest / Never Odd Or Even | 03/2014 |
336 | (978970^81920+1)/(978970^16384+1) | 392612 | Serge Batalov | 01/2017 |
337 | 2^1303102+1866409 | 392273 | Enzo Doria | 09/2017 |
338 | 2^1302818+283429 | 392188 | Enzo Doria | 01/2017 |
339 | (934422^81920+1)/(934422^16384+1) | 391286 | Serge Batalov | 01/2017 |
340 | 2^1299181+1886867 | 391093 | Enzo Doria | 04/2017 |
341 | (37^249341-1)/36 | 391016 | Paul Bourdelais | 08/2020 |
342 | 2^1298304+1882891 | 390829 | Enzo Doria | 01/2017 |
343 | 95196^12497+12497^95196 | 390000 | Hans Havermann | 12/2021 |
344 | (874207^81920+1)/(874207^16384+1) | 389390 | Serge Batalov | 01/2017 |
345 | 79455^73828+73828^79455 | 386805 | Hans Havermann | 03/2023 |
346 | 81650^54369+54369^81650 | 386642 | Yusuf AttarBashi | 06/2021 |
347 | 80565^62824+62824^80565 | 386561 | Hans Havermann | 08/2021 |
348 | 83747^41272+41272^83747 | 386548 | Hans Havermann | 08/2021 |
349 | 15^328574+328574^15 | 386434 | Serge Batalov | 05/2014 |
350 | 2^1280078+1885099 | 385342 | Enzo Doria | 08/2017 |
351 | 2^1279921+17 | 385295 | Stefano Morozzi | 10/2022 |
352 | 2^1274941+1880717 | 383796 | Enzo Doria | 10/2016 |
353 | 2^1272632+383431 | 383101 | Enzo Doria | 01/2017 |
354 | 2^1271346+1889839 | 382714 | Enzo Doria | 08/2017 |
355 | (10^380976-7)/3 | 380976 | Leonid Durman | 01/2012 |
356 | (4*10^380056+11)/3 | 380057 | Tyler Busby | 03/2023 |
357 | 2^1257787+1447761 | 378632 | Makoto Morimoto | 10/2013 |
358 | (2^1257787+32270)/(2*233*281*2207*3011) | 378620 | Makoto Morimoto | 12/2016 |
359 | (77^200657-1)/76 | 378536 | Paul Bourdelais | 08/2020 |
360 | (98^189619+1)/99 | 377573 | Paul Bourdelais | 02/2021 |
361 | F(1803059) | 376817 | Henri Lifchitz | 06/2009 |
362 | 2^1245230+19 | 374852 | Stefano Morozzi | 10/2022 |
363 | 7^442674+4 | 374103 | Paul Bourdelais | 02/2021 |
364 | (97^187393-1)/96 | 372306 | Paul Bourdelais | 09/2020 |
365 | 10^371696+7 | 371697 | Alfred Reich | 05/2021 |
366 | 2^1234709+883127 | 371685 | Enzo Doria | 12/2016 |
367 | (67^203431+1)/68 | 371479 | Paul Bourdelais | 09/2021 |
368 | 2^1231466+283819 | 370709 | Enzo Doria | 07/2017 |
369 | (2^1222097+19)/3 | 367888 | Stefano Morozzi | 09/2022 |
370 | 2^1220335+1881263 | 367358 | Enzo Doria | 11/2016 |
371 | 2^1216694+1884769 | 366262 | Enzo Doria | 02/2017 |
372 | 2^1215889-3 | 366020 | Paul Bourdelais | 06/2019 |
373 | 2^1215296+1885441 | 365841 | Enzo Doria | 03/2017 |
374 | (80^192133+1)/81 | 365645 | Paul Bourdelais | 01/2021 |
375 | 2^1214307+1888115 | 365543 | Enzo Doria | 05/2017 |
376 | 2^1213815+3 | 365395 | Paul Bourdelais | 06/2019 |
377 | (80^191953+1)/81 | 365302 | Paul Bourdelais | 01/2021 |
378 | 2^1207345+1882577 | 363448 | Enzo Doria | 12/2016 |
379 | 2^1207073+883727 | 363366 | Enzo Doria | 03/2017 |
380 | 3^761457-2 | 363308 | Ryan Propper | 07/2015 |
381 | (10^363030+7)/337/443 | 363025 | Alfred Reich | 12/2021 |
382 | 2^1200972+141811 | 361529 | Stefano Morozzi | 10/2022 |
383 | (2^1200924+324730)/2 | 361514 | Stefano Morozzi | 06/2021 |
384 | (2^1200912+274110)/2 | 361511 | Stefano Morozzi | 01/2021 |
385 | 2^1200906+165249 | 361509 | Stefano Morozzi | 07/2022 |
386 | 2^1200890+166339 | 361504 | Stefano Morozzi | 01/2023 |
387 | (2^1200887+344126)/2 | 361503 | Stefano Morozzi | 10/2020 |
388 | 2^1200877+186755 | 361500 | Stefano Morozzi | 09/2022 |
389 | 2^1200861+198521 | 361495 | Stefano Morozzi | 11/2021 |
390 | (2^1200856+305790)/2 | 361494 | Stefano Morozzi | 10/2020 |
391 | (2^1200853+372822)/2 | 361493 | Stefano Morozzi | 06/2021 |
392 | 2^1200812+324178)/2 | 361481 | Stefano Morozzi | 06/2021 |
393 | (2^1200768+380458)/2 | 361467 | Stefano Morozzi | 01/2021 |
394 | 2^1200756+140917 | 361464 | Stefano Morozzi | 05/2022 |
395 | 2^1200741+184781 | 361460 | Stefano Morozzi | 09/2022 |
396 | (2^1200741+293402)/2 | 361459 | Stefano Morozzi | 07/2021 |
397 | 2^1200734+142653 | 361457 | Stefano Morozzi | 02/2023 |
399 | 2^1200672+1880881 | 361439 | Enzo Doria | 10/2016 |
398 | 2^1200672+141535 | 361439 | Stefano Morozzi | 09/2022 |
400 | 2^1200669+178805 | 361438 | Stefano Morozzi | 11/2022 |
401 | 2^1200660+198555 | 361435 | Stefano Morozzi | 12/2021 |
402 | 2^1200657+164837 | 361434 | Stefano Morozzi | 05/2022 |
403 | 2^1200631+166431 | 361426 | Stefano Morozzi | 02/2023 |
404 | 2^1200627+150669 | 361425 | Stefano Morozzi | 02/2023 |
405 | (2^1200603+356030)/2 | 361418 | Stefano Morozzi | 10/2020 |
406 | (2^1200590+275854)/2 | 361414 | Stefano Morozzi | 03/2021 |
407 | 2^1200550+139297 | 361402 | Stefano Morozzi | 10/2021 |
408 | 2^1200486+172855 | 361383 | Stefano Morozzi | 01/2023 |
409 | (2^1200456+320526)/2 | 361373 | Stefano Morozzi | 10/2020 |
410 | 2^1200443+142121 | 361370 | Stefano Morozzi | 01/2023 |
411 | 2^1200416+164065 | 361362 | Stefano Morozzi | 01/2022 |
412 | 2^1200331+155429 | 361336 | Stefano Morozzi | 10/2021 |
414 | (2^1200289+348366)/2 | 361323 | Stefano Morozzi | 10/2020 |
413 | 2^1200289+141885 | 361323 | Stefano Morozzi | 11/2022 |
415 | (2^1200284+273162)/2 | 361322 | Stefano Morozzi | 10/2020 |
416 | 2^1200252+194535 | 361312 | Stefano Morozzi | 11/2021 |
417 | (2^1200250+364230)/2 | 361311 | Stefano Morozzi | 10/2020 |
418 | 2^1200227+156881 | 361305 | Stefano Morozzi | 05/2022 |
419 | (2^1200209+305990)/2 | 361299 | Stefano Morozzi | 10/2020 |
420 | (2^1200210+376278)/2 | 361299 | Stefano Morozzi | 10/2020 |
421 | (2^1200182+274462)/2 | 361291 | Stefano Morozzi | 01/2021 |
422 | 2^1200178+149193 | 361290 | Stefano Morozzi | 07/2022 |
423 | 2^1200168+140403 | 361287 | Stefano Morozzi | 03/2022 |
424 | (2^1200162+275910)/2 | 361285 | Stefano Morozzi | 03/2021 |
425 | 2^1200157+168927 | 361284 | Stefano Morozzi | 02/2023 |
426 | 2^1200134+141385 | 361277 | Stefano Morozzi | 08/2022 |
427 | (2^1200131+360150)/2 | 361276 | Stefano Morozzi | 10/2020 |
428 | (2^1200118+290718)/2 | 361272 | Stefano Morozzi | 01/2021 |
429 | 2^1200022+192777 | 361243 | Stefano Morozzi | 09/2022 |
430 | 2^1200021+149777 | 361243 | Stefano Morozzi | 10/2022 |
431 | (64*10^360173-1)/243 | 360173 | Serge Batalov | 09/2014 |
432 | (59^203309+1)/60 | 360029 | Paul Bourdelais | 09/2021 |
433 | (2*10^359860-11)/9 | 359860 | Rytis Slatkevicius | 01/2023 |
434 | 2^1195093+1882577 | 359759 | Enzo Doria | 12/2016 |
435 | (6^461108-11)/5 | 358812 | Paul Bourdelais | 04/2019 |
436 | 2^1191375+8543 | 358640 | Phil Moore | 06/2008 |
437 | 2^1190972+1880191 | 358519 | Enzo Doria | 11/2016 |
438 | (45^216551-1)/44 | 358004 | Paul Bourdelais | 08/2020 |
439 | (50^210319-1)/49 | 357324 | Paul Bourdelais | 08/2020 |
440 | (531^131072+25^131072)/2 | 357184 | Kellen Shenton | 03/2021 |
441 | 2^1179836+1885021 | 355167 | Enzo Doria | 02/2017 |
442 | (19*10^353884-91)/9 | 353885 | Alfred Reich | 02/2023 |
443 | 20^271951+3 | 353817 | Paul Bourdelais | 01/2021 |
444 | 2^1173095+21 | 353137 | Stefano Morozzi | 10/2022 |
445 | (63^195893-1)/62 | 352477 | Paul Bourdelais | 08/2020 |
446 | 2^1170326+7 | 352304 | Stefano Morozzi | 10/2022 |
447 | numbpart(100000135540) | 352269 | Serge Batalov | 04/2017 |
448 | (10^352237-1)/9/10567111/950335427 | 352221 | Maksym Voznyy | 01/2015 |
449 | 2^1168554+783529 | 351770 | Enzo Doria | 01/2017 |
450 | (2^1168183-1)/54763676838381762583 | 351639 | Matthias Wurtinger | 01/2011 |
451 | 2^1166152+1882411 | 351047 | Enzo Doria | 12/2016 |
452 | 10^350071+7 | 350072 | Alfred Reich | 05/2021 |
453 | 2^1162154+1890207 | 349844 | Enzo Doria | 08/2017 |
454 | (7*10^348724-61)/9 | 348724 | Erik Branger | 09/2016 |
455 | (4*10^348453+41)/9 | 348453 | Serge Batalov | 11/2022 |
456 | (127^165601-1)/126 | 348390 | Alexander Zhirkov | 09/2015 |
457 | 2^1153083+1883693 | 347113 | Enzo Doria | 04/2017 |
458 | (2^1148729+2^574365+1)/5 | 345802 | Borys Jaworski | 03/2007 |
459 | 2^1145882+80779 | 344945 | Enzo Doria | 09/2016 |
460 | 2^1136462+1887289 | 342110 | Enzo Doria | 05/2017 |
461 | F(1636007) | 341905 | Henri Lifchitz | 03/2009 |
462 | (2^1135567+13)/3 | 341840 | Stefano Morozzi | 09/2022 |
463 | 2^1133678+782569 | 341272 | Enzo Doria | 11/2016 |
464 | (11^327001+1)/12 | 340536 | Paul Bourdelais | 09/2013 |
465 | (2^1127239+2^563620+1)/5 | 339333 | Borys Jaworski | 11/2006 |
466 | Tau(907^20848) | 339132 | Nik Lygeros / Olivier Rozier | 01/2016 |
467 | 2^1126380-3 | 339075 | Paul Bourdelais | 06/2019 |
468 | 2^1125446+1885099 | 338794 | Enzo Doria | 08/2017 |
469 | (63^188147+1)/64 | 338539 | Paul Bourdelais | 12/2020 |
470 | 2^1124549+143807 | 338523 | Enzo Doria | 10/2016 |
471 | (4*10^338476+23)/9 | 338476 | Serge Batalov | 11/2022 |
472 | 2^1121187+1886783 | 337511 | Enzo Doria | 04/2017 |
473 | (48^200443-1)/47 | 336992 | Paul Bourdelais | 08/2020 |
474 | (2*10^336405+43)/9 | 336405 | Rytis Slatkevicius | 01/2023 |
475 | (94^170371-1)/93 | 336162 | Paul Bourdelais | 09/2020 |
476 | 2^1116184+1883521 | 336005 | Enzo Doria | 02/2017 |
477 | 2^1114517+1880087 | 335504 | Enzo Doria | 10/2016 |
478 | (5*10^335480+31)/9 | 335480 | Serge Batalov | 11/2022 |
479 | (101^166849+1)/102 | 334418 | Paul Bourdelais | 12/2020 |
480 | (3^700897+1)/4 | 334413 | Paul Bourdelais | 04/2010 |
481 | 2^1104408-114539 | 332460 | Enzo Doria | 03/2015 |
482 | 2^1101921+82085 | 331712 | Enzo Doria | 10/2016 |
483 | 2^1100655+683513 | 331331 | Enzo Doria | 01/2017 |
484 | (10^330906+71)/9 | 330906 | Serge Batalov | 07/2015 |
485 | 2^1098346+482899 | 330636 | Enzo Doria | 11/2016 |
486 | (2^1096212+19)/5 | 329992 | Stefano Morozzi | 09/2022 |
487 | 2^1095679+1878713 | 329833 | Enzo Doria | 09/2016 |
488 | 2^1094740-1851539 | 329550 | Enzo Doria | 08/2015 |
489 | 2^1092242+19 | 328798 | Stefano Morozzi | 10/2022 |
490 | 2^1091469-379369 | 328565 | Enzo Doria | 03/2014 |
491 | (69^178093-1)/68 | 327485 | Paul Bourdelais | 08/2020 |
492 | (10^326884+7)/421 | 326882 | Alfred Reich | 12/2021 |
493 | 2^1085750+582349 | 326844 | Enzo Doria | 11/2016 |
494 | 2^1083596+483061 | 326195 | Enzo Doria | 12/2016 |
495 | (2^541456-1)*10^162995+2^541455-1 | 325990 | paolo galliani | 01/2019 |
496 | 2^1082908+583561 | 325988 | Enzo Doria | 05/2017 |
497 | 30^220411-29^220411 | 325574 | Jean-Louis Charton | 10/2018 |
498 | 2^1081308+7 | 325507 | Stefano Morozzi | 10/2022 |
499 | 2^1078242+1881649 | 324584 | Enzo Doria | 11/2016 |
500 | 2^1077737+1880117 | 324432 | Enzo Doria | 10/2016 |