## PRP Records

### Probable Primes Top 10000

#### (295756 PRPs in the top)

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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See the Latest PRPs
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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 (152^270217-1)/(152-1) 589570 Michael Stocker 06/2015 252 Phi(177147,94259) 587458 Anonymous 09/2022 253 2^1950002+1867369 587010 Enzo Doria 02/2018 254 116265^111218+111218^116265 586694 Ryan Propper 10/2023 255 2^1940812+3 584243 Paul Bourdelais 06/2020 256 1933695^2+2^1933695 582101 Ryan Propper 05/2023 257 (5^832151-2^832151)/3 581649 Jon Grantham 08/2023 258 (129810^113569-1)/(129810^337-1) 578991 Ryan Propper 11/2023 259 2^1923104+153 578912 Stefano Morozzi 07/2021 260 116761^87652+87652^116761 577122 Ryan Propper 10/2023 261 116395^87994+87994^116395 575510 Ryan Propper 10/2023 262 (3^1205459+1)/4 575150 Paul Bourdelais 08/2015 263 (160972^109561-1)/(160972^331-1) 568734 Ryan Propper 11/2023 264 (37015^124609-1)/(37015^353-1) 567649 Ryan Propper 11/2023 265 2^1882800+384541 566780 Enzo Doria 12/2017 266 (2^1882787-2^941394+1)/5 566775 Borys Jaworski 11/2012 267 2^1882474+71389 566682 Enzo Doria 04/2018 268 (6^727496-11)/5 566102 Paul Bourdelais 08/2019 269 2^1875552+3 564598 Paul Bourdelais 04/2020 270 (145373^109561-1)/(145373^331-1) 563899 Ryan Propper 11/2023 271 (10^563535-7)/3 563535 Rytis Slatkevicius 02/2023 272 3^1180181-2 563090 Jorge Coveiro 05/2020 273 (15063^134689-1)/(15063^367-1) 561186 Ryan Propper 11/2023 274 2^1852265+1890425 557588 Enzo Doria 11/2017 275 5^797390-2 557352 Paul Bourdelais 03/2021 276 (10^556441-7^556441)/3 556441 Jon Grantham 07/2023 277 8^615997-7^615997 556301 Jean-Louis Charton 07/2009 278 (5^795829-2^795829)/3 556261 Jon Grantham 08/2023 279 Tau(773^34960) 555339 Nik Lygeros / Olivier Rozier 09/2015 280 ((((((((((1361^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840)^3+1623568 555154 Serge Batalov 08/2013 281 2^1825513+32507 549535 Enzo Doria 07/2024 282 (42^337081-1)/41 547165 Paul Bourdelais 09/2021 283 114868^57423+57423^114868 546667 Ryan Propper 10/2023 284 109092^100999+100999^109092 545931 Ryan Propper 10/2023 285 2^1812234+31879 545537 Enzo Doria 05/2024 286 (64814^113569-1)/(64814^337-1) 544835 Ryan Propper 11/2023 287 (92170^109561-1)/(92170^331-1) 542283 Ryan Propper 11/2023 288 (28262^121801-1)/(28262^349-1) 540608 Ryan Propper 11/2023 289 2^1791569+33587 539317 Enzo Doria 09/2024 290 (2^1790743-1)/(146840927*158358984977*3835546416767873*20752172271489035681) 539014 Dario Alpern 06/2015 291 10^538640-3 538640 Paul Bourdelais 01/2021 292 (10^538508+53)/9 538508 Rytis Slatkevicius 01/2023 293 2^1787167+71963 537991 Enzo Doria 12/2018 294 (7^636043-5^636043)/2 537519 Jon Grantham 08/2023 295 108309^91610+91610^108309 537424 Ryan Propper 10/2023 296 (12^495953+1)/13 535223 Paul Bourdelais 11/2018 297 2^1774781+30197 534263 Enzo Doria 08/2024 298 2^1773644+72511 533921 Enzo Doria 10/2018 299 (92^271639-1)/91 533440 Paul Bourdelais 02/2022 300 2^1771408+223201 533247 Enzo Doria 07/2024 301 2^1770613+212597 533008 Enzo Doria 10/2023 302 (11559^131072+1)/2 532535 Serge Batalov 04/2018 303 (85^275881-1)/84 532289 Paul Bourdelais 02/2022 304 2^1767579+213683 532095 Enzo Doria 10/2023 305 2^1767218+25249 531986 Enzo Doria 02/2024 306 2^1762004-3 530417 Paul Bourdelais 04/2020 307 2^1754760+217465 528236 Enzo Doria 01/2024 308 2^1753261+25367 527785 Enzo Doria 11/2023 309 105006^105006-133^133 527258 Sergey Batalov 05/2024 310 2^1750727+213683 527022 Enzo Doria 10/2023 311 2^1750208+218371 526866 Enzo Doria 01/2024 312 2^1743981+28997 524991 Enzo Doria 03/2024 313 2^1737680+23161 523094 Enzo Doria 01/2024 314 (73^280697+1)/74 523028 Paul Bourdelais 02/2022 315 2^1737207+218153 522952 Enzo Doria 05/2024 316 (21^394579+1)/22 521719 Paul Bourdelais 10/2018 317 2^1730246+384439 520856 Enzo Doria 09/2017 318 (55^299087+1)/56 520519 Paul Bourdelais 02/2022 319 5^744171-3^744171-1 520154 Jon Grantham 08/2023 320 2^1727856+31951 520137 Enzo Doria 04/2024 321 (18^414269-1)/17 520020 Paul Bourdelais 12/2014 322 2^1726522+30859 519735 Enzo Doria 06/2024 323 2^1717949+30077 517155 Enzo Doria 08/2024 324 2^1717612+31891 517053 Enzo Doria 04/2024 325 (144171^100489-1)/(144171^317-1) 516776 Ryan Propper 11/2023 326 2^1714462+217465 516105 Enzo Doria 01/2024 327 2^1714021+29777 515972 Enzo Doria 03/2024 328 2^1713855+220703 515922 Enzo Doria 03/2024 329 2^1712979+222143 515659 Enzo Doria 05/2024 330 20^396120-3 515365 Paul Bourdelais 01/2021 331 (136102^100489-1)/(136102^317-1) 514270 Ryan Propper 11/2023 332 (7^608347-5^608347)/2 514113 Jon Grantham 08/2023 333 (62^286483+1)/63 513488 Paul Bourdelais 02/2022 334 (20^393257+1)/21 511638 Paul Bourdelais 12/2014 335 2^1698083+24743 511174 Enzo Doria 11/2023 336 2^1696453+219257 510684 Enzo Doria 06/2024 337 (124869^100489-1)/(124869^317-1) 510523 Ryan Propper 11/2023 338 (124292^100489-1)/(124292^317-1) 510321 Ryan Propper 11/2023 339 10^509546+3 509547 Paul Bourdelais 01/2021 340 101876^99207+99207^101876 509028 Gabor Levai 08/2023 341 2^1690434+213589 508872 Enzo Doria 12/2023 342 2^1688450+221989 508275 Enzo Doria 07/2024 343 2^1688111+217313 508173 Enzo Doria 04/2024 344 (118270^100489-1)/(118270^317-1) 508160 Ryan Propper 11/2023 345 105196^67205+67205^105196 507824 Miklos Levai 09/2023 346 2^1686452+220681 507673 Enzo Doria 04/2024 347 2^1685708+27781 507449 Enzo Doria 01/2024 348 (72^273149-1)/71 507327 Paul Bourdelais 02/2022 349 105154^66373+66373^105154 507052 Miklos Levai 09/2023 350 2^1683331+225413 506734 Enzo Doria 09/2024 351 107890^49423+49423^107890 506429 Miklos Levai 02/2022 352 (14^441697-1)/13 506241 Paul Bourdelais 12/2014 353 101645^94522+94522^101645 505739 Gabor Levai 02/2023 354 3^1059503-2^1059503 505512 Mike Oakes 04/2012 355 2^1678670+21529 505331 Enzo Doria 11/2023 356 101542^92885+92885^101542 504456 Gabor Levai 04/2022 357 105273^60238+60238^105273 503192 Miklos Levai 09/2023 358 105098^61113+61113^105098 503014 Miklos Levai 09/2022 359 2^1670703+60293 502932 Enzo Doria 11/2017 360 (2^1669219-2^834610+1)/5 502485 Borys Jaworski 01/2011 361 101311^90816+90816^101311 502317 Gabor Levai 12/2021 362 101643^87368+87368^101643 502254 Gabor Levai 11/2022 363 (161502^96721-1)/(161502^311-1) 502121 Ryan Propper 11/2023 364 101863^84922+84922^101863 502085 Gabor Levai 10/2022 365 2^1666440+212671 501649 Enzo Doria 09/2023 366 100291^100291+172^172 501582 Serge Batalov 04/2024 367 100207^99856+99856^100207 500973 Gabor Levai 11/2021 368 101839^83028+83028^101839 500969 Gabor Levai 11/2022 369 100263^98600+98600^100263 500702 Gabor Levai 09/2021 370 101761^82168+82168^101761 500126 Gabor Levai 03/2022 371 2^1661176+336631 500064 Tony Prest / Never Odd Or Even 09/2019 372 101070^88579+88579^101070 500027 Gabor Levai 01/2022 373 (85^259159-1)/84 500025 Paul Bourdelais 11/2021 374 2^1660973+368139 500003 Tony Prest / Never Odd Or Even 08/2020 375 2^1660964-382425 500000 Tony Prest / Never Odd Or Even 05/2020 376 (87^257689-1)/86 499791 Paul Bourdelais 01/2021 377 (64*10^499210+53)/9 499211 Serge Batalov 03/2015 378 Tau(631^32370) 498503 Nik Lygeros / Olivier Rozier 05/2015 379 29^339887-28^339887 497051 Jean-Louis Charton 05/2019 380 2^1650975+185225 496993 Stefano Morozzi 09/2024 381 2^1650959+198513 496989 Stefano Morozzi 09/2024 382 2^1650942+181575 496984 Stefano Morozzi 09/2024 383 2^1650905+193947 496972 Stefano Morozzi 09/2024 384 2^1650867+192615 496961 Stefano Morozzi 09/2024 385 2^1650819+198315 496947 Stefano Morozzi 07/2024 386 2^1650788+185823 496937 Stefano Morozzi 09/2024 387 2^1650749+185235 496925 Stefano Morozzi 06/2024 388 2^1650695+183141 496909 Stefano Morozzi 04/2024 389 2^1650640+185311 496893 Stefano Morozzi 03/2024 390 2^1650593+187871 496879 Stefano Morozzi 03/2024 391 2^1650538+196863 496862 Stefano Morozzi 03/2024 392 2^1650484+181413 496846 Stefano Morozzi 03/2024 393 2^1650473+193151 496842 Stefano Morozzi 03/2024 394 2^1650443+193613 496833 Stefano Morozzi 01/2024 395 2^1650426+183543 496828 Stefano Morozzi 01/2024 396 2^1650388+189741 496817 Stefano Morozzi 10/2023 397 2^1650267+193743 496780 Stefano Morozzi 09/2023 398 2^1650196+191835 496759 Stefano Morozzi 07/2023 399 2^1650190+185733 496757 Stefano Morozzi 07/2023 400 2^1650141+189525 496742 Stefano Morozzi 07/2023 401 2^1650103+189519 496731 Stefano Morozzi 05/2023 402 2^1648342+215029 496201 Enzo Doria 01/2024 403 (136688^96721-1)/(136688^311-1) 495136 Ryan Propper 11/2023 404 2^1643411+26213 494717 Enzo Doria 03/2024 405 2^1640056+216241 493707 Enzo Doria 02/2024 406 2^1636027+25763 492494 Enzo Doria 01/2024 407 2^1632498+30397 491431 Enzo Doria 08/2024 408 2^1631030+73519 490989 Enzo Doria 08/2023 409 (2^1629469-1)/644908484660139264379223 490496 Gord Palameta 11/2017 410 2^1627834+225529 490027 Enzo Doria 08/2024 411 2^1626709+30407 489689 Enzo Doria 07/2024 412 2^1619885+28229 487634 Enzo Doria 04/2024 413 10^487291+7 487292 Alfred Reich 06/2021 414 2^1617579+1889543 486940 Enzo Doria 09/2017 415 2^1613632+215011 485752 Enzo Doria 11/2023 416 2^1612600+27331 485441 Enzo Doria 03/2024 417 2^1610146+24739 484703 Enzo Doria 11/2023 418 L(2316773) 484177 Serge Batalov 06/2017 419 (57^275669-1)/56 484039 Paul Bourdelais 04/2021 420 2^1601964+215491 482240 Enzo Doria 11/2023 421 2^1599624+20011 481535 Enzo Doria 07/2023 422 2^1599205+27047 481409 Enzo Doria 03/2024 423 2^1599120-5 481384 Stefano Morozzi 12/2022 424 10^480684-3 480684 Paul Bourdelais 01/2021 425 2^1595483+184133 480289 Enzo Doria 07/2017 426 2^1594947+3 480127 Paul Bourdelais 07/2019 427 2^1594129+22697 479881 Enzo Doria 11/2023 428 2^1593922+213289 479819 Enzo Doria 10/2023 429 2^1592234+26809 479311 Enzo Doria 03/2024 430 (94^241993-1)/93 477482 Paul Bourdelais 09/2020 431 2^1585195+1888373 477192 Enzo Doria 08/2017 432 (33^313553+1)/34 476134 Paul Bourdelais 02/2021 433 2^1581306+220309 476021 Enzo Doria 03/2024 434 2^1578654+215029 475223 Enzo Doria 01/2024 435 (84615^96721-1)/(84615^311-1) 475056 Ryan Propper 11/2023 436 3^994536+16 474515 Robert Price 10/2020 437 2^1575391+71483 474240 Enzo Doria 04/2018 438 (2^1572882+5)/3 473485 Serge Batalov 08/2015 439 (6^608099-1)/5 473193 Paul Bourdelais 05/2010 440 2^1569708+20371 472530 Enzo Doria 09/2023 441 2^1569375+29153 472429 Enzo Doria 05/2024 442 3^989124+16 471933 Robert Price 10/2020 443 2^1567006+1888099 471716 Enzo Doria 05/2017 444 2^1563067+1889813 470531 Enzo Doria 08/2017 445 2^1562428+215851 470338 Enzo Doria 02/2024 446 2^1556730+222829 468623 Enzo Doria 07/2024 447 2^1551415+215813 467023 Enzo Doria 02/2024 448 2^1551411+212933 467022 Enzo Doria 09/2023 449 2^1549797+60197 466536 Enzo Doria 02/2018 450 2^1549030+1887619 466305 Enzo Doria 05/2017 451 416^177481-415^177481 464840 Jean-Louis Charton 12/2016 452 (78^245183-1)/77 463908 Paul Bourdelais 02/2021 453 2^1540117+31907 463622 Enzo Doria 04/2024 454 2^1537058+29839 462701 Enzo Doria 07/2024 455 2^1534770+20809 462012 Enzo Doria 08/2023 456 2^1531286+24799 460964 Enzo Doria 11/2023 457 10^459480-11 459480 Mischa Rodermond 04/2023 458 (5^656657-2^656657)/3 458984 Jon Grantham 08/2023 459 2^1522569+71657 458339 Enzo Doria 04/2018 460 (55814^96721-1)/(55814^311-1) 457634 Ryan Propper 11/2023 461 2^1518191+75353 457022 Ben Maloney / Five or Bust 01/2009 462 2^1510915+223463 454831 Enzo Doria 06/2024 463 6^584279-5 454658 Paul Bourdelais 02/2021 464 2^1509037-13 454266 Stefano Morozzi 12/2022 465 (52^264697-1)/51 454220 Paul Bourdelais 10/2021 466 2^1507169+29027 453704 Enzo Doria 05/2024 467 2^1506029+1890167 453360 Enzo Doria 02/2018 468 2^1504232+26101 452819 Enzo Doria 01/2024 469 2^1498015+219113 450948 Enzo Doria 03/2024 470 2^1497532+220471 450803 Enzo Doria 04/2024 471 2^1497369+216977 450753 Enzo Doria 01/2024 472 (34^294277+1)/35 450678 Paul Bourdelais 06/2018 473 2^1495434+1890439 450171 Enzo Doria 12/2017 474 2^1494634+7 449930 Stefano Morozzi 10/2022 475 2^1493170+784129 449489 Enzo Doria 08/2017 476 2^1489873+1888277 448497 Enzo Doria 06/2017 477 2^1487389+32417 447749 Enzo Doria 06/2024 478 2^1485471+224789 447172 Enzo Doria 09/2024 479 2^1485203+71663 447091 Enzo Doria 09/2023 480 2^1484671+1888463 446931 Enzo Doria 06/2017 481 2^1483112+23961 446462 Enzo Doria 12/2023 482 2^1482867+1886783 446388 Enzo Doria 04/2017 483 2^1482148+284011 446172 Enzo Doria 04/2017 484 2^1481363+215843 445935 Enzo Doria 12/2023 485 2^1480415+217643 445650 Enzo Doria 02/2024 486 2^1479356+1888291 445331 Enzo Doria 06/2017 487 (157742^85849-1)/(157742^293-1) 444716 Ryan Propper 11/2023 488 2^1476810+23299 444565 Enzo Doria 12/2023 489 2^1473184+212671 443473 Enzo Doria 09/2023 490 2^1466432+20371 441441 Enzo Doria 08/2023 491 14^384558+3 440753 Paul Bourdelais 01/2021 492 2^1463913+219047 440682 Enzo Doria 04/2024 493 2^1461244+784531 439879 Enzo Doria 10/2017 494 2^1461058+34429 439823 Enzo Doria 08/2024 495 2^1459599+215813 439384 Enzo Doria 01/2024 496 2^1457449+25757 438736 Enzo Doria 12/2023 497 3^919094+5*2^919094 438520 Jon Grantham 08/2023 498 2^1456277+28229 438384 Enzo Doria 03/2024 499 2^1455129+218027 438038 Enzo Doria 01/2024 500 2^1454061+216977 437716 Enzo Doria 01/2024

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 12 2024 08:27 (Time in France)

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