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
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
8251 | 10^99434+155571 | 99435 | Patrick De Geest | 04/2020 |
8252 | 10^99434-123456789 | 99434 | Robert Price | 02/2020 |
8253 | 10^99434-191237 | 99434 | Patrick De Geest | 04/2020 |
8254 | 46^59791-45^59791 | 99418 | Jean-Louis Charton | 01/2013 |
8255 | 23839^14802+14802^23839 | 99417 | Hans Havermann | 02/2018 |
8256 | (2*10^99408+529)/9 | 99408 | Robert Price | 01/2017 |
8257 | (2^330216+3510)/2 | 99405 | Stefano Morozzi | 09/2020 |
8258 | 53^57646-2 | 99398 | Lelio R Paula | 09/2013 |
8259 | 2^330165+1870025 | 99390 | Enzo Doria | 05/2016 |
8260 | 7*10^99383+97 | 99384 | Robert Price | 09/2021 |
8261 | 2^330142-155 | 99383 | Lelio R Paula | 12/2012 |
8262 | 2^330088-115259 | 99367 | Enzo Doria | 06/2015 |
8263 | 24216^12671+12671^24216 | 99354 | Hans Havermann | 01/2018 |
8264 | Phi(200548,10)/3208769 | 99354 | Makoto Kamada | 04/2019 |
8265 | (746*10^99303+1)/9 | 99305 | Robert Price | 02/2017 |
8266 | 3^208107+40 | 99293 | Lelio R Paula | 08/2016 |
8267 | (3939^27617-1)/3938 | 99291 | Serge Batalov | 06/2022 |
8268 | (5*2^329833-1)/369 | 99288 | Lelio R Paula | 02/2014 |
8269 | 8*3^208093+5 | 99287 | Lelio R Paula | 08/2014 |
8270 | 5^142043+56 | 99284 | Lelio R Paula | 08/2016 |
8271 | (13*10^99282-157)/9 | 99283 | Robert Price | 05/2021 |
8272 | (10^99284+7)/53/67 | 99281 | Alfred Reich | 06/2021 |
8273 | 22*10^99275+7 | 99277 | Robert Price | 04/2016 |
8274 | 2^329778+1876189 | 99274 | Enzo Doria | 07/2016 |
8275 | (6580^25997-1)/6579 | 99259 | Serge Batalov | 06/2022 |
8276 | (2249^29611-1)/2248 | 99253 | Serge Batalov | 06/2022 |
8277 | (10^99239-13)/3 | 99239 | Robert Price | 02/2017 |
8278 | (1199^32233-1)/1198 | 99237 | Serge Batalov | 06/2022 |
8280 | 3^207987+62 | 99236 | Lelio R Paula | 08/2016 |
8279 | (62*10^99235+91)/9 | 99236 | Robert Price | 07/2021 |
8281 | 2^329638+49 | 99231 | Lelio R Paula | 12/2012 |
8282 | 7^117413-18 | 99226 | Lelio R Paula | 08/2016 |
8283 | 2^329586-458903 | 99216 | Enzo Doria | 04/2015 |
8284 | (6290^26119-1)/6289 | 99214 | Serge Batalov | 06/2022 |
8286 | 2^329553+101 | 99206 | Lelio R Paula | 12/2012 |
8285 | (21297^22921-1)/21296 | 99206 | Serge Batalov | 06/2022 |
8287 | 2^329551-112897 | 99205 | Enzo Doria | 06/2014 |
8288 | (3^207925+7)/50 | 99204 | Lelio R Paula | 09/2013 |
8289 | 6^127458-17993 | 99182 | Enzo Doria | 03/2013 |
8290 | 27197^4428+4428^27197 | 99166 | Hans Havermann | 10/2017 |
8291 | (46*10^99143-1)/9 | 99144 | Robert Price | 12/2014 |
8292 | (64*10^99135+161)/9 | 99136 | Robert Price | 08/2022 |
8293 | 7*10^99133+69 | 99134 | Robert Price | 10/2017 |
8294 | (21701^22861-1)/21700 | 99132 | Serge Batalov | 06/2022 |
8295 | 18^78968-3065 | 99127 | Enzo Doria | 03/2013 |
8297 | 25927^6654+6654^25927 | 99122 | Hans Havermann | 10/2017 |
8296 | 87915!4+16 | 99122 | Robert Price | 09/2019 |
8298 | 2^329259+189 | 99117 | Lelio R Paula | 12/2012 |
8299 | 8*10^99113+39 | 99114 | Robert Price | 01/2017 |
8300 | 6^127364+77 | 99109 | Lelio R Paula | 08/2016 |
8301 | (82*10^99103+143)/9 | 99104 | Robert Price | 06/2021 |
8302 | (11414^24421-1)/11413 | 99083 | Serge Batalov | 06/2022 |
8303 | (2^329135+1110)/2 | 99080 | Stefano Morozzi | 09/2020 |
8304 | (22089^22807-1)/22088 | 99074 | Serge Batalov | 06/2022 |
8305 | (59*10^99069+391)/9 | 99070 | Robert Price | 03/2021 |
8306 | (797*10^99061-41)/9 | 99063 | Robert Price | 04/2022 |
8307 | 2^329058-287681 | 99057 | Harrison Mesh | 06/2022 |
8308 | 6^127285+13 | 99047 | Lelio R Paula | 08/2016 |
8309 | (228581#+235862)/(2^3*11*71*151) | 99044 | Makoto Morimoto | 10/2017 |
8310 | 2^329007+73283 | 99041 | Enzo Doria | 04/2016 |
8311 | 5*3^207543-8 | 99024 | Lelio R Paula | 08/2014 |
8312 | (2^328930+570)/2 | 99018 | Stefano Morozzi | 09/2020 |
8313 | 2^328885+149 | 99005 | Lelio R Paula | 12/2012 |
8315 | 23392^17075+17075^23392 | 99004 | Hans Havermann | 09/2017 |
8314 | (7424^25579-1)/7423 | 99004 | Serge Batalov | 06/2022 |
8316 | (2^328879-9)/119 | 99001 | Lelio R Paula | 10/2013 |
8317 | 5^141618+54 | 98987 | Lelio R Paula | 08/2016 |
8318 | 8*10^98982+51 | 98983 | Robert Price | 05/2017 |
8319 | (21*2^328809-1)/7709 | 98979 | Lelio R Paula | 03/2014 |
8320 | 2^328794-2797601 | 98977 | Enzo Doria | 04/2016 |
8321 | (88331^20011-1)/88330 | 98972 | Serge Batalov | 06/2022 |
8322 | 6^127176+5 | 98963 | Lelio R Paula | 11/2014 |
8323 | 2*10^98961-21 | 98962 | Robert Price | 09/2020 |
8324 | 24262^11989+11989^24262 | 98960 | Hans Havermann | 09/2017 |
8325 | (60138^20707-1)/60137 | 98958 | Serge Batalov | 06/2022 |
8326 | 2^328700-109709 | 98949 | Enzo Doria | 04/2014 |
8327 | (2^328698+1810)/2 | 98948 | Stefano Morozzi | 01/2021 |
8328 | (1014^32917-1)/1013 | 98947 | Serge Batalov | 06/2022 |
8329 | 87771!4-128 | 98944 | Robert Price | 11/2019 |
8330 | (4576^27031-1)/4575 | 98943 | Serge Batalov | 06/2022 |
8331 | (2^328658+3042)/2 | 98936 | Stefano Morozzi | 09/2020 |
8332 | (1933^30103-1)/1932 | 98923 | Serge Batalov | 06/2022 |
8333 | 46711!2-2^46711 | 98916 | Robert Price | 09/2015 |
8334 | 9*7^117037+4 | 98909 | Lelio R Paula | 11/2014 |
8335 | 127^47012+126 | 98905 | Norbert Schneider | 01/2019 |
8336 | (93826^19891-1)/93825 | 98900 | Serge Batalov | 06/2022 |
8337 | (2^328525+1250)/2 | 98896 | Stefano Morozzi | 09/2020 |
8338 | (10^98890+149)/3 | 98890 | Serge Batalov | 12/2014 |
8339 | 22775^21978+21978^22775 | 98889 | Hans Havermann | 08/2017 |
8340 | 2^328497-216933 | 98888 | Enzo Doria | 05/2014 |
8341 | 2^328487+32769 | 98885 | Lelio R Paula | 08/2016 |
8342 | 3^207250-112358 | 98884 | Enzo Doria | 06/2014 |
8343 | 13^88754-90 | 98867 | Lelio R Paula | 08/2016 |
8344 | 2^328406+709 | 98861 | Lelio R Paula | 02/2013 |
8345 | 2*10^98860-21 | 98861 | Robert Price | 09/2020 |
8346 | (17*2^328413-1)/16173 | 98860 | Lelio R Paula | 03/2014 |
8347 | 7^116976+76 | 98857 | Lelio R Paula | 08/2016 |
8348 | (2^328378+2710)/2 | 98852 | Stefano Morozzi | 09/2020 |
8349 | (25411^22441-1)/25410 | 98849 | Serge Batalov | 06/2022 |
8350 | (18668^23143-1)/18667 | 98842 | Serge Batalov | 06/2022 |
8352 | 2^328335+1155 | 98839 | Lelio R Paula | 08/2016 |
8351 | 2^328333-349003 | 98839 | Harrison Mesh | 06/2022 |
8354 | (3*2^328311+1)/5 | 98832 | Lelio R Paula | 11/2013 |
8353 | 287^40210+40210^287 | 98832 | Norbert Schneider | 11/2014 |
8355 | (2^328284+9)/1325 | 98821 | Lelio R Paula | 10/2013 |
8356 | (21*2^328258+1)/2125 | 98814 | Lelio R Paula | 11/2013 |
8357 | (28623^22171-1)/28622 | 98806 | Serge Batalov | 06/2022 |
8358 | 24746^9825+9825^24746 | 98795 | Hans Havermann | 07/2020 |
8359 | 26620^5143+5143^26620 | 98793 | Hans Havermann | 07/2020 |
8360 | 65^54491+48 | 98788 | Lelio R Paula | 04/2016 |
8361 | 3^207042+98 | 98785 | Lelio R Paula | 08/2016 |
8362 | (2^328121+3110)/2 | 98774 | Stefano Morozzi | 09/2020 |
8363 | 10^98754+73383 | 98755 | Patrick De Geest | 02/2021 |
8366 | 3^206977-112756 | 98754 | Enzo Doria | 07/2014 |
8365 | 10^98754-40000000001 | 98754 | Robert Price | 09/2020 |
8364 | 10^98754-169343 | 98754 | Patrick De Geest | 02/2021 |
8367 | 7^116846-50 | 98747 | Lelio R Paula | 08/2016 |
8368 | (19152^23059-1)/19151 | 98740 | Serge Batalov | 06/2022 |
8369 | 23267^17512+17512^23267 | 98730 | Hans Havermann | 04/2020 |
8370 | 2^327967-28635 | 98728 | Lelio R Paula | 08/2016 |
8371 | 707^34642+34642^707 | 98710 | Norbert Schneider | 12/2017 |
8372 | (10771^24481-1)/10770 | 98710 | Serge Batalov | 06/2022 |
8373 | 6^126850-47 | 98709 | Lelio R Paula | 08/2016 |
8374 | (2^327886+2170)/2 | 98704 | Stefano Morozzi | 09/2020 |
8375 | (22*10^98697+47)/3 | 98698 | Robert Price | 06/2021 |
8376 | 8*6^126830-7 | 98694 | Lelio R Paula | 11/2014 |
8377 | 11^94770-270 | 98693 | Enzo Doria | 08/2012 |
8378 | (2^327846+3250)/2 | 98692 | Stefano Morozzi | 01/2021 |
8379 | 2^327832+43 | 98688 | Lelio R Paula | 12/2012 |
8380 | 2^327795+761 | 98677 | Lelio R Paula | 02/2013 |
8381 | (2^327796+1522)/2 | 98677 | Stefano Morozzi | 09/2020 |
8382 | 10^98669+147411 | 98670 | Patrick De Geest | 11/2016 |
8384 | 10^98669-9^(98669-1) | 98669 | Robert Price | 05/2016 |
8383 | 10^98669-105249 | 98669 | Patrick De Geest | 11/2016 |
8385 | (7911^25309-1)/7910 | 98657 | Serge Batalov | 06/2022 |
8386 | 2^327671-109801 | 98639 | Enzo Doria | 04/2014 |
8387 | 24398^11037+11037^24398 | 98638 | Hans Havermann | 10/2019 |
8388 | 5^141090-14 | 98618 | Lelio R Paula | 08/2016 |
8389 | 20^75799+47 | 98617 | Lelio R Paula | 08/2016 |
8390 | (5452^26393-1)/5451 | 98616 | Serge Batalov | 06/2022 |
8391 | 28101^3226+3226^28101 | 98597 | Hans Havermann | 07/2020 |
8392 | 2^327515-1017 | 98592 | Lelio R Paula | 08/2016 |
8393 | 6^126692+97681 | 98586 | Mike Oakes | 04/2011 |
8394 | 2^327467-741 | 98578 | Lelio R Paula | 08/2016 |
8395 | (2947^28411-1)/2946 | 98566 | Serge Batalov | 06/2022 |
8396 | 22713^21800+21800^22713 | 98540 | Hans Havermann | 05/2020 |
8397 | (2^327329+9)/19 | 98535 | Lelio R Paula | 10/2013 |
8398 | 7^116577-66 | 98519 | Lelio R Paula | 08/2016 |
8399 | (3*2^327250+1)/7 | 98512 | Lelio R Paula | 11/2013 |
8400 | 23220^17479+17479^23220 | 98512 | Hans Havermann | 03/2020 |
8401 | (2^327240+3798)/2 | 98509 | Stefano Morozzi | 02/2021 |
8402 | (28514^22111-1)/28513 | 98502 | Serge Batalov | 06/2022 |
8403 | (19*2^327192+1)/275 | 98494 | Lelio R Paula | 11/2013 |
8404 | 2^327162-66945 | 98486 | Lelio R Paula | 08/2016 |
8405 | 30139^1852+1852^30139 | 98484 | Hans Havermann | 02/2020 |
8406 | 23182^17703+17703^23182 | 98479 | Hans Havermann | 01/2020 |
8407 | 4*10^98472-3 | 98473 | Erik Branger | 11/2013 |
8408 | 26167^5794+5794^26167 | 98466 | Hans Havermann | 01/2020 |
8409 | (6883*2^327047-1)/77 | 98453 | Lelio R Paula | 05/2015 |
8410 | (71*10^98446+1)/9 | 98447 | Serge Batalov | 11/2010 |
8411 | (2009^29803-1)/2008 | 98436 | Serge Batalov | 06/2022 |
8412 | 13^88363+94 | 98432 | Lelio R Paula | 08/2016 |
8413 | 48^58543-47^58543 | 98425 | Jean-Louis Charton | 11/2005 |
8414 | 6^126481+41 | 98422 | Lelio R Paula | 08/2016 |
8415 | 78*10^98413-7 | 98415 | Robert Price | 05/2017 |
8416 | 22634^22263+22263^22634 | 98404 | Hans Havermann | 07/2020 |
8417 | (47*10^98386+241)/9 | 98387 | Robert Price | 06/2022 |
8418 | 7^116416+46 | 98383 | Lelio R Paula | 08/2016 |
8419 | 7^116407-24 | 98376 | Lelio R Paula | 07/2016 |
8420 | 439^37228+37228^439 | 98374 | Norbert Schneider | 08/2018 |
8421 | 2^326782-1860671 | 98372 | Enzo Doria | 03/2016 |
8422 | 17^79948+58 | 98372 | Lelio R Paula | 08/2016 |
8423 | 22499^22602-22602^22499 | 98368 | Norbert Schneider | 08/2020 |
8424 | 3^206143-98 | 98356 | Lelio R Paula | 08/2016 |
8425 | 8*5^140705+7 | 98350 | Lelio R Paula | 11/2014 |
8426 | (2^326632+1662)/2 | 98326 | Stefano Morozzi | 09/2020 |
8427 | (638^35053-1)/637 | 98315 | Serge Batalov | 06/2022 |
8428 | 2^326585+11 | 98312 | Lelio R Paula | 12/2012 |
8429 | 2^326582-459161 | 98311 | Enzo Doria | 05/2015 |
8430 | (1266^31687-1)/1265 | 98304 | Serge Batalov | 06/2022 |
8432 | (2^326548+9)/5 | 98301 | Lelio R Paula | 10/2013 |
8431 | (2^326549+18)/10 | 98301 | Stefano Morozzi | 03/2020 |
8433 | 2^326538+71659 | 98298 | Enzo Doria | 04/2016 |
8434 | (2^326520+2082)/2 | 98293 | Stefano Morozzi | 09/2020 |
8435 | (2^326521+1002)/2 | 98293 | Stefano Morozzi | 09/2020 |
8436 | 15^83575-58 | 98292 | Lelio R Paula | 08/2016 |
8437 | 10^98288+3 | 98289 | Robert Price | 03/2011 |
8438 | 10^98288-117017 | 98288 | Patrick De Geest | 11/2011 |
8439 | (44*10^98284-719)/9 | 98285 | Robert Price | 12/2017 |
8440 | (5985^26021-1)/5984 | 98280 | Serge Batalov | 06/2022 |
8441 | 23466^15419+15419^23466 | 98277 | Hans Havermann | 02/2020 |
8442 | 2^326421-2797573 | 98263 | Enzo Doria | 04/2016 |
8443 | 2^326401+16095 | 98257 | Lelio R Paula | 07/2016 |
8444 | (6494^25771-1)/6493 | 98249 | Serge Batalov | 06/2022 |
8445 | 7^116240-116240^7 | 98235 | Norbert Schneider | 05/2017 |
8446 | 17^79826-78 | 98222 | Lelio R Paula | 08/2016 |
8447 | 2^326268-809 | 98217 | Yves Minet | 04/2011 |
8448 | 22659^21590+21590^22659 | 98210 | Hans Havermann | 10/2019 |
8449 | 22268^22587-22587^22268 | 98202 | Norbert Schneider | 08/2020 |
8450 | (418*10^98199+23)/9 | 98201 | Robert Price | 08/2017 |
8451 | 12*10^98198-7 | 98200 | Robert Price | 11/2017 |
8452 | 15^83496-76 | 98199 | Lelio R Paula | 08/2016 |
8453 | (10223*2^326179+1)/6125 | 98190 | Lelio R Paula | 07/2014 |
8454 | 9*5^140471-4 | 98186 | Lelio R Paula | 11/2014 |
8455 | (35103^21601-1)/35102 | 98180 | Serge Batalov | 06/2022 |
8457 | 22774^20455+20455^22774 | 98175 | Hans Havermann | 07/2020 |
8456 | (4516^26863-1)/4515 | 98175 | Serge Batalov | 06/2022 |
8458 | 2^326069-2383 | 98157 | Yves Minet | 10/2013 |
8459 | (9661^24631-1)/9660 | 98152 | Serge Batalov | 06/2022 |
8460 | (4175^27109-1)/4174 | 98149 | Serge Batalov | 06/2022 |
8461 | (57801^20611-1)/57800 | 98144 | Serge Batalov | 06/2022 |
8462 | 2^325973+1185 | 98128 | Lelio R Paula | 07/2016 |
8463 | (25*2^325949-1)/17 | 98121 | Lelio R Paula | 02/2014 |
8464 | 2^325945-1847269 | 98120 | Enzo Doria | 07/2015 |
8465 | 8*10^98111-67 | 98112 | Robert Price | 10/2017 |
8466 | (2^325902+1138)/2 | 98106 | Stefano Morozzi | 09/2020 |
8467 | (215^42061-1)/214 | 98103 | Serge Batalov | 06/2022 |
8468 | (6775^25609-1)/6774 | 98102 | Serge Batalov | 06/2022 |
8469 | (6718^25633-1)/6717 | 98100 | Serge Batalov | 06/2022 |
8470 | 2^325866+15 | 98096 | Lelio R Paula | 12/2012 |
8471 | 22591^21952+21952^22591 | 98079 | Hans Havermann | 02/2020 |
8472 | 2^325765+1974305 | 98066 | Enzo Doria | 06/2016 |
8473 | 2^325733-58695 | 98056 | Lelio R Paula | 07/2016 |
8474 | (7*10^98055-529)/9 | 98055 | Robert Price | 08/2021 |
8475 | 2^325717-3645 | 98051 | Lelio R Paula | 07/2016 |
8476 | (2^325704+718)/2 | 98047 | Stefano Morozzi | 09/2020 |
8477 | (15679^23371-1)/15678 | 98045 | Serge Batalov | 06/2022 |
8478 | (23342^22441-1)/23341 | 98022 | Serge Batalov | 06/2022 |
8479 | 23968^12293+12293^23968 | 98021 | Hans Havermann | 11/2019 |
8480 | (23*2^325583-1)/21 | 98011 | Lelio R Paula | 02/2014 |
8481 | (7*10^98007-13)/3 | 98008 | Robert Price | 06/2016 |
8482 | (2^325544+1110)/2 | 97999 | Stefano Morozzi | 09/2020 |
8483 | 2^325512-459959 | 97989 | Enzo Doria | 05/2015 |
8484 | (2^325492+682)/2 | 97983 | Stefano Morozzi | 09/2020 |
8485 | (3^205354-8)/17 | 97978 | Lelio R Paula | 09/2013 |
8486 | 2^325433+76817 | 97966 | Enzo Doria | 05/2016 |
8487 | 5*10^97963+81 | 97964 | Robert Price | 08/2017 |
8488 | (13208^23773-1)/13207 | 97961 | Serge Batalov | 06/2022 |
8489 | 2^325390-109061 | 97953 | Enzo Doria | 04/2014 |
8490 | (55*10^97940+323)/9 | 97941 | Robert Price | 10/2021 |
8491 | 13^87921+24 | 97940 | Lelio R Paula | 08/2016 |
8492 | 10^97930+188277 | 97931 | Patrick De Geest | 09/2022 |
8494 | 10^97930-7000001 | 97930 | Robert Price | 06/2021 |
8493 | 10^97930-66951 | 97930 | Patrick De Geest | 09/2022 |
8495 | 961^32831-960^32831 | 97926 | Jean-Louis Charton | 02/2011 |
8496 | (17968^23017-1)/17967 | 97922 | Serge Batalov | 06/2022 |
8497 | (3337^27793-1)/3336 | 97922 | Serge Batalov | 06/2022 |
8499 | 22600^21499+21499^22600 | 97913 | Hans Havermann | 05/2020 |
8498 | (18703^22921-1)/18702 | 97913 | Serge Batalov | 06/2022 |
8500 | 2^325215+12909 | 97900 | Lelio R Paula | 07/2016 |