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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See the Latest PRPs
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 6501 | (2^406583-1)/813167 | 122388 | Jens K. Andersen | 02/2009 |
| 6502 | 4*10^122377+19 | 122378 | Robert Price | 10/2018 |
| 6503 | 28227^21634+21634^28227 | 122368 | Hans Havermann | 03/2021 |
| 6504 | Phi(246362,10) | 122365 | Makoto Kamada | 09/2019 |
| 6505 | 3*10^122345-97 | 122346 | Robert Price | 07/2018 |
| 6506 | 97^61575-2 | 122336 | Lelio R Paula | 12/2014 |
| 6507 | 2*10^122319+47 | 122320 | Robert Price | 12/2021 |
| 6508 | 208^52765+52765^208 | 122313 | Norbert Schneider | 11/2020 |
| 6510 | 2^406298+2799109 | 122308 | Enzo Doria | 04/2016 |
| 6509 | 2^406296+213691 | 122308 | Enzo Doria | 09/2023 |
| 6511 | 7*10^122294+57 | 122295 | Robert Price | 06/2019 |
| 6512 | (27*2^406241-1)/10277 | 122289 | Lelio R Paula | 04/2014 |
| 6513 | 2^406229-1849993 | 122288 | Enzo Doria | 08/2015 |
| 6514 | 4^203111-203111 | 122286 | Anonymous | 08/2026 |
| 6515 | 3*10^122274+7 | 122275 | Robert Price | 07/2015 |
| 6516 | 2^406117+1876577 | 122254 | Enzo Doria | 07/2016 |
| 6517 | 29308^14835+14835^29308 | 122253 | Hans Havermann | 03/2021 |
| 6518 | 28119^22268+22268^28119 | 122253 | Hans Havermann | 03/2021 |
| 6519 | 32167^6312+6312^32167 | 122240 | Hans Havermann | 03/2021 |
| 6520 | 3^256199-2^256199 | 122238 | Mike Oakes | 06/2005 |
| 6521 | 27678^26053+26053^27678 | 122223 | Hans Havermann | 03/2021 |
| 6522 | 2^405992-78557 | 122216 | Jorge Menendez | 03/2018 |
| 6523 | (8*10^122203+43)/3 | 122204 | Robert Price | 06/2018 |
| 6524 | (58*10^122170+329)/9 | 122171 | Robert Price | 05/2019 |
| 6525 | 2^405774+179149 | 122151 | Enzo Doria | 06/2016 |
| 6526 | 2^405693+20417 | 122126 | Enzo Doria | 07/2023 |
| 6527 | (218*10^122109+7)/9 | 122111 | Robert Price | 06/2022 |
| 6528 | 29189^15246+15246^29189 | 122103 | Hans Havermann | 03/2021 |
| 6529 | (42^75217-5^75217)/37 | 122095 | Robert Price | 06/2026 |
| 6530 | 34*10^122082-9 | 122084 | Robert Price | 06/2020 |
| 6531 | 33442^4473+4473^33442 | 122084 | Hans Havermann | 03/2021 |
| 6532 | 5*10^122082+41 | 122083 | Robert Price | 03/2019 |
| 6533 | 31849^6808+6808^31849 | 122078 | Hans Havermann | 03/2021 |
| 6535 | 2^405514-3311 | 122072 | Yves Minet | 12/2014 |
| 6536 | 2^405514-115511 | 122072 | Enzo Doria | 07/2015 |
| 6534 | 23*10^122070-7 | 122072 | Robert Price | 02/2020 |
| 6537 | 2^405422-113261 | 122045 | Enzo Doria | 07/2014 |
| 6538 | 95^61698-61698^95 | 122022 | Norman Luhn | 10/2024 |
| 6539 | 2^405173+71237 | 121970 | Enzo Doria | 04/2016 |
| 6540 | fibonacci(583574)+2 | 121960 | Jon Grantham | 08/2023 |
| 6541 | (154*10^121953+17)/9 | 121955 | Robert Price | 06/2022 |
| 6542 | (34*10^121924+191)/9 | 121925 | Robert Price | 08/2021 |
| 6543 | (2^405016+1)/257 | 121920 | Lelio R Paula | 04/2014 |
| 6544 | 28557^18590+18590^28557 | 121918 | Hans Havermann | 03/2021 |
| 6545 | 28641^18002+18002^28641 | 121877 | Hans Havermann | 03/2021 |
| 6546 | 2^404858+71329 | 121875 | Enzo Doria | 04/2016 |
| 6547 | 2^404813-114703 | 121861 | Enzo Doria | 04/2015 |
| 6549 | 2^404764+77791 | 121847 | Enzo Doria | 05/2016 |
| 6548 | 28830^16841+16841^28830 | 121847 | Hans Havermann | 03/2021 |
| 6550 | (4*10^121825+89)/3 | 121826 | Robert Price | 08/2021 |
| 6551 | 317^48694+48694^317 | 121787 | Norbert Schneider | 08/2015 |
| 6552 | 2^404536-115259 | 121778 | Enzo Doria | 06/2015 |
| 6553 | 2^404501-631 | 121767 | Yves Minet | 07/2012 |
| 6554 | 5*10^121764-69 | 121765 | Robert Price | 02/2021 |
| 6555 | (34^79493-3^79493)/31 | 121741 | Robert Price | 07/2025 |
| 6556 | 28236^20485+20485^28236 | 121738 | Hans Havermann | 02/2021 |
| 6557 | (382*10^121694-31)/9 | 121696 | Robert Price | 06/2022 |
| 6558 | 63^67620+2 | 121672 | Lelio R Paula | 08/2015 |
| 6559 | (25*34^79445-28062367)/33 | 121669 | Eric Chen | 08/2023 |
| 6560 | (13*33^80110-121453)/32 | 121648 | Eric Chen | 12/2023 |
| 6561 | (16*10^121633+167)/3 | 121634 | Robert Price | 06/2019 |
| 6562 | 29955^11494+11494^29955 | 121632 | Hans Havermann | 02/2021 |
| 6563 | (17*10^121621+1)/9 | 121622 | Serge Batalov | 05/2010 |
| 6564 | 31088^8163+8163^31088 | 121612 | Hans Havermann | 02/2021 |
| 6565 | (15*2^403912+1)/271 | 121589 | Lelio R Paula | 05/2014 |
| 6566 | (211^52301-1)/210 | 121560 | Anonymous | 04/2024 |
| 6567 | (10^121543-79)/3 | 121543 | Robert Price | 01/2018 |
| 6568 | Phi(85408,1105) | 121540 | Henri Lifchitz | 12/2025 |
| 6569 | 801^41852-41852^801 | 121523 | Norman Luhn | 10/2024 |
| 6570 | 2^403676+76831 | 121519 | Enzo Doria | 05/2016 |
| 6571 | (41^75337-1)/98233421080 | 121492 | Paul Vanderveen | 05/2025 |
| 6572 | 715^42564-42564^715 | 121491 | Norman Luhn | 10/2024 |
| 6573 | (7*10^121487+143)/3 | 121488 | Robert Price | 03/2018 |
| 6574 | 27965^22086+22086^27965 | 121484 | Hans Havermann | 02/2021 |
| 6575 | (893*10^121470+7)/9 | 121472 | Robert Price | 06/2021 |
| 6576 | (206*10^121462-11)/3 | 121464 | Robert Price | 02/2022 |
| 6577 | 26282^27481-27481^26282 | 121457 | Frank Doornink | 03/2024 |
| 6578 | (77*10^121455+67)/9 | 121456 | Robert Price | 12/2021 |
| 6579 | 2^403363-113635 | 121425 | Enzo Doria | 08/2014 |
| 6580 | 25531^27552-27552^25531 | 121424 | Frank Doornink | 02/2024 |
| 6581 | (17*10^121418-113)/3 | 121419 | Robert Price | 06/2021 |
| 6582 | 2^403336-1861469 | 121417 | Enzo Doria | 03/2016 |
| 6583 | 27929^22186+22186^27929 | 121382 | Hans Havermann | 02/2021 |
| 6584 | p(24442)#/2-64 | 121381 | Robert Price | 04/2017 |
| 6585 | 11^116555-720 | 121380 | Enzo Doria | 11/2012 |
| 6586 | (873^41263+1)/874 | 121353 | Jinyuan Wang | 12/2024 |
| 6587 | 2^403100-461267 | 121346 | Enzo Doria | 07/2015 |
| 6588 | 2^403093-112213 | 121344 | Enzo Doria | 06/2014 |
| 6589 | 29404^13385+13385^29404 | 121340 | Hans Havermann | 02/2021 |
| 6590 | 28106^20745+20745^28106 | 121332 | Hans Havermann | 02/2021 |
| 6591 | (316^48539+1)/317 | 121330 | Eric Chen | 10/2017 |
| 6592 | (23*10^121320-71)/3 | 121321 | Robert Price | 07/2020 |
| 6593 | 2^403004+1866361 | 121317 | Enzo Doria | 03/2016 |
| 6594 | 2^402953+89 | 121301 | Lelio R Paula | 10/2013 |
| 6595 | 2^402944-2788319 | 121299 | Enzo Doria | 03/2016 |
| 6596 | (44*10^121297-719)/9 | 121298 | Robert Price | 12/2018 |
| 6597 | Phi(171913,7) | 121289 | Henri Lifchitz | 12/2025 |
| 6598 | (27*2^402865+1)/5 | 121276 | Lelio R Paula | 04/2014 |
| 6599 | 2^402828-113183 | 121264 | Enzo Doria | 07/2014 |
| 6600 | (17*10^121242+1)/9 | 121243 | Serge Batalov | 05/2010 |
| 6601 | (15*2^402757+1)/101 | 121242 | Lelio R Paula | 05/2014 |
| 6602 | 282^49477-49477^282 | 121231 | Norman Luhn | 10/2024 |
| 6604 | 2^402715+1874223 | 121230 | Enzo Doria | 06/2016 |
| 6603 | (35*10^121229-593)/9 | 121230 | Robert Price | 07/2018 |
| 6605 | (91^61879+1)/92 | 121222 | Paul Bourdelais | 09/2017 |
| 6606 | 291^49190-49190^291 | 121199 | Norman Luhn | 10/2024 |
| 6607 | 981^40512+980 | 121199 | Alfred Reich | 05/2026 |
| 6608 | (10^121243)/(121243^10) | 121193 | Henri Lifchitz | 05/2025 |
| 6609 | 28719^16568+16568^28719 | 121174 | Hans Havermann | 02/2021 |
| 6610 | Phi(24773,-17#) | 121170 | Henri Lifchitz | 12/2025 |
| 6611 | 7*10^121144+9 | 121145 | Robert Price | 09/2015 |
| 6612 | 27490^25467+25467^27490 | 121121 | Hans Havermann | 02/2021 |
| 6613 | 34575^3182+3182^34575 | 121106 | Hans Havermann | 02/2021 |
| 6614 | 5*10^121100-37 | 121101 | Robert Price | 11/2021 |
| 6615 | F(579521)/516247738177 | 121101 | Serge Batalov | 07/2024 |
| 6616 | 25592^27467-27467^25592 | 121078 | Frank Doornink | 02/2024 |
| 6617 | 29954^10935+10935^29954 | 120979 | Hans Havermann | 02/2021 |
| 6618 | 33585^3992+3992^33585 | 120946 | Hans Havermann | 02/2021 |
| 6619 | 40296^1003+1003^40296 | 120941 | Hans Havermann | 02/2021 |
| 6620 | 2^401725-113251 | 120932 | Enzo Doria | 07/2014 |
| 6621 | (15*2^401677-1)/19 | 120917 | Lelio R Paula | 05/2014 |
| 6622 | 2^401652+73711 | 120910 | Enzo Doria | 04/2016 |
| 6623 | (2^401632+3)/79 | 120902 | Lelio R Paula | 04/2014 |
| 6624 | 40450^973+973^40450 | 120870 | Hans Havermann | 01/2021 |
| 6625 | (8*10^120851-11)/3 | 120852 | Robert Price | 07/2023 |
| 6626 | 10^120841+88417 | 120842 | Patrick De Geest | 04/2020 |
| 6627 | 10^120841-123456789 | 120841 | Robert Price | 02/2020 |
| 6628 | 10^120841-176853 | 120841 | Patrick De Geest | 04/2020 |
| 6629 | 2^401406-2791331 | 120836 | Enzo Doria | 03/2016 |
| 6630 | (28^83497+1)/29 | 120832 | Robert Price | 07/2013 |
| 6631 | (22*10^120828+161)/3 | 120829 | Robert Price | 05/2019 |
| 6632 | 2^401369+1867367 | 120825 | Enzo Doria | 03/2016 |
| 6633 | (5*10^120821+43)/3 | 120822 | Robert Price | 12/2021 |
| 6634 | 26990^27263-27263^26990 | 120808 | Frank Doornink | 03/2024 |
| 6635 | (10^120782+29)/3 | 120782 | Serge Batalov | 12/2014 |
| 6636 | 2^401215-1657 | 120778 | Yves Minet | 07/2014 |
| 6637 | 2^401159+53 | 120761 | Lelio R Paula | 10/2013 |
| 6638 | 27782^22179+22179^27782 | 120739 | Hans Havermann | 01/2021 |
| 6639 | 242^50649-50649^242 | 120738 | Norman Luhn | 09/2024 |
| 6640 | 32974^4585+4585^32974 | 120730 | Hans Havermann | 02/2021 |
| 6641 | 2^401031-113047 | 120723 | Enzo Doria | 07/2014 |
| 6642 | 30598^8813+8813^30598 | 120713 | Hans Havermann | 02/2021 |
| 6643 | (71*10^120703-287)/9 | 120704 | Robert Price | 09/2019 |
| 6644 | 25671^27370-27370^25671 | 120687 | Frank Doornink | 02/2024 |
| 6645 | (29*2^400909-1)/303 | 120685 | Lelio R Paula | 04/2014 |
| 6646 | 34793^2940+2940^34793 | 120675 | Hans Havermann | 02/2021 |
| 6647 | 26028^27329-27329^26028 | 120670 | Frank Doornink | 03/2024 |
| 6648 | (2^400846+538)/2 | 120667 | Stefano Morozzi | 09/2020 |
| 6649 | (166*10^120654+11)/3 | 120656 | Robert Price | 03/2021 |
| 6650 | 34066^3481+3481^34066 | 120652 | Hans Havermann | 02/2021 |
| 6651 | 8*10^120637-27 | 120638 | Robert Price | 10/2021 |
| 6652 | (2^400709+3546)/2 | 120626 | Stefano Morozzi | 09/2020 |
| 6653 | (2^400700+3126)/2 | 120623 | Stefano Morozzi | 09/2020 |
| 6654 | (2^400693+2634)/2 | 120621 | Stefano Morozzi | 09/2020 |
| 6655 | 9*10^120617-61 | 120618 | Robert Price | 06/2021 |
| 6656 | (29*10^120590-71)/3 | 120591 | Robert Price | 07/2021 |
| 6657 | 2^400571-15 | 120584 | Lelio R Paula | 10/2013 |
| 6658 | (10^120574+359)/9 | 120574 | Serge Batalov | 12/2014 |
| 6659 | (8*10^120552-17)/9 | 120552 | Serge Batalov | 11/2022 |
| 6660 | 27431^24810+24810^27431 | 120550 | Hans Havermann | 02/2021 |
| 6661 | 2^400424-216413 | 120540 | Enzo Doria | 04/2013 |
| 6662 | 29090^13911+13911^29090 | 120531 | Hans Havermann | 02/2021 |
| 6663 | (2^400346+1722)/2 | 120516 | Stefano Morozzi | 09/2020 |
| 6664 | 27899^20868+20868^27899 | 120510 | Hans Havermann | 02/2021 |
| 6665 | 33740^3729+3729^33740 | 120506 | Hans Havermann | 02/2021 |
| 6666 | (17*2^400200-1)/587 | 120471 | Lelio R Paula | 05/2014 |
| 6667 | 17228^28437-28437^17228 | 120466 | Norbert Schneider | 08/2025 |
| 6668 | 1069^39770-39770^1069 | 120463 | Norbert Schneider | 05/2025 |
| 6670 | 2^400166+1874899 | 120462 | Enzo Doria | 06/2016 |
| 6669 | (2^400165+1602)/2 | 120462 | Stefano Morozzi | 09/2020 |
| 6671 | 2739^35038-35038^2739 | 120447 | Norbert Schneider | 05/2025 |
| 6672 | 37078^1771+1771^37078 | 120438 | Hans Havermann | 02/2021 |
| 6673 | (2^400084+1638)/2 | 120437 | Stefano Morozzi | 09/2020 |
| 6674 | (3*2^400045-1)/865 | 120424 | Lelio R Paula | 04/2014 |
| 6675 | 12857^29306-29306^12857 | 120423 | Norbert Schneider | 07/2025 |
| 6676 | 2^399999+54173 | 120412 | Norman Luhn | 08/2023 |
| 6677 | (2^399974+2790)/2 | 120404 | Stefano Morozzi | 02/2021 |
| 6678 | 2^399966+73759 | 120402 | Enzo Doria | 04/2016 |
| 6679 | (2^399961+2306)/2 | 120400 | Stefano Morozzi | 02/2021 |
| 6680 | (112*10^120395-1)/3 | 120397 | Serge Batalov | 12/2014 |
| 6681 | 2^399918-95 | 120388 | Lelio R Paula | 04/2013 |
| 6682 | 2^399918+214009 | 120388 | Enzo Doria | 10/2023 |
| 6683 | (28*10^120381-67)/3 | 120382 | Robert Price | 10/2020 |
| 6684 | (49*10^120380-139)/9 | 120381 | Robert Price | 03/2019 |
| 6685 | (2^399874+2194)/2 | 120374 | Stefano Morozzi | 09/2020 |
| 6686 | 2^399792-1849259 | 120350 | Enzo Doria | 08/2015 |
| 6687 | 9*10^120342-7 | 120343 | Robert Price | 09/2015 |
| 6688 | (2^399751+786)/2 | 120337 | Stefano Morozzi | 09/2020 |
| 6689 | (331*10^120332-7)/9 | 120334 | Robert Price | 04/2022 |
| 6690 | 14609^28890-28890^14609 | 120316 | Norbert Schneider | 09/2025 |
| 6691 | (13*10^120306-37)/3 | 120307 | Robert Price | 01/2019 |
| 6692 | (23*10^120299+37)/3 | 120300 | Robert Price | 02/2022 |
| 6693 | 25935^27254-27254^25935 | 120297 | Frank Doornink | 03/2024 |
| 6694 | (2^399604+3070)/2 | 120293 | Stefano Morozzi | 09/2020 |
| 6695 | (2^399549+1062)/2 | 120276 | Stefano Morozzi | 09/2020 |
| 6696 | 2^399526-1861721 | 120270 | Enzo Doria | 11/2015 |
| 6697 | 12199^29430-29430^12199 | 120261 | Norbert Schneider | 08/2025 |
| 6698 | (10^(2*60126+1)+36*10^60126-1)/9 | 120253 | Robert Price | 10/2015 |
| 6699 | 32016^5687+5687^32016 | 120217 | Hans Havermann | 01/2021 |
| 6700 | (205*10^120212-1)/3 | 120214 | Robert Price | 11/2021 |
| 6701 | 13302^29149-29149^13302 | 120209 | Norbert Schneider | 08/2025 |
| 6702 | 2^399322-2798111 | 120208 | Enzo Doria | 04/2016 |
| 6703 | 30438^8867+8867^30438 | 120163 | Hans Havermann | 02/2021 |
| 6704 | 3^251841-5*2^251841 | 120159 | Jon Grantham | 08/2023 |
| 6706 | 72^64693-71^64693 | 120157 | Robert Price | 03/2014 |
| 6705 | (17*10^120156-161)/9 | 120157 | Robert Price | 02/2021 |
| 6707 | Phi(81997,-5#) | 120150 | Henri Lifchitz | 12/2025 |
| 6708 | 2^399111-28489 | 120145 | Enzo Doria | 08/2015 |
| 6709 | 2958^34607-34607^2958 | 120121 | Norbert Schneider | 04/2025 |
| 6710 | (2^399014+1318)/2 | 120115 | Stefano Morozzi | 02/2021 |
| 6711 | 30254^9333+9333^30254 | 120110 | Hans Havermann | 02/2021 |
| 6712 | 2^398972+6561 | 120103 | Henri Lifchitz | 10/2024 |
| 6713 | 30882^7745+7745^30882 | 120101 | Hans Havermann | 02/2021 |
| 6714 | 23687^27452-27452^23687 | 120090 | Norbert Schneider | 08/2025 |
| 6715 | 2^398877+105 | 120074 | Donovan Johnson | 01/2006 |
| 6716 | (101*10^120072-87)/7 | 120074 | Hans Havermann | 02/2015 |
| 6717 | (88^61751+1)/89 | 120072 | Paul Bourdelais | 09/2017 |
| 6718 | U(686581)/4280145953 | 120067 | Serge Batalov | 07/2024 |
| 6719 | 16651^28442-28442^16651 | 120067 | Norbert Schneider | 07/2025 |
| 6720 | 12284^29359-29359^12284 | 120059 | Norbert Schneider | 06/2025 |
| 6721 | 3207^34240-34240^3207 | 120049 | Norbert Schneider | 04/2025 |
| 6722 | 2^398710+57 | 120024 | Lelio R Paula | 04/2013 |
| 6723 | (2^398698+1138)/2 | 120020 | Stefano Morozzi | 09/2020 |
| 6724 | 2^398691-115057 | 120018 | Enzo Doria | 06/2015 |
| 6725 | 12134^29385-29385^12134 | 120009 | Norbert Schneider | 06/2025 |
| 6726 | 6089^31710-31710^6089 | 120008 | Norbert Schneider | 05/2025 |
| 6727 | L(574219) | 120005 | Renaud Lifchitz | 03/2004 |
| 6728 | 2^398571+60413 | 119982 | Yves Minet | 03/2011 |
| 6729 | 28623^15538+15538^28623 | 119971 | Hans Havermann | 02/2021 |
| 6730 | p(24179)#/2-64 | 119949 | Robert Price | 04/2017 |
| 6731 | 2^398448+1872001 | 119945 | Enzo Doria | 05/2016 |
| 6732 | (10^119946*19-91)/6093 | 119944 | Alfred Reich | 10/2023 |
| 6733 | (19*10^119946-91)/9/677 | 119944 | Alfred Reich | 11/2023 |
| 6734 | (191*10^119941-17)/3 | 119943 | Robert Price | 11/2021 |
| 6735 | 634^42803+42803^634 | 119938 | Norbert Schneider | 07/2019 |
| 6736 | 31083^7220+7220^31083 | 119935 | Hans Havermann | 01/2021 |
| 6737 | (68*10^119931-11)/3 | 119933 | Robert Price | 01/2020 |
| 6738 | 8*10^119930-3 | 119931 | Ray Chandler | 04/2011 |
| 6739 | (2^398398+774)/2 | 119930 | Stefano Morozzi | 09/2020 |
| 6740 | (10^119880+179)/9 | 119880 | Serge Batalov | 12/2014 |
| 6741 | (9*2^398145+1)/73 | 119853 | Lelio R Paula | 04/2014 |
| 6742 | (10^119836+77)/3 | 119836 | Robert Price | 01/2018 |
| 6743 | 26681^27074-27074^26681 | 119835 | Frank Doornink | 03/2024 |
| 6744 | 28179^17870+17870^28179 | 119821 | Hans Havermann | 02/2021 |
| 6745 | 2^398029+1872527 | 119819 | Enzo Doria | 05/2016 |
| 6746 | 33142^4119+4119^33142 | 119802 | Hans Havermann | 01/2021 |
| 6747 | 2^397897-113541 | 119779 | Enzo Doria | 08/2014 |
| 6748 | 28636^15171+15171^28636 | 119728 | Hans Havermann | 02/2021 |
| 6749 | 87^61730-61730^87 | 119727 | Norman Luhn | 09/2024 |
| 6750 | (10556^29929-1)/(10556^173-1) | 119724 | Ryan Propper | 11/2023 |
