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
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 8251 | (2^350399+3618)/2 | 105481 | Stefano Morozzi | 09/2020 |
| 8252 | (2^350379+1010)/2 | 105475 | Stefano Morozzi | 09/2020 |
| 8253 | 2^350356+24241 | 105468 | Enzo Doria | 10/2023 |
| 8254 | 25233^15118+15118^25233 | 105462 | Hans Havermann | 09/2020 |
| 8255 | 26261^10366+10366^26261 | 105454 | Hans Havermann | 09/2020 |
| 8256 | 2^350307-110329 | 105453 | Enzo Doria | 05/2014 |
| 8257 | 2^350253-20365 | 105437 | Enzo Doria | 06/2013 |
| 8258 | (3*29^72089-1075)/4 | 105423 | Curtis Bright | 05/2015 |
| 8259 | (2^350187+2658)/2 | 105417 | Stefano Morozzi | 09/2020 |
| 8260 | 4*10^105415-69 | 105416 | Robert Price | 01/2022 |
| 8261 | 21^79725-22 | 105414 | Anonymous | 09/2024 |
| 8262 | (22*10^105407+179)/3 | 105408 | Robert Price | 02/2022 |
| 8263 | 2^350139-109009 | 105403 | Enzo Doria | 04/2014 |
| 8264 | (2^350129+3026)/2 | 105400 | Stefano Morozzi | 09/2020 |
| 8265 | (2^350097+2070)/2 | 105390 | Stefano Morozzi | 09/2020 |
| 8266 | 3*5^150763+4 | 105380 | Lelio R Paula | 11/2014 |
| 8267 | 12^97643+91 | 105375 | Lelio R Paula | 02/2017 |
| 8268 | 6*5^150744-7 | 105367 | Lelio R Paula | 11/2014 |
| 8269 | (2^350018+2074)/2 | 105366 | Stefano Morozzi | 09/2020 |
| 8270 | 4*10^105364-39 | 105365 | Robert Price | 09/2020 |
| 8271 | Phi(156135,-5#) | 105361 | Henri Lifchitz | 12/2025 |
| 8274 | 2^349996-112169 | 105360 | Enzo Doria | 06/2014 |
| 8273 | (2^349997+3702)/2 | 105360 | Stefano Morozzi | 09/2020 |
| 8272 | (29^72047+4^72047)/33 | 105360 | Robert Price | 06/2026 |
| 8275 | (418*10^105343+23)/9 | 105345 | Robert Price | 02/2020 |
| 8276 | 25490^13563+13563^25490 | 105334 | Hans Havermann | 10/2020 |
| 8277 | (5^504004)%F(504004) | 105330 | Henri Lifchitz | 06/2025 |
| 8278 | 11^101142-1080 | 105329 | Enzo Doria | 12/2012 |
| 8279 | (68*10^105320-41)/9 | 105321 | Robert Price | 10/2013 |
| 8280 | 24800^17649+17649^24800 | 105319 | Hans Havermann | 09/2020 |
| 8281 | 3^220712-9934 | 105307 | Enzo Doria | 05/2014 |
| 8282 | 7*10^105296+9 | 105297 | Robert Price | 09/2015 |
| 8283 | 89*10^105284-7 | 105286 | Robert Price | 04/2020 |
| 8284 | 2^349739+1873373 | 105282 | Enzo Doria | 06/2016 |
| 8285 | 7^124574+24 | 105278 | Lelio R Paula | 11/2016 |
| 8286 | 2^349708-20957 | 105273 | Enzo Doria | 06/2013 |
| 8287 | 34115^1218+1218^34115 | 105267 | Hans Havermann | 09/2020 |
| 8288 | 24029^24029-24020^24020 | 105265 | Henri Lifchitz | 09/2024 |
| 8289 | 2^349649-20469 | 105255 | Enzo Doria | 06/2013 |
| 8290 | 2^349607-20109 | 105243 | Enzo Doria | 06/2013 |
| 8291 | (85*10^105242+473)/9 | 105243 | Robert Price | 01/2020 |
| 8292 | 2^349594-19085 | 105239 | Enzo Doria | 05/2013 |
| 8293 | 2^349530+1874479 | 105220 | Enzo Doria | 06/2016 |
| 8294 | (3^220528+8)/8081 | 105215 | Lelio R Paula | 12/2013 |
| 8295 | (106*10^105199+17)/3 | 105201 | Robert Price | 04/2021 |
| 8296 | (2^349452+3570)/2 | 105196 | Stefano Morozzi | 09/2020 |
| 8297 | 3^220464-112852 | 105189 | Enzo Doria | 07/2014 |
| 8298 | 2^349419-17349 | 105186 | Enzo Doria | 05/2013 |
| 8299 | 2^349400-2579 | 105180 | Yves Minet | 07/2014 |
| 8300 | 8*5^150471+3 | 105176 | Lelio R Paula | 11/2014 |
| 8301 | (2^349359+2298)/2 | 105168 | Stefano Morozzi | 02/2021 |
| 8302 | 655^37342+37342^655 | 105165 | Norbert Schneider | 08/2018 |
| 8303 | 13^94403+94 | 105160 | Lelio R Paula | 12/2016 |
| 8304 | 349315*2^349315+3 | 105160 | Anonymous | 09/2025 |
| 8305 | 2^349301-112309 | 105151 | Enzo Doria | 06/2014 |
| 8306 | 30291^2960+2960^30291 | 105149 | Hans Havermann | 09/2020 |
| 8307 | Phi(269776,7) | 105144 | Henri Lifchitz | 02/2026 |
| 8308 | 27350^6981+6981^27350 | 105132 | Hans Havermann | 09/2020 |
| 8310 | 9*2^349220+5 | 105127 | Lelio R Paula | 09/2014 |
| 8309 | (2^349225+3122)/2 | 105127 | Stefano Morozzi | 09/2020 |
| 8311 | 7*3^220317+8 | 105119 | Lelio R Paula | 09/2014 |
| 8312 | 7^124386+88 | 105119 | Lelio R Paula | 11/2016 |
| 8313 | (2^349197+570)/2 | 105119 | Stefano Morozzi | 09/2020 |
| 8314 | 2^349171-19657 | 105111 | Enzo Doria | 06/2013 |
| 8315 | (2^349115+590)/2 | 105094 | Stefano Morozzi | 09/2020 |
| 8316 | (2^(6*58185+1)-5)/3 | 105093 | Kevin Acres | 11/2013 |
| 8317 | (2^349111-5)/3 | 105093 | Lelio R Paula | 12/2013 |
| 8318 | 675^37142+37142^675 | 105087 | Norbert Schneider | 08/2018 |
| 8319 | 2^348981-2797573 | 105054 | Enzo Doria | 04/2016 |
| 8320 | (445^39667+1)/446 | 105050 | Jinyuan Wang | 05/2024 |
| 8321 | 2^348869-6555 | 105021 | Lelio R Paula | 01/2017 |
| 8322 | 10^105003-17319 | 105003 | Alfred Reich | 08/2024 |
| 8323 | 5^150217+78 | 104998 | Lelio R Paula | 11/2016 |
| 8324 | (88*10^104989-1)/3 | 104991 | Robert Price | 04/2020 |
| 8325 | (28*10^104972+149)/3 | 104973 | Robert Price | 12/2019 |
| 8326 | 24927^16262+16262^24927 | 104972 | Hans Havermann | 10/2020 |
| 8327 | 2^348703-113005 | 104971 | Enzo Doria | 06/2014 |
| 8328 | (191*10^104956-17)/3 | 104958 | Robert Price | 11/2021 |
| 8329 | 2^348612-809 | 104943 | Yves Minet | 05/2013 |
| 8330 | (73*10^104942-1)/9 | 104943 | Robert Price | 01/2015 |
| 8331 | (29^71761-5^71761)/24 | 104942 | Robert Price | 03/2026 |
| 8332 | 2^348583-350407 | 104934 | Enzo Doria | 06/2015 |
| 8333 | 2^348531-949 | 104919 | Yves Minet | 05/2012 |
| 8334 | 20^80636-59 | 104910 | Lelio R Paula | 12/2016 |
| 8335 | 8*10^104893-13 | 104894 | Robert Price | 08/2019 |
| 8337 | 2^348437+35 | 104890 | Lelio R Paula | 09/2011 |
| 8336 | 25208^14487+14487^25208 | 104890 | Hans Havermann | 09/2020 |
| 8338 | 906^35468+905 | 104884 | Alfred Reich | 06/2026 |
| 8339 | 2^348348+135 | 104864 | Lelio R Paula | 09/2011 |
| 8340 | (29*10^104858+349)/9 | 104859 | Robert Price | 06/2021 |
| 8341 | 6*10^104852-31 | 104853 | Robert Price | 07/2020 |
| 8343 | (2^348284+9)/25 | 104843 | Lelio R Paula | 12/2013 |
| 8342 | 75^55914-74 | 104843 | Norbert Schneider | 01/2015 |
| 8344 | 2^348268+255255 | 104840 | Lelio R Paula | 01/2017 |
| 8345 | 35540^891+891^35540 | 104839 | Hans Havermann | 09/2020 |
| 8346 | 5^149985-52 | 104836 | Lelio R Paula | 11/2016 |
| 8347 | 2^348224-20249 | 104826 | Enzo Doria | 06/2013 |
| 8348 | (2^348217+2522)/2 | 104824 | Stefano Morozzi | 09/2020 |
| 8349 | 2^348212-20105 | 104823 | Enzo Doria | 06/2013 |
| 8350 | 24647^17898+17898^24647 | 104819 | Hans Havermann | 10/2020 |
| 8351 | 20^80562+19 | 104814 | Lelio R Paula | 12/2016 |
| 8352 | 2*10^104811-87 | 104812 | Robert Price | 04/2018 |
| 8353 | 2^348149-20053 | 104804 | Enzo Doria | 06/2013 |
| 8354 | Phi(341301,3) | 104792 | Henri Lifchitz | 12/2025 |
| 8355 | 2^348095-171 | 104788 | Lelio R Paula | 09/2011 |
| 8356 | 25383^13412+13412^25383 | 104769 | Hans Havermann | 09/2020 |
| 8357 | 2^348003-20377 | 104760 | Enzo Doria | 06/2013 |
| 8358 | 26^74036-27 | 104759 | Anonymous | 09/2024 |
| 8360 | 2^347994-741 | 104757 | Lelio R Paula | 12/2016 |
| 8359 | (2^347993+2234)/2 | 104757 | Stefano Morozzi | 01/2021 |
| 8361 | (2^347990+790)/2 | 104756 | Stefano Morozzi | 09/2020 |
| 8362 | 25137^14702+14702^25137 | 104756 | Hans Havermann | 09/2020 |
| 8363 | (13*2^347972-1)/282309 | 104746 | Lelio R Paula | 03/2014 |
| 8364 | 12883^25484-25484^12883 | 104740 | Norbert Schneider | 08/2022 |
| 8365 | 2^347910-109937 | 104732 | Enzo Doria | 04/2014 |
| 8366 | (88*10^104709-637)/9 | 104710 | Robert Price | 11/2020 |
| 8367 | (13*10^104702+71)/3 | 104703 | Robert Price | 06/2021 |
| 8368 | 5^149794+28 | 104702 | Lelio R Paula | 11/2016 |
| 8369 | 105^51800-2 | 104698 | Lelio R Paula | 10/2017 |
| 8370 | (16^86939+3^86939)/19 | 104684 | Robert Price | 06/2013 |
| 8371 | (15^89009-1)/14 | 104682 | Paul Bourdelais | 03/2010 |
| 8372 | 2^347731-18609 | 104678 | Enzo Doria | 05/2013 |
| 8373 | 4*6^134519+7 | 104677 | Lelio R Paula | 11/2014 |
| 8374 | (34*10^104672-259)/9 | 104673 | Robert Price | 12/2021 |
| 8375 | 25321^13588+13588^25321 | 104656 | Hans Havermann | 09/2020 |
| 8376 | 2^347625+5367 | 104646 | Riley Fisher | 04/2023 |
| 8377 | 2^347612-18545 | 104642 | Enzo Doria | 05/2013 |
| 8378 | 6^134465+95 | 104635 | Lelio R Paula | 11/2016 |
| 8379 | (2^347588+3718)/2 | 104635 | Stefano Morozzi | 09/2020 |
| 8380 | (166*10^104633-7)/3 | 104635 | Robert Price | 11/2020 |
| 8381 | V(750972)/15019441 | 104621 | Serge Batalov | 07/2024 |
| 8382 | 2^347517-17301 | 104614 | Enzo Doria | 05/2013 |
| 8383 | (2^347493+3186)/2 | 104606 | Stefano Morozzi | 09/2020 |
| 8384 | (2^347490+2574)/2 | 104605 | Stefano Morozzi | 09/2020 |
| 8385 | 3^219222-310 | 104596 | Lelio R Paula | 11/2016 |
| 8386 | 25993^10554+10554^25993 | 104581 | Hans Havermann | 09/2020 |
| 8387 | (15*2^347399-1)/13 | 104578 | Lelio R Paula | 03/2014 |
| 8388 | 2^347372-17853 | 104570 | Enzo Doria | 05/2013 |
| 8389 | 2^347314+99 | 104552 | Lelio R Paula | 09/2011 |
| 8390 | 2^347300-22233 | 104548 | Enzo Doria | 06/2013 |
| 8391 | 2^347287-19845 | 104544 | Enzo Doria | 06/2013 |
| 8392 | 2^347258-231191 | 104536 | Harrison Mesh | 06/2022 |
| 8393 | (31*2^347254-1)/891 | 104533 | Lelio R Paula | 03/2014 |
| 8394 | 5*F(250091)*(F(250091)-1)+1 | 104532 | Serge Batalov | 04/2015 |
| 8395 | 7*2^347239-3 | 104531 | Lelio R Paula | 09/2014 |
| 8396 | (3^219098-8)/514147439969 | 104525 | Lelio R Paula | 12/2013 |
| 8397 | 5*3^219047+8 | 104513 | Lelio R Paula | 09/2014 |
| 8398 | 2^347148-109073 | 104502 | Enzo Doria | 04/2014 |
| 8399 | 2^347129-20145 | 104497 | Enzo Doria | 06/2013 |
| 8400 | 4*10^104461-57 | 104462 | Robert Price | 10/2018 |
| 8401 | 2^346999+198831 | 104458 | Stefano Morozzi | 11/2024 |
| 8402 | 2^346996+166273 | 104457 | Stefano Morozzi | 11/2024 |
| 8403 | 2^346997+105755 | 104457 | Stefano Morozzi | 11/2024 |
| 8404 | 2^346997+115259 | 104457 | Stefano Morozzi | 11/2024 |
| 8405 | 2^346992+97515 | 104456 | Stefano Morozzi | 11/2024 |
| 8406 | 2^346992+169593 | 104456 | Stefano Morozzi | 11/2024 |
| 8407 | 2^346994+182215 | 104456 | Stefano Morozzi | 11/2024 |
| 8408 | 2^346994+187933 | 104456 | Stefano Morozzi | 11/2024 |
| 8409 | (7*10^(2*52227+1)+9*10^52227-7)/9 | 104455 | Robert Price | 10/2023 |
| 8412 | (2^346989+590)/2 | 104454 | Stefano Morozzi | 09/2020 |
| 8410 | 2^346988+295 | 104454 | Stefano Morozzi | 11/2024 |
| 8411 | 2^346988+47241 | 104454 | Stefano Morozzi | 11/2024 |
| 8413 | 2^346983+4203 | 104453 | Stefano Morozzi | 11/2024 |
| 8414 | 2^346983+119259 | 104453 | Stefano Morozzi | 11/2024 |
| 8415 | 2^346983+47729 | 104453 | Stefano Morozzi | 11/2024 |
| 8416 | 2^346985+124437 | 104453 | Stefano Morozzi | 11/2024 |
| 8417 | 2^346979+72443 | 104452 | Stefano Morozzi | 11/2024 |
| 8418 | 2^346980+167731 | 104452 | Stefano Morozzi | 11/2024 |
| 8419 | 2^346978+64933 | 104451 | Stefano Morozzi | 11/2024 |
| 8420 | 2^346974+105865 | 104450 | Stefano Morozzi | 11/2024 |
| 8421 | 2^346972+95343 | 104449 | Stefano Morozzi | 11/2024 |
| 8422 | 2^346966+63519 | 104448 | Stefano Morozzi | 11/2024 |
| 8423 | 2^346963+42825 | 104447 | Stefano Morozzi | 11/2024 |
| 8424 | 2^346963+140153 | 104447 | Stefano Morozzi | 11/2024 |
| 8425 | 2^346965+144537 | 104447 | Stefano Morozzi | 11/2024 |
| 8426 | 2^346962+128917 | 104446 | Stefano Morozzi | 11/2024 |
| 8427 | 2^346956+110455 | 104445 | Stefano Morozzi | 11/2024 |
| 8428 | 2^346956+72711 | 104445 | Stefano Morozzi | 11/2024 |
| 8429 | 2^346954+178093 | 104444 | Stefano Morozzi | 11/2024 |
| 8430 | 2^346955+46205 | 104444 | Stefano Morozzi | 11/2024 |
| 8431 | 2^346954+186043 | 104444 | Stefano Morozzi | 11/2024 |
| 8432 | 2^346949+140865 | 104443 | Stefano Morozzi | 11/2024 |
| 8433 | 2^346950+79857 | 104443 | Stefano Morozzi | 11/2024 |
| 8434 | 2^346951+161939 | 104443 | Stefano Morozzi | 11/2024 |
| 8435 | 2^346950+143647 | 104443 | Stefano Morozzi | 11/2024 |
| 8436 | 2^346950+103369 | 104443 | Stefano Morozzi | 11/2024 |
| 8437 | 2^346952+128895 | 104443 | Stefano Morozzi | 11/2024 |
| 8438 | 2^346946+106593 | 104442 | Stefano Morozzi | 11/2024 |
| 8439 | 2^346947+63431 | 104442 | Stefano Morozzi | 11/2024 |
| 8440 | 2^346947+75735 | 104442 | Stefano Morozzi | 11/2024 |
| 8441 | 2^346948+135547 | 104442 | Stefano Morozzi | 11/2024 |
| 8442 | 2^346944+20295 | 104441 | Stefano Morozzi | 11/2024 |
| 8443 | 2^346944+93783 | 104441 | Stefano Morozzi | 11/2024 |
| 8444 | 2^346939+116879 | 104440 | Stefano Morozzi | 11/2024 |
| 8445 | 2^346939+138489 | 104440 | Stefano Morozzi | 11/2024 |
| 8446 | 2^346940+40675 | 104440 | Stefano Morozzi | 11/2024 |
| 8447 | 2^346942+108495 | 104440 | Stefano Morozzi | 11/2024 |
| 8448 | 2^346942+137535 | 104440 | Stefano Morozzi | 11/2024 |
| 8449 | 2^346936+78235 | 104439 | Stefano Morozzi | 11/2024 |
| 8450 | 2^346936+156271 | 104439 | Stefano Morozzi | 11/2024 |
| 8451 | 2^346937+180909 | 104439 | Stefano Morozzi | 11/2024 |
| 8452 | 2^346938+159885 | 104439 | Stefano Morozzi | 11/2024 |
| 8453 | 2^346933+7865 | 104438 | Stefano Morozzi | 11/2024 |
| 8454 | 2^346933+119759 | 104438 | Stefano Morozzi | 11/2024 |
| 8455 | 2^346934+187797 | 104438 | Stefano Morozzi | 11/2024 |
| 8456 | 2^346935+198629 | 104438 | Stefano Morozzi | 11/2024 |
| 8457 | 2^346929+85449 | 104437 | Stefano Morozzi | 11/2024 |
| 8458 | 2^346929+155487 | 104437 | Stefano Morozzi | 11/2024 |
| 8459 | 2^346931+60719 | 104437 | Stefano Morozzi | 11/2024 |
| 8460 | 2^346932+49215 | 104437 | Stefano Morozzi | 11/2024 |
| 8461 | 2^346927+65709 | 104436 | Stefano Morozzi | 11/2024 |
| 8462 | 2^346928+126963 | 104436 | Stefano Morozzi | 11/2024 |
| 8463 | 2^346928+143721 | 104436 | Stefano Morozzi | 11/2024 |
| 8468 | 2^346923-19585 | 104435 | Enzo Doria | 05/2013 |
| 8464 | 2^346923+73001 | 104435 | Stefano Morozzi | 11/2024 |
| 8465 | 2^346924+28671 | 104435 | Stefano Morozzi | 11/2024 |
| 8466 | 2^346924+58657 | 104435 | Stefano Morozzi | 11/2024 |
| 8467 | 2^346924+173475 | 104435 | Stefano Morozzi | 11/2024 |
| 8469 | 2^346921+59357 | 104434 | Stefano Morozzi | 11/2024 |
| 8470 | 2^346916+18183 | 104433 | Stefano Morozzi | 11/2024 |
| 8471 | 2^346914+44625 | 104432 | Stefano Morozzi | 11/2024 |
| 8472 | 2^346912+26343 | 104431 | Stefano Morozzi | 11/2024 |
| 8473 | 2^346912+42367 | 104431 | Stefano Morozzi | 11/2024 |
| 8474 | 2^346908+123705 | 104430 | Stefano Morozzi | 11/2024 |
| 8475 | 2^346899+194015 | 104428 | Stefano Morozzi | 11/2024 |
| 8476 | 2^346900+63393 | 104428 | Stefano Morozzi | 11/2024 |
| 8477 | 2^346901+106215 | 104428 | Stefano Morozzi | 11/2024 |
| 8478 | 2^346901+119309 | 104428 | Stefano Morozzi | 11/2024 |
| 8479 | 2^346902+62587 | 104428 | Stefano Morozzi | 11/2024 |
| 8480 | 2^346897+120207 | 104427 | Stefano Morozzi | 11/2024 |
| 8481 | 2^346897+121107 | 104427 | Stefano Morozzi | 11/2024 |
| 8482 | 2^346897+134289 | 104427 | Stefano Morozzi | 11/2024 |
| 8483 | 2^346898+57429 | 104427 | Stefano Morozzi | 11/2024 |
| 8484 | 2^346898+162267 | 104427 | Stefano Morozzi | 11/2024 |
| 8485 | 2^346890+148989 | 104425 | Stefano Morozzi | 11/2024 |
| 8486 | 2^346891+46313 | 104425 | Stefano Morozzi | 11/2024 |
| 8487 | 2^346892+121191 | 104425 | Stefano Morozzi | 11/2024 |
| 8488 | 2^346888+39211 | 104424 | Stefano Morozzi | 11/2024 |
| 8489 | 2^346883+100949 | 104423 | Stefano Morozzi | 11/2024 |
| 8490 | 2^346883+138341 | 104423 | Stefano Morozzi | 11/2024 |
| 8491 | 2^346885+78357 | 104423 | Stefano Morozzi | 11/2024 |
| 8492 | 2^346882+167169 | 104422 | Stefano Morozzi | 11/2024 |
| 8493 | 2^346877+43587 | 104421 | Stefano Morozzi | 11/2024 |
| 8494 | 2^346879+69983 | 104421 | Stefano Morozzi | 11/2024 |
| 8495 | 2^346875+24885 | 104420 | Stefano Morozzi | 11/2024 |
| 8496 | 2^346875+131835 | 104420 | Stefano Morozzi | 11/2024 |
| 8497 | 2^346875+161301 | 104420 | Stefano Morozzi | 11/2024 |
| 8498 | 2^346871+85491 | 104419 | Stefano Morozzi | 11/2024 |
| 8499 | 2^346866+135849 | 104418 | Stefano Morozzi | 11/2024 |
| 8500 | 2^346868+445 | 104418 | Stefano Morozzi | 11/2024 |
